JEE Physics

StemEZ

Chapter 10

Oscillations And Waves - all with Video Answers

Educators

Chapter Questions

Problem 1337

If the equation for a particle performing S.H.M. is given by $\mathrm{y}=\sin 2 \mathrm{t}+\sqrt{3} \cos 2 \mathrm{t}$, its periodic time will be $\ldots \ldots .$ s.
(A) 21
(B) $\pi$
(C) $2 \pi$
(D) $4 \pi$.

Supratim Pal

Supratim Pal

Numerade Educator

Problem 1338

The distance travelled by a particle performing S.H.M. during time interval equal to its periodic time is $\ldots \ldots$
(A) A
(B) $2 \mathrm{~A}$
(C) $4 \mathrm{~A}$
(D) Zero.

Supratim Pal

Numerade Educator

Problem 1339

A person standing in a stationary lift measures the periodic time of a simple pendulum inside the lift to be equal to $\mathrm{T}$. Now, if the lift moves along the vertically upward direction with an acceleration of $(\mathrm{g} / 3)$, then the periodic time of the lift will now be
$(\mathrm{A}) \sqrt{3} \mathrm{~T}$
(B) $\sqrt{(3 / 2) \mathrm{T}}$
(C) $(\mathrm{T} / 3)$
(D) $(\mathrm{T} / \sqrt{3})$

Supratim Pal

Numerade Educator

Problem 1340

If the equation for displacement of two particles executing S.H.M. is given by $\mathrm{y}_{1}=2 \sin (10 \mathrm{t}+\theta)$ and $\mathrm{y}_{2}=3 \cos 10 \mathrm{t}$
respectively, then the phase difference between the velocity of two particles will be $\ldots \ldots \ldots$
(A) $-\theta$
(B) $\theta$
(C) $\theta-(\pi / 2)$
(D) $\theta+(\pi / 2)$.

Supratim Pal

Numerade Educator

Problem 1341

When a body having mass $\mathrm{m}$ is suspended from the free end of two springs suspended from a rigid support, as shown in figure, its periodic time of oscillation is $\mathrm{T}$. If only one of the two springs are used, then the periodic time would be .........
(A) $(\mathrm{T} / \sqrt{2})$
(B) $(\mathrm{T} / 2)$
(C) $\sqrt{2} \mathrm{~T}$
(D) $2 \mathrm{~T}$

Supratim Pal

Numerade Educator

Problem 1342

If the maximum velocity of two springs (both has same mass) executing S.H.M. and having force constants $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ respectively are same, then the ratio of their amplitudes will be $\ldots \ldots$
(A) $\left(\mathrm{k}_{1} / \mathrm{k}_{2}\right)$
(B) $\left(\mathrm{k}_{2} / \mathrm{k}_{1}\right)$
(C) $\sqrt{\left(k_{1} / k_{2}\right)}$
(D) $\sqrt{\left(k_{2} / k_{1}\right)}$

Supratim Pal

Numerade Educator

Problem 1343

As shown in figure, two masses of $3.0 \mathrm{~kg}$ and $1.0 \mathrm{~kg}$ are attached at the two ends of a spring having force constant $300 \mathrm{Nm}^{-1}$. The natural frequency of oscillation for the system will be $\ldots \ldots \ldots \ldots . .$ hz. (Ignore friction)
(A) $(1 / 4)$
(B) $1 / 3$
(C) 4
(D) 3

Supratim Pal

Numerade Educator

Problem 1344

The bob of a simple pendulum having length ' $\ell$ ' is displaced from its equilibrium position by an angle of $\theta$ and released. If the velocity of the bob, while passing through its equilibrium position is $\mathrm{v}$, then $\mathrm{v}=\ldots \ldots \ldots$
(A) $\sqrt{\{2 g \ell(1-\cos \theta)\}}$
(B) $\sqrt{\{2 g \ell(1+\sin \theta)\}}$
(C) $\sqrt{\{2 g \ell(1-\sin \theta)\}}$
(D) $\sqrt{\{2 g \ell(1+\cos \theta)\}}$

Supratim Pal

Numerade Educator

Problem 1345

If $(1 / 4)$ of a spring having length $\ell$ is cutoff, then what will be the spring constant of remaining part?
(A) $\mathrm{k}$
(B) $4 \mathrm{k}$
(C) $(4 \mathrm{k} / 3)$
(D) $(3 \mathrm{k} / 4)$

Supratim Pal

Numerade Educator

Problem 1346

The amplitude for a S.H.M. given by the equation $\mathrm{x}=3 \sin 3 \mathrm{pt}+4 \cos 3 \mathrm{pt}$ is $\ldots \ldots \ldots \ldots \mathrm{m}$
(A) 5
(B) 7
(C) 4
(D) $3 .$

Supratim Pal

Numerade Educator

Problem 1347

When an elastic spring is given a displacement of $10 \mathrm{~mm}$, it gains an potential energy equal to $\mathrm{U}$. If this spring is given an additional displacement of $10 \mathrm{~mm}$, then its potential energy will be..............
(A) $\mathrm{U}$
(B) $2 \mathrm{U}$
(C) $4 \mathrm{U}$
(D) $\mathrm{U} / 4$.

Supratim Pal

Numerade Educator

Problem 1348

The increase in periodic time of a simple pendulum executing S.H.M. is $\ldots \ldots \ldots \ldots \ldots \ldots$ when its length is increased by $21 \%$.
(A) $42 \%$
(B) $10 \%$
(C) $11 \%$
(D) $21 \%$.

Supratim Pal

Numerade Educator

Problem 1349

A particle executing S.H.M. has an amplitude $\mathrm{A}$ and periodic time $\mathrm{T}$. The minimum time required by the particle to get displaced by $(\mathrm{A} / \sqrt{2})$ from its equilibrium position is $\ldots \ldots \ldots \mathrm{s}$.
(A) $\mathrm{T}$
(B) $\mathrm{T} / 4$
(C) $\mathrm{T} / 8$
(D) $\mathrm{T} / 16$

Supratim Pal

Numerade Educator

Problem 1350

If a body having mass $\mathrm{M}$ is suspended from the free ends of two springs $\mathrm{A}$ and $\mathrm{B}$, their periodic time are found to be $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ respectively. If both these springs are now connected in series and if the same mass is suspended from the free end, then the periodic time is found to be $\mathrm{T}$. Therefore ............
(A) $\mathrm{T}=\mathrm{T}_{1}+\mathrm{T}_{2}$
(B) $(1 / \mathrm{T})=\left(1 / \mathrm{T}_{1}\right)+\left(1 / \mathrm{T}_{2}\right)$
(C) $\mathrm{T}^{2}=\mathrm{T}_{1}^{2}+\mathrm{T}_{2}^{2}$
(D) $\left(1 / T^{2}\right)=\left(1 / \mathrm{T}_{1}^{2}\right)+\left(1 / \mathrm{T}_{2}^{2}\right)$

Supratim Pal

Numerade Educator

Problem 1351

The displacement of a S.H.O. is given by the equation $\mathrm{x}=\mathrm{A}$ $\cos \{\omega t+(\pi / 8)\}$. At what time will it attain maximum velocity?
(A) $(3 \pi / 8 \omega)$
(B) $(8 \pi / 3 \omega)$
(C) $(3 \pi / 16 \omega)$
(D) $(\pi / 16 \pi)$.

Supratim Pal

Numerade Educator

Problem 1352

At what position will the potential energy of a S.H.O. become equal to one third its kinetic energy ?
(A) $\pm(\mathrm{A} / 2)$
$(B) \pm(A / \sqrt{2})$
(C) $\pm(\mathrm{A} / \sqrt{3})$
(D) $\pm \sqrt{3} \mathrm{~A}$

Supratim Pal

Numerade Educator

Problem 1353

3: Three identical springs are shown in figure. When a $4 \mathrm{~kg}$ mass is suspended from spring $\mathrm{A}$, its length increases by $1 \mathrm{~cm}$. Now if a $6 \mathrm{~kg}$ mass is suspended from the free end of spring $\mathrm{C}$, then increase in its length is $\ldots \ldots \mathrm{cm}$.
(A) $1.5$
(B) $3.0$
(C) $4.5$
(D) $6.0$

Supratim Pal

Numerade Educator

Problem 1354

For particles $\mathrm{A}$ and $\mathrm{B}$ executing S.H.M., the equation for displacement is given by $\mathrm{y}_{1}=0.1 \sin (100 \mathrm{t}+\mathrm{p} / 3)$ and
$\mathrm{y}_{2}=0.1$ cos pt respectively. The phase difference between velocity of particle $\mathrm{A}$ with respect to that of $\mathrm{B}$ is $\ldots \ldots$
$(\mathrm{A})-(\pi / 3)$
(B) $(\pi / 6)$
(C) $-(\pi / 6)$
(D) $(\pi / 3)$

Supratim Pal

Numerade Educator

Problem 1355

The periodic time of a simple pendulum is $\mathrm{T}_{1}$. Now if the point of suspension of this pendulum starts moving along the vertical direction according to the equation $\mathrm{y}=\mathrm{kt}^{2}$, the periodic time of the pendulum becomes $\mathrm{T}_{2}$ Therefore, $\left(\mathrm{T}_{1}^{2} / \mathrm{T}_{2}^{2}\right)=\ldots \ldots \ldots .\left(\mathrm{k}=1 \mathrm{~m} / \mathrm{s}^{2} \& \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $6 / 5$
(B) $5 / 6$
(C) $4 / 5$
(D) 1

Supratim Pal

Numerade Educator

Problem 1356

A hollow sphere is filled with water. There is a hole at the bottom of this sphere. This sphere is suspended with a string from a rigid support and given an oscillation. During oscillation, the hole is opened up and the periodic time of this oscillating system is measured. The periodic time of the system $\ldots \ldots \ldots \ldots$
(A) will remain constant
(B) Will increase upto a certain time
(C) Increases initially and then decreases to attain its initial periodic time
(D) Initially decreases and then will attain the initial periodic time value.

Supratim Pal

Numerade Educator

Problem 1357

The periodic time of a S.H.O. oscillating about a fixed point is $2 \mathrm{~s}$. After what time will the kinetic energy of the oscillator become $25 \%$ of its total energy?
(A) $1 / 12 \mathrm{~s}$
(B) $1 / 6 \mathrm{~s}$
(C) $1 / 4 \mathrm{~s}$
(D) $1 / 3 \mathrm{~s}$.

Supratim Pal

Numerade Educator

Problem 1358

A body having mass $5 \mathrm{~g}$ is executing S.H.M. with an amplitude of $0.3 \mathrm{~m}$. If the periodic time of the system is $(\pi / 10) \mathrm{s}$, then the maximum force acting on body is $\ldots \ldots \ldots \ldots$
(A) $0.6 \mathrm{~N}$
(B) $0.3 \mathrm{~N}$
(C) $6 \mathrm{~N}$
(D) $3 \mathrm{~N}$

Supratim Pal

Numerade Educator

Problem 1359

As shown in figure, a body having mass $\mathrm{m}$ is attached with two springs having spring constants $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$. The frequency of oscillation is $\mathrm{f}$. Now, if the springs constants of both the springs are increased 4 times, then the frequency of oscillation will be equal to ..........
(A) $2 \mathrm{f}$
(B) $\mathrm{f} / 2$
(C) $\mathrm{f} / 4$
(D) $4 \mathrm{f}$

Supratim Pal

Numerade Educator

Problem 1360

The figure shows a graph of displacement versus time for a particle executing S.H.M. The acceleration of the S.H.O. at the end of time $t=(4 / 3)$ second is $\ldots \ldots \ldots . \mathrm{cm} \cdot \mathrm{s}^{-2}$
(A) $(\sqrt{3} / 32) \pi^{2}$
(B) $-\left(\pi^{2} / 32\right)$
(C) $\left(\pi^{2} / 32\right)$
(D) $-(\sqrt{3} / 32) \pi^{2}$

Supratim Pal

Numerade Educator

Problem 1361

As shown in figure, the object having mass $\mathrm{M}$ is executing
S.H.M. with an amplitude $A$. The amplitude of point $P$ shown in figure will be.......
(A) $\left\{\left(\mathrm{K}_{1} \mathrm{~A}\right) / \mathrm{K}_{2}\right\}$
(B) $\left\{\left(\mathrm{K}_{2} \mathrm{~A}\right) / \mathrm{K}_{1}\right\}$
(C) $\left\{\left(\mathrm{K}_{1} \mathrm{~A}\right) /\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)\right\}$
(D) $\left\{\left(\mathrm{K}_{2} \mathrm{~A}\right) /\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)\right\}$

Supratim Pal

Numerade Educator

Problem 1362

A particle is executing S.H.M. between $\mathrm{x}=-\mathrm{A}$ and $\mathrm{x}=+\mathrm{A}$. If the time taken by the particle to travel from $\mathrm{x}=0$ to $\mathrm{A} / 2$ is $\mathrm{T}_{1}$ and that taken to travel from $\mathrm{x}=\mathrm{A} / 2$ to $\mathrm{x}=\mathrm{A}$ is $\mathrm{T}_{2}=$ then $\ldots .$
(A) $\mathrm{T}_{1}<\mathrm{T}_{2}$
(B) $\mathrm{T}_{1}>\mathrm{T}_{2}$
(C) $\mathrm{T}_{1}=2 \mathrm{~T}_{2}$
(D) $\mathrm{T}_{1}=\mathrm{T}_{2}$

Supratim Pal

Numerade Educator

Problem 1363

For a particle executing $\mathrm{S} . \mathrm{H} \mathrm{M} .$, when the potential energy of the oscillator becomes $1 / 8$ the maximum potential energy, the displacement of the oscillator in terms of amplitude A will be...........
(A) $(\mathrm{A} / \sqrt{2})$
(B) $\{\mathrm{A} /(2 \sqrt{2})\}$
(C) $(\mathrm{A} / 2)$
(D) $\{\mathrm{A} /(3 \sqrt{2})\}$

Supratim Pal

Numerade Educator

Problem 1364

The average values of potential energy and kinetic energy over a cycle for a S.H.O. will be ............ respectively.
(A) $0,(1 / 2) \mathrm{m} \omega^{2} \mathrm{~A}^{2}$
(B) $(1 / 2) \mathrm{m} \omega^{2} \mathrm{~A}^{2}, 0$
(C) $(1 / 2) \mathrm{m} \omega^{2} \mathrm{~A}^{2},(1 / 2) \mathrm{m} \omega^{2} \mathrm{~A}^{2}$
(D) $(1 / 4) \mathrm{m} \omega^{2} \mathrm{~A}^{2},(1 / 4) \mathrm{m} \omega^{2} \mathrm{~A}^{2}$

Supratim Pal

Numerade Educator

Problem 1365

The ratio of force constants of two springs is $1: 5$. The equal mass suspended at the free ends of both springs are performing S.H.M. If the maximum acceleration for both springs are equal, the ratio of amplitudes for both springs is $\ldots \ldots$
(A) $(1 / \sqrt{5})$
(B) $(1 / 5)$
(C) $(5 / 1)$
(D) $(\sqrt{5} / 1)$

Supratim Pal

Numerade Educator

Problem 1366

When a mass $M$ is suspended from the free end of a spring, its periodic time is found to be $\mathrm{T}$. Now, if the spring is divided into two equal parts and the same mass $\mathrm{M}$ is suspended and oscillated, the periodic time of oscillation is found to be $\mathrm{T}$ '. Then $\ldots \ldots \ldots$
(A) $\mathrm{T}<\mathrm{T}^{\prime}$
(B) $\mathrm{T}=\mathrm{T}^{\prime}$
(C) $\mathrm{T}>\mathrm{T}^{\prime}$
(D) Nothing can be said.

Supratim Pal

Numerade Educator

Problem 1367

The periodic time of two oscillators are $\mathrm{T}$ and $(5 \mathrm{~T} / 4)$ respectively. Both oscillators starts their oscillation simultaneously from the midpoint of their path of motion. When the oscillator having periodic time $\mathrm{T}$ completes one oscillation, the phase difference between the two oscillators will be $\ldots \ldots \ldots$
(A) $90^{\circ}$
(B) $112^{\circ}$
(C) $72^{\circ}$
(D) $45^{\circ}$

Supratim Pal

Numerade Educator

Problem 1368

A rectangular block having mass $\mathrm{m}$ and cross sectional area A is floating in a liquid having density $\rho$. If this block in its equilibrium position is given a small vertical displacement, its starts oscillating with periodic time $\mathrm{T}$. Then in this case $\ldots \ldots$
(A) $\mathrm{T} \propto(1 / \sqrt{\mathrm{m}})$
(B) $T \propto \sqrt{\rho}$
(C) $\mathrm{T} \propto(1 / \sqrt{\mathrm{A}})$
(D) $\mathrm{T} \propto(1 / \sqrt{\rho})$

Supratim Pal

Numerade Educator

Problem 1369

As shown in figure, a spring attached to the ground vertically has a horizontal massless plate with a $2 \mathrm{~kg}$ mass in it. When the spring (massless) is pressed slightly and released, the $2 \mathrm{~kg}$ mass, starts executing S.H.M. The force constant of the spring is $200 \mathrm{Nm}^{-1}$. For what minimum value of amplitude, will the mass loose contact with the plate? (Take $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
(A) $10.0 \mathrm{~cm}$
(B) $8.0 \mathrm{~cm}$
(C) $4.0 \mathrm{~cm}$
(D) For any value less than $12.0 \mathrm{~cm}$.

Supratim Pal

Numerade Educator

Problem 1370

Which of the equation given below represents a S.H.M.?
(A) acceleration $=-\mathrm{k}(\mathrm{x}+\mathrm{a})$
(B) acceleration $=\mathrm{k}(\mathrm{x}+\mathrm{a})$
(C) acceleration $=\mathrm{kx}$
(D) acceleration $=-\mathrm{k}_{0} \mathrm{x}+\mathrm{k}_{1} \mathrm{x}^{2}$
\{Here $\mathrm{k}, \mathrm{k}_{0}$ and $\mathrm{k}_{1}$ are force constants and units of $\mathrm{x}$ and a is meter $\}$

Supratim Pal

Numerade Educator

Problem 1371

The displacement for a particle performing S.H.M. is given by $\mathrm{x}=\mathrm{A} \cos (\omega \mathrm{t}+\theta)$. If the initial position of the particle is $1 \mathrm{~cm}$ and its initial velocity is $\pi \mathrm{cms}^{-1}$, then what will be its initial phase ? The angular frequency of the particle is $\pi \mathrm{s}^{-1}$.
(A) $(2 \pi / 4)$
(B) $(7 \pi / 4)$
(C) $(5 \pi / 4)$
(D) $(3 \pi / 4)$

Supratim Pal

Numerade Educator

Problem 1372

Two simple pendulums having lengths $144 \mathrm{~cm}$ and $121 \mathrm{~cm}$ starts executing oscillations. At some time, both bobs of the pendulum are at the equilibrium positions and in same phase. After how many oscillations of the shorter pendulum will both the bob's pass through the equilibrium position and will have same phase ?
(A) 11
(B) 12
(C) 21
(D) 20

Supratim Pal

Numerade Educator

Problem 1373

The maximum velocity and maximum acceleration of a particle executing S.H.M. are $1 \mathrm{~m} / \mathrm{s}$ and $3.14 \mathrm{~m} / \mathrm{s}^{2}$ respectively. The frequency of oscillation for this particle is......
(A) $0.5 \mathrm{~s}^{-1}$
(B) $3.14 \mathrm{~s}^{-1}$
(C) $0.25 \mathrm{~s}^{-1}$
(D) $2 \mathrm{~s}^{-1}$

Supratim Pal

Numerade Educator

Problem 1374

A particle having mass $1 \mathrm{~kg}$ is executing S.H.M. with an amplitude of $0.01 \mathrm{~m}$ and a frequency of $60 \mathrm{hz}$. The maximum force acting on this particle is $\ldots \ldots . . \mathrm{N}$
(A) $144 \pi^{2}$
(B) $288 \pi^{2}$
(C) $188 \pi^{2}$
(D) None of these.
(A) $x=a \sin 2 p \sqrt{(\ell / g) t}$
(B) $x=a \cos 2 p \sqrt{(g / \ell) t}$
(C) $\mathrm{x}=\mathrm{a} \sin \sqrt{(\mathrm{g} / \ell) \mathrm{t}}$
(D) $\mathrm{x}=\mathrm{a} \cos \sqrt{(\mathrm{g} / \ell) \mathrm{t}}$

Supratim Pal

Numerade Educator

Problem 1375

A simple pendulum having length $\ell$ is given a small angular displacement at time $t=0$ and released. After time $t$, the linear displacement of the bob of the pendulum is given by $\ldots \ldots \ldots \ldots$
(A) $x=a \sin 2 p \sqrt{(\ell / g) t}$
(B) $\mathrm{x}=\mathrm{a} \cos 2 \mathrm{p} \sqrt{(\mathrm{g} / \ell) t}$
(C) $\mathrm{x}=\mathrm{a} \sin \sqrt{(\mathrm{g} / \ell) \mathrm{t}}$
(D) $\mathrm{x}=\mathrm{a} \cos \sqrt{(\mathrm{g} / \ell) \mathrm{t}}$

Supratim Pal

Numerade Educator

Problem 1376

Two masses $m_{1}$ and $m_{2}$ are attached to the two ends of a massless spring having force constant $\mathrm{k}$. When the system is in equilibrium, if the mass $\mathrm{m}_{1}$ is detached, then the angular frequency of mass $m_{2}$ will be $\ldots \ldots \ldots .$
(A) $\sqrt{\left(\mathrm{k} / \mathrm{m}_{1}\right)}$
(B) $\sqrt{\left(\mathrm{k} / \mathrm{m}^{2}\right)}$
(C) $\sqrt{\left(k / m_{2}\right)+m_{1}}$
(D) $\sqrt{\left\{k /\left(m_{1}+m_{2}\right)\right\}}$

Supratim Pal

Numerade Educator

Problem 1377

When the displacement of a S.H.O. is equal to $\mathrm{A} / 2$, what fraction of total energy will be equal to kinetic energy ? \{A is amplitude $\}$
(A) $2 / 7$
(B) $3 / 4$
(C) $2 / 9$
(D) $5 / 7$

Supratim Pal

Numerade Educator

Problem 1378

The speed of a particle executing motion changes with time according to the equation $\mathrm{y}=\mathrm{a} \sin \omega \mathrm{t}+\mathrm{b} \cos \omega \mathrm{t}$, then $\ldots \ldots \ldots$
(A) Motion is periodic but not a S.H.M.
(B) It is a S.H.M. with amplitude equal to $\mathrm{a}+\mathrm{b}$
(C) It is a S.H.M. with amplitude equal to $\mathrm{a}^{2}+\mathrm{b}^{2}$

Supratim Pal

Numerade Educator

Problem 1379

A body is placed on a horizontal plank executing S.H.M. along vertical direction. Its amplitude of oscillation is $3.92 \times 10^{-3} \mathrm{~m}$. What should be the minimum periodic time so that the body does not loose contact with the plank?
(A) $0.1256 \mathrm{~s}$
(B) $0.1356 \mathrm{~s}$
(C) $0.1456 \mathrm{~s}$
(D) $0.1556 \mathrm{~s}$

Supratim Pal

Numerade Educator

Problem 1380

If the kinetic energy of a particle executing S.H.M. is given by $\mathrm{K}=\mathrm{K}_{0} \cos ^{2} \omega \mathrm{t}$, then the displacement of the particle is given by $\ldots \ldots$
(A) $\left\{\mathrm{K}_{0} / \mathrm{m} \omega^{2}\right\} \sin \omega \mathrm{t}$
(B) $\left\{\left(2 \mathrm{~K}_{0}\right) /\left(\mathrm{m} \omega^{2}\right)\right\}^{1 / 2} \sin \omega t$
(C) $\left\{2 \omega^{2} / \mathrm{mK}_{0}\right\} \sin \omega t$
(D) $\left\{2 \mathrm{~K}_{0} / \mathrm{m} \omega\right\}^{1 / 2} \sin \omega t$

Supratim Pal

Numerade Educator

Problem 1381

The equation for displacement of two identical particles performing S.H.M. is given by $\mathrm{x}_{1}=4 \sin (20 \mathrm{t}+\mathrm{p} / 6)$ and $\mathrm{K}_{2}=10 \mathrm{sin} \omega \mathrm{t}$. For what value of $\mathrm{u}$ will both particles have same energy ?
(A) 4 units
(B) 8 units
(C) 16 units
(D) 20 unite

Supratim Pal

Numerade Educator

Problem 1382

A spring having length $\ell$ and spring constant $\mathrm{k}$ is divided into two parts having lengths $\ell_{1}$ and $\ell_{2}$. If $\ell_{1}=n \ell_{2}$, the force constant of the spring having length $1_{2}$ is $\ldots \ldots \ldots$
(A) $\mathrm{k}(1+\mathrm{n})$
(B) $\mathrm{k}\{(1+\mathrm{n}) / \mathrm{n}\}$
(C) $\mathrm{k}$
(D) $\{\mathrm{k} /(\mathrm{n}+1)\}$

Supratim Pal

Numerade Educator

Problem 1383

When a mass $\mathrm{m}$ is suspended from the free end of a massless spring having force constant $\mathrm{k}$, its oscillates with frequency $\mathrm{f}$. Now if the spring is divided into two equal parts and a mass $2 \mathrm{~m}$ is suspended from the end of anyone of them, it will oscillate with a frequency equal to.........
(A) $\mathrm{f}$
(B) $2 \mathrm{f}$
(C) $(\mathrm{f} / \sqrt{2})$
(D) $\sqrt{2 f}$

Supratim Pal

Numerade Educator

Problem 1384

A mass $\mathrm{m}$ on an inclined smooth surface is attached to two springs as shown in figure. The other ends of both springs are attached to rigid surface. If the force constant of both spring is $k$, then the periodic time of oscillation for the system is $\ldots \ldots \ldots$
(A) $2 \pi(\mathrm{M} / 2 \mathrm{k})^{1 / 2}$
(B) $2 \pi(2 \mathrm{M} / \mathrm{k})^{1 / 2}$
(C) $2 \pi\{(\mathrm{Mg} \operatorname{Sin} \theta) /(2 \mathrm{k})\}^{1 / 2}$
(C) $2 \pi\{(2 \mathrm{Mg}) / \mathrm{k}\}^{1 / 2}$

Supratim Pal

Numerade Educator

Problem 1385

A body of mass $1 \mathrm{~kg}$ suspended from the free end of a spring having force constant $400 \mathrm{Nm}^{-1}$ is executing S.H.M. When the total energy of the system is 2 joule, the maximum acceleration is $\ldots \ldots . \mathrm{ms}^{-2}$.
(A) $8 \mathrm{~ms}^{-2}$
(B) $10 \mathrm{~ms}^{-2}$
(C) $40 \mathrm{~ms}^{-2}$
(D) $40 \mathrm{cms}^{-2}$

Supratim Pal

Numerade Educator

Problem 1386

When a block of mass $\mathrm{m}$ is suspended from the free end of a massless spring having force constant $\mathrm{k}$, its length increases by y. Now when the block is slightly pulled downwards and released, it starts executing S.H.M with amplitude $\mathrm{A}$ and angular frequency $\omega$. The total energy of the system comprising of the block and spring is $\ldots \ldots \ldots$
(A) $(1 / 2) \mathrm{m} \omega^{2} \mathrm{~A}^{2}$
(B) $(1 / 2) m \omega^{2} A^{2}+(1 / 2) \mathrm{ky}^{2}$
(C) $(1 / 2) \mathrm{ky}^{2}$
(D) $(1 / 2) m \omega^{2} A^{2}-(1 / 2) k y^{2}$

Supratim Pal

Numerade Educator

Problem 1387

A spring is attached to the center of a frictionless horizontal turn table and at the other end a body of mass $2 \mathrm{~kg}$ is attached. The length of the spring is $35 \mathrm{~cm}$. Now when the turn table is rotated with an angular speed of $10 \mathrm{rad} \mathrm{s}^{-1}$, the length of the spring becomes $40 \mathrm{~cm}$ then the force constant of the spring is $\ldots \ldots \mathrm{N} / \mathrm{m}$.
(A) $1.2 \times 10^{3}$
(B) $1.6 \times 10^{3}$
(C) $2.2 \times 10^{3}$
(D) $2.6 \times 10^{3}$

Supratim Pal

Numerade Educator

Problem 1388

As shown in figure (a) and (b), a body of mass $\mathrm{m}$ is attached at the ends of the spring system. All springs have the same spring constant $\mathrm{k}$. Now when both systems oscillate along vertical direction, the ratio of their periodic time is .......
(A) $1 / 4$
(B) $1 / 2$
(C) 2
(D) 4

Supratim Pal

Numerade Educator

Problem 1389

A simple pendulum is executing S.H.M. around point $\mathrm{O}$ between the end points $B$ and $C$ with a periodic time of $6 \mathrm{~s}$. If the distance between $\mathrm{B}$ and $\mathrm{C}$ is $20 \mathrm{~cm}$ then in what time will the bob move from $C$ to $D$ ? Point $D$ is at the mid-point of $C$ and $\mathrm{O}$.
(A) $1 \mathrm{~s}$
(B) $2 \mathrm{~s}$
(C) $3 \mathrm{~s}$
(D) $4 \mathrm{~s}$

Supratim Pal

Numerade Educator

Problem 1390

A small spherical steel ball is placed at a distance slightly away from the center of a concave mirror having radius of curvature $250 \mathrm{~cm}$. If the ball is released, it will now move on the curved surface. What will be the periodic time of this motion? Ignore frictional force and take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.
(A) $(\pi / 4) \mathrm{s}$
(B) $\pi \mathrm{s}$
(C) $(\pi / 2) \mathrm{s}$
(D) $2 \pi \mathrm{s}$

Supratim Pal

Numerade Educator

Problem 1391

Two identical springs are attached at the opposite ends of a rod having length $\ell$ and mass $\mathrm{m}$. The rod could rotate about its mid-point $O$ as shown in figure. Now, if the point $A$ of the rod is pressed slightly and released, the rod starts executing oscillatory motion. The periodic time of this motion is ...........
(A) $2 \pi \sqrt{(\mathrm{m} / 2 \mathrm{k})}$
(B) $2 \pi \sqrt{(} 2 \mathrm{~m} / \mathrm{k})$
(C) $\pi \sqrt{(2 \mathrm{~m} / 3 \mathrm{k})}$
(D) $\pi \sqrt{(3 \mathrm{~m} / 2 \mathrm{k})}$

Supratim Pal

Numerade Educator

Problem 1392

A simple pendulum having length $\ell$ is suspended at the roof of a train moving with constant acceleration 'a' along horizontal direction. The periodic time of this pendulum is....
(A) $\mathrm{T}=2 \pi \sqrt{(\ell / \mathrm{g})}$
(B) $\mathrm{T}=2 \pi \sqrt{\{\ell /(\mathrm{g}+\mathrm{a})\}}$
(C) $\mathrm{T}=2 \pi \sqrt{\{\ell /(\mathrm{g}-\mathrm{a})\}}$
(D) $\left.\mathrm{T}=2 \pi \sqrt{\{\ell} /\left(\mathrm{g}^{2}+\mathrm{a}^{2}\right)\right\}$

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Numerade Educator

Problem 1393

A trolley is sliding down a frictionless slope having inclination $\theta$. If a simple pendulum is suspended on top of this trolley, its periodic time is given by $\mathrm{T}=2 \pi \sqrt{\left(1 / \mathrm{g}_{\mathrm{eff}}\right)}$, where $g_{\mathrm{eff}}=\ldots \ldots$
(A) $\mathrm{g}$
(B) $g \sin \theta$
(C) $g \cos \theta$
(D) $g \tan \theta$

Supratim Pal

Numerade Educator

Problem 1394

One end of a mass less spring having force constant $\mathrm{k}$ and length $50 \mathrm{~cm}$ is attached at the upper end of a plane inclined at an angle $e=30^{\circ} .$ When a body of mass $m=1.5 \mathrm{~kg}$ is attached at the lower end of the spring, the length of the spring increases by $2.5 \mathrm{~cm}$. Now, if the mass is displaced by a small amount and released, the amplitude of the resultant oscillation is .........
(A) $(\pi / 7)$
(B) $(2 \pi / 7)$
(C) $(\pi / 5)$
(D) $(2 \pi / 5)$

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Numerade Educator

Problem 1395

Two blocks $\mathrm{A}$ and $\mathrm{B}$ are attached to the two ends of a spring having length $\mathrm{L}$ and force constant $\mathrm{k}$ on a horizontal surface. Initially the system is in equilibrium. Now a third block having same mass $\mathrm{m}$, moving with velocity v collides with block A. In this situation ..........
(A) During maximum contraction of the spring, the kinetic energy of the system $\mathrm{A}-\mathrm{B}$ will be zero.
(B) During maximum contraction of the spring, the kinetic energy of the system $\mathrm{A}-\mathrm{B}$ will be $\mathrm{mV}^{2} / 4$
(C) Maximum contraction of the spring is $\mathrm{V} \sqrt{(\mathrm{m} / \mathrm{k})}$
(D) Maximum contraction of the spring is $\mathrm{V} \sqrt{(2 \mathrm{~m} / \mathrm{k})}$

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Numerade Educator

Problem 1396

The displacement of a particle executing S.H.M. is given by $\mathrm{y}=4 \cos ^{2}(\mathrm{t} / 2) \sin 1000 \mathrm{t}$. This displacement is due to
superposition of .........S.H.M. 's.
(A) 2
(B) 3
(C) 4
(D) 5

Supratim Pal

Numerade Educator

Problem 1397

The displacement of a particle is given by. $\mathrm{x}=\mathrm{A} \cos \omega \mathrm{t}$. Which of the following graph represents variation in potential energy as a function of time $t$ and displacement $\mathrm{x}$.
(A) I,III
(B) II,IV
(C) II,III
(D) I,IV

Supratim Pal

Numerade Educator

Problem 1398

A system is executing S.H.M. The potential energy of the system for displacement $\mathrm{x}$ is $\mathrm{E}_{1}$ and for a displacement of $\mathrm{y}$, the potential energy of the system is $E_{2}$. The potential energy for a displacement of $(x+j)$ is $\ldots \ldots \ldots$
(A) $E_{1}+E_{2}$
(B) $\left.\sqrt{(} \mathrm{E}_{1}^{2}+\mathrm{E}_{2}{ }^{2}\right)$
(C) $\mathrm{E}_{1}+\mathrm{E}_{2}+2 \sqrt{\mathrm{E}}_{1} \mathrm{E}_{2}$
(D) $\sqrt{E}_{1} E_{2}$

Supratim Pal

Numerade Educator

Problem 1399

A system is executing S.H.M. with a periodic time of $4 / 5 \mathrm{~s}$ under the influence of force $\mathrm{F}_{1}$ When a force $\mathrm{F}_{2}$ is applied, the periodic time is $(2 / 5) \mathrm{s}$. Now if $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ are applied simultaneously along the same direction, the periodic time will be.........
(A) $\{4 /(5 \sqrt{5})\}$
(B) $\{4 /(4 \sqrt{5})\}$
(C) $\{8 /(4 \sqrt{5})\}$
(D) $\{8 /(5 \sqrt{5})\}$

Supratim Pal

Numerade Educator

Problem 1400

The periodic time of a simple pendulum is $3.3 \mathrm{~s}$. Now if the point of support of the pendulum starts moving along the vertically upward direction with a velocity $\mathrm{v}=\mathrm{kt}$ (where $\left.\mathrm{k}=2.1 \mathrm{~m} / \mathrm{s}^{2}\right)$, then the new periodic time is $\ldots \ldots \ldots$ s. \{Take $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right\}$
(A) 3
(B) $2.5$
(C) $3.33$
(D) $2.33$

Supratim Pal

Numerade Educator

Problem 1401

A block is placed on a horizontal table. The table executes
S.H.M. along the horizontal plane with a period $\mathrm{T}$. The coefficient of static friction between the table and block is $\mu$. The maximum amplitude of oscillation should be $\ldots \ldots$.. so that the block does not slide off the table.
(A) $(\mu \mathrm{g} \mathrm{T} / 5 \pi)$
(B) $\left\{\left(\mu \mathrm{g} \mathrm{T}^{2}\right) / 4 \pi^{2}\right\}$
(C) $\{(\mu \mathrm{gT}) / 2 \pi\}$
(D) $\mu \mathrm{gT}$

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Numerade Educator

Problem 1402

As shown in figure, a block A having mass $M$ is attached to one end of a massless spring. The block is on a frictionless horizontal surface and the free end of the spring is attached to a wall. Another block B having mass ' $\mathrm{m}$ ' is placed on top of block A. Now on displacing this system horizontally and released, it executes S.H.M. What should be the maximum amplitude of oscillation so that B does not slide off A? Coefficient of static friction between the surfaces of the block's is $\mu$.
(A) $A_{\max }=\{(\mu \mathrm{mg}) / \mathrm{k}\}$
(B) $A_{\max }=[\{\mu(m+M) g\} / k]$
(C) $A_{\max }=[\{\mu(M-\mathrm{m}) g\} / \mathrm{k}]$
(D) $A_{\max }=[\{2 \mu(M+m)\} / k]$

Supratim Pal

Numerade Educator

Problem 1403

A particle is executing S.H.M. about the origin at $\mathrm{x}=0$. Which of the following graph shows variation in potential energy with displacement?

Supratim Pal

Numerade Educator

Problem 1404

A horizontal plank is executing SHM along the vertical direction with angular frequency $\omega .$ A coin is placed on top of this plank. If the amplitude of oscillation is increased gradually, for what maximum amplitude will the coin be on the verge of loosing contact with the plank?
(A) When is plank is at its maximum height
(B) When the plank is at the midpoint.
(C) When the amplitude is $\left(\mathrm{g} / \omega^{2}\right)$
(D) When the amplitude is $\left(\mathrm{g}^{2} / \omega^{2}\right)$

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Numerade Educator

Problem 1405

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1$ : If a spring having spring constant $\mathrm{k}$ is divided into equal parts, then the spring constant of each part will be $2 \mathrm{k}$. Statement $-2:$ When the length of the elastic spring is increased ( stretched) by $\mathrm{x}$, then the amount of work required to be done is $(1 / 2) \mathrm{kx}^{2}$
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) d

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Numerade Educator

Problem 1406

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ The periodic time of a S.H.O. depends on its amplitude and force constant. Statement $-2:$ The elasticity and inertia decides the frequency of S.H.O.
(A) a
(B) $b$
(C) c
(D) $\mathrm{d}$

Supratim Pal

Numerade Educator

Problem 1407

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1 .$
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $d$
Statement $-1:$ For small amplitude, the motion of a simple pendulum is a S.H.M. with periodic time $\mathrm{T}=2 \pi \sqrt{(\ell / \mathrm{g}) . \text { For }}$ large amplitudes, periodic time is greater than $2 \pi \sqrt{(\ell / g)}$. Statement $-2:$ For large amplitude, the speed of the bob is more when it passes through the mid-point (equilibrium point).
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $d$

Supratim Pal

Numerade Educator

Problem 1408

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ Periodic time of a simple pendulum is independent of the mass of the bob. Statement $-2:$ The restoring force does not depend on the mass of the bob.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

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Numerade Educator

Problem 1409

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ The periodic time of a simple pendulum increases on the surface of moon. Statement $-2:$ Moon is very small as compared to Earth.
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

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Numerade Educator

Problem 1410

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) b
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ If the length of a simple pendulum is increased by $3 \%$, then the periodic time changes by $1.5 \%$. Statement $-2:$ Periodic time of a simple pendulum is proportional to its length.
(A) a
(B) $b$
(C) $c$
(D) d

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Numerade Educator

Problem 1411

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement
$-2$ is not the correct explanation of statement $-1$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) d
Statement $-1:$ For a particle executing S.H.M. with an amplitude of $0.01 \mathrm{~m}$ and frequency $30 \mathrm{hz}$, the maximum acceleration is $36 \pi^{2} \mathrm{~m} / \mathrm{s}^{2}$.
Statement $-2:$ The maximum acceleration for the above particle is $\pm \omega 2 \mathrm{~A}$, where $\mathrm{A}$ is amplitude.
(A) a
(B) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$

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Problem 1412

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1 .$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) $a$
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ The periodic time of a stiff spring is less than that of a soft spring. Statement $-2:$ The periodic time of a spring depends on its force constant value and for a stiff spring, it is more.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

Supratim Pal

Numerade Educator

Problem 1413

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement
$-2$ is not the correct explanation of statement $-1$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $\mathrm{b}$
(C) $\mathrm{c}$
(D) $\mathrm{d}$
Statement $-1:$ The amplitude of an oscillator decreases with time. Statement $-2:$ The frequency of an oscillator decreases with time.
(A) a
(B) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$

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Problem 1414

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
(A) a
(B) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$
Statement $-1:$ For a particle executing SHM, the amplitude and phase is decided by its initial position and initial velocity. Statement $-2:$ In a SHM, the amplitude and phase is dependent on the restoring force.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

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Problem 1415

As shown in figure, two light springs having force constants $\mathrm{k}_{1}=1.8 \mathrm{~N} \mathrm{~m}^{-1}$ and $\mathrm{k}_{2}=3.2 \mathrm{~N} \mathrm{~m}^{-1}$ and a block having mass
$\mathrm{m}=200 \mathrm{~g}$ are placed on a frictionless horizontal surface. One end of both springs are attached to rigid supports. The distance between the free ends of the spring is $60 \mathrm{~cm}$ and the block is moving in this gap with a speed $\mathrm{v}=120 \mathrm{~cm} \mathrm{~s}^{-1}$.When the block is moving towards spring $\mathrm{k}_{2}$, what will be the time taken for the spring to get maximum compressed from point D ?
(A) $\pi \mathrm{s}$
(B) $(\pi / 2) \mathrm{s}$
(C) $(\pi / 3) \mathrm{s}$
(D) $(\pi / 4) \mathrm{s}$

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Problem 1416

As shown in figure, two light springs having force constants $\mathrm{k}_{1}=1.8 \mathrm{~N} \mathrm{~m}^{-1}$ and $\mathrm{k}_{2}=3.2 \mathrm{~N} \mathrm{~m}^{-1}$ and a block having mass
$\mathrm{m}=200 \mathrm{~g}$ are placed on a frictionless horizontal surface. One end of both springs are attached to rigid supports. The distance between the free ends of the spring is $60 \mathrm{~cm}$ and the block is moving in this gap with a speed $\mathrm{v}=120 \mathrm{~cm} \mathrm{~s}^{-1}$.When the block is moving towards $k_{1}$, what will be the time taken for it to get maximum compressed from point $\mathrm{C}$ ?
(A) $\pi \mathrm{s}$
(B) $(2 / 3) \mathrm{s}$
(C) $(\pi / 3) \mathrm{s}$
(D) $(\pi / 4) \mathrm{s}$

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Problem 1417

As shown in figure, two light springs having force constants $\mathrm{k}_{1}=1.8 \mathrm{~N} \mathrm{~m}^{-1}$ and $\mathrm{k}_{2}=3.2 \mathrm{~N} \mathrm{~m}^{-1}$ and a block having mass
$\mathrm{m}=200 \mathrm{~g}$ are placed on a frictionless horizontal surface. One end of both springs are attached to rigid supports. The distance between the free ends of the spring is $60 \mathrm{~cm}$ and the block is moving in this gap with a speed $\mathrm{v}=120 \mathrm{~cm} \mathrm{~s}^{-1}$.What will be the periodic time of the block, between the two springs?
(A) $1+(5 \pi / 6) \mathrm{s}$
(B) $1+(7 \pi / 6) \mathrm{s}$
(C) $1+(5 \pi / 12) \mathrm{s}$
(D) $1+(7 \pi / 12) \mathrm{s}$

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Problem 1418

A block having mass $\mathrm{M}$ is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant $\mathrm{k}$. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass $\mathrm{M}$ is executing SHM with amplitude $\mathrm{A}$ and frequency $\mathrm{f}$. When the block is passing through the mid-point of its path of motion, a body of mass $\mathrm{m}$ is placed on top of it, as a result of which its amplitude and frequency changes to $\mathrm{A}^{\prime}$ and $\mathrm{f}$.
The ratio of frequencies $(\mathrm{f} / \mathrm{f})=\ldots \ldots \ldots$
(A) $\sqrt{\{} \mathrm{M} /(\mathrm{m}+\mathrm{M})\}$
(B) $\sqrt{\{\mathrm{m} /(\mathrm{m}+\mathrm{M})\}}$
(C) $\sqrt{\{\mathrm{MA} / \mathrm{mA}}\}$
(D) $\sqrt{[}\{(\mathrm{M}+\mathrm{m}) \mathrm{A}\} / \mathrm{mA}]$

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Problem 1419

A block having mass $\mathrm{M}$ is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant $\mathrm{k}$. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass $\mathrm{M}$ is executing SHM with amplitude $\mathrm{A}$ and frequency $\mathrm{f}$. When the block is passing through the mid-point of its path of motion, a body of mass $\mathrm{m}$ is placed on top of it, as a result of which its amplitude and frequency changes to $\mathrm{A}^{\prime}$ and $\mathrm{f}$.

If the velocity before putting the mass and after putting it is $\mathrm{v}$ and $\mathrm{v}^{1}$ respectively, then $\left(\mathrm{v}^{1} / \mathrm{v}\right)=\ldots \ldots \ldots \ldots$
(A) $\{\mathrm{M} /(\mathrm{m}+\mathrm{M})\}$
(B) $\{(\mathrm{M}+\mathrm{m}) / \mathrm{M}\}$
(C) $\{(M+m) /(M-m)\}\left(A^{1} / A\right)$
(D) $\{(M-m) /(M+m)\}\left(A^{1} / A\right)$

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Problem 1420

A block having mass $\mathrm{M}$ is placed on a horizontal frictionless surface. This mass is attached to one end of a spring having force constant $\mathrm{k}$. The other end of the spring is attached to a rigid wall. This system consisting of spring and mass $\mathrm{M}$ is executing SHM with amplitude $\mathrm{A}$ and frequency $\mathrm{f}$. When the block is passing through the mid-point of its path of motion, a body of mass $\mathrm{m}$ is placed on top of it, as a result of which its amplitude and frequency changes to $\mathrm{A}^{\prime}$ and $\mathrm{f}$.
The ratio of amplitudes $\left(\mathrm{A}^{1} / \mathrm{A}\right)=\ldots \ldots \ldots$
(A) $\sqrt{\{}(\mathrm{M}+\mathrm{m}) / \mathrm{m}\}$
(B) $\sqrt{\{m} /(\mathrm{M}+\mathrm{m})\}$
(C) $\sqrt{\{} \mathrm{M} /(\mathrm{M}+\mathrm{m})\}$
(D) $\sqrt{\{}(\mathrm{M}+\mathrm{m}) / \mathrm{M}\}$

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Problem 1421

The equation for displacement of a particle at time $t$ is given by the equation $\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}$.
The motion of the particle is $\ldots \ldots$
(A) Damped motion
(B) Periodic motion
(C) Rotational motion
(D) S.H.M.

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Problem 1422

The equation for displacement of a particle at time $t$ is given by the equation $\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}$.
The periodic time of oscillation is $\ldots \ldots \ldots \ldots$
(A) $2 \mathrm{~s}$
(B) $\pi \mathrm{s}$
(C) $(\pi / 2) \mathrm{s}$
(D) $2 \pi \mathrm{s}$

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Problem 1423

The equation for displacement of a particle at time $\mathrm{t}$ is given by the equation $\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}$.
The amplitude of oscillation is $\ldots \ldots \ldots . \mathrm{cm}$.
(A) 1
(B) 3
(C) 5
(D) 7

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Problem 1424

The equation for displacement of a particle at time $t$ is given by the equation $\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}$.
The maximum acceleration of the particle is $\ldots \ldots . . \mathrm{cm} / \mathrm{s}^{2}$.
(A) 4
(B) 12
(C) 20
(D) 28

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Problem 1425

The equation for displacement of a particle at time $\mathrm{t}$ is given by the equation $\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}$.
If the mass of the particle is $5 \mathrm{gm}$, then the total energy of the particle is $\ldots \ldots \ldots$ erg
(A) 250
(B) 125
(C) 500
(D) 375

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Problem 1426

The equation for displacement of a particle at time $t$ is given by the equation $\mathrm{y}=3 \cos 2 \mathrm{t}+4 \sin 2 \mathrm{t}$.
The frequency of the particle is $\ldots \ldots \mathrm{s}^{-1}$.
(A) $(1 / \pi)$
(B) $\pi$
(C) $(1 / 2 \pi)$
(D) $(\pi / 2)$

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Problem 1427

Equation for a harmonic progressive wave is given by $\mathrm{y}=\mathrm{A}$ $\sin (15 \pi t+10 \pi x+\pi / 3)$ where $x$ is in meter and $t$ is in seconds. This wave is $\ldots \ldots$
(A) Travelling along the positive $\mathrm{x}$ direction with a speed of $1.5 \mathrm{~ms}^{-1}$
(B) Travelling along the negative $\mathrm{x}$ direction with a speed of $1.5 \mathrm{~ms}^{-1} .$
(C) Has a wavelength of $1.5 \mathrm{~m}$ along the $-\mathrm{x}$ direction.
(D) Has a wavelength of $1.5 \mathrm{~m}$ along the positive $\mathrm{x}$ - direction.

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Problem 1428

If the velocity of sound wave in humid air is $\mathrm{v}_{\mathrm{m}}$ and that in dry air is $\mathrm{v}_{\mathrm{d}}$, then $\ldots \ldots$
(A) $\mathrm{v}_{\mathrm{m}}>\mathrm{v}_{\mathrm{d}}$
(B) $\mathrm{v}_{\mathrm{m}}<\mathrm{v}_{\mathrm{d}}$
(C) $\mathrm{v}_{\mathrm{m}}=\mathrm{v}_{\mathrm{d}}$
$(\mathrm{D}) \mathrm{v}_{\mathrm{m}} \gg \mathrm{v}_{\mathrm{d}}$

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Problem 1429

The ratio of frequencies of two waves travelling through the same medium is $2: 5 .$ The ratio of their wavelengths will be....
(A) $2: 5$
(B) $5: 2$
(C) $3: 5$
(D) $5: 3$

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Problem 1430

If the maximum frequency of a sound wave at room temperature is $20,000 \mathrm{~Hz}$ then its minimum wavelength will be approximately $\ldots \ldots\left(\mathrm{v}=340 \mathrm{~ms}^{-1}\right)$
(A) $0.2 \AA$
(B) $5 \AA$
(C) $5 \mathrm{~cm}$ to $2 \mathrm{~m}$
(D) $20 \mathrm{~mm}$

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Problem 1431

If the equation of a wave in a string having linear mass density $0.04 \mathrm{~kg} \mathrm{~m}^{-1}$ is given by $\mathrm{y}=0.02$ $\sin [2 \pi\{1 /(0.04)\}-\{\mathrm{x} /(0.50)\}]$, then the tension in the string
is $\ldots \ldots \ldots \ldots$ N. (All values are in $\mathrm{mks}$ )
(A) $6.25$
(B) $4.0$
(C) $12.5$
(D) $0.5$

Supratim Pal

Numerade Educator

Problem 1432

If the equation for a transverse wave is $\mathrm{y}=\mathrm{A} \operatorname{Sin} 2 \pi$ $\{(1 / \mathrm{T})-(\mathrm{x} / \lambda)\}$. then for what wavelength will the maximum velocity of the particle be double the wave velocity ?
(A) $(\pi \mathrm{A} / 4)$
(B) $(\pi \mathrm{A} / 2)$
(C) $\pi \mathrm{A}$
(D) $2 \pi \mathrm{A}$

Supratim Pal

Numerade Educator

Problem 1433

Consider two points lying at a distance of $10 \mathrm{~m}$ and $15 \mathrm{~m}$ from an oscillating source. If the periodic time of oscillation is $0.05 \mathrm{~s}$ and the velocity of wave produced is $300 \mathrm{~m} / \mathrm{s}$, then what will be the phase difference the two points?
(A) $\pi$
(B) $\pi / 6$
(C) $\pi / 3$
(D) $2 \pi / 3$

Akshaya Rs

Numerade Educator

Problem 1434

A string is divided into three parts having lengths $\ell_{1}, \ell_{2}$ and $\ell_{3}$ each. If the fundamental frequency of these parts are $\mathrm{f}_{1}, \mathrm{f}_{2}$ and $\mathrm{f}_{3}$ respectively, then the fundamental frequency of the original string $\mathrm{f}=\ldots \ldots \ldots$
(A) $\sqrt{f}=\sqrt{f}_{1}+\sqrt{f}_{2}+\sqrt{f}_{3}$
(B) $\mathrm{f}=\mathrm{f}_{1}+\mathrm{f}_{2}+\mathrm{f}_{3}$
(C) $(1 / \mathrm{f})=\left(1 / \mathrm{f}_{1}\right)+\left(1 / \mathrm{f}_{2}\right)+\left(1 / \mathrm{f}_{3}\right)$
(D) $(1 / \sqrt{f})=\left(1 / \sqrt{f}_{1}\right)+\left(1 / \sqrt{f}_{2}\right)+\left(1 / \sqrt{f}_{2}\right)$

Akshaya Rs

Numerade Educator

Problem 1436

Equation for a progressive harmonic wave is given by $\mathrm{y}=8 \sin 2 \pi(0.1 \mathrm{x}-2 \mathrm{t})$, where $\mathrm{x}$ and $\mathrm{y}$ are in $\mathrm{cm}$ and $\mathrm{t}$ is in
seconds. What will be the phase difference between two particles of this wave separated by a distance of $2 \mathrm{~cm} ?$
(A) $18^{\circ}$
(B) $36^{\circ}$
(C) $72^{\circ}$
(D) $54^{\circ}$

Akshaya Rs

Numerade Educator

Problem 1437

As shown in figure, two pulses in a string having center to center distance of $8 \mathrm{~cm}$ are travelling along mutually opposite direction. If the speed of both the pulse is $2 \mathrm{~cm} / \mathrm{s}$, then after $2 \mathrm{~s}$, the energy of these pulses will be $\ldots \ldots \ldots \ldots \ldots$
(A) zero
(B) totally kinetic energy
(C) totally potential energy
(D) Partially potential energy and partially kinetic energy.

Akshaya Rs

Numerade Educator

Problem 1438

Two waves are represented by $\mathrm{y}_{1}=\mathrm{A} \sin \omega \mathrm{t}$ and $\mathrm{y}_{2}=\mathrm{A}$ cos $\omega \mathrm{t}$. The phase of the first wave, $\mathrm{w}$. r. t. to the second wave is
(A) more by radian
(B) less by $\pi$ radian
(C) more by $\pi / 2$
(D) less by $\pi / 2$

Akshaya Rs

Numerade Educator

Problem 1439

If the resultant of two waves having amplitude $\mathrm{b}$ is $\mathrm{b}$, then the phase difference between the two waves is
(A) $120^{\circ}$
(B) $60^{\circ}$
(C) $90^{\circ}$
(D) $180^{\circ}$

Akshaya Rs

Numerade Educator

Problem 1440

If two antinodes and three nodes are formed in a distance of $1.21 \AA$, then the wavelength of the stationary wave is
(A) $2.42 \AA$
(B) $6.05 \AA$
(C) $3.63 \AA$
(D) $1.21 \AA$

Akshaya Rs

Numerade Educator

Problem 1441

The function $\sin ^{2}(\omega t)$ represents
(A) A SHM with periodic time $\pi / \omega$
(B) A SHM with a periodic time $2 \pi / \omega$
(C) A periodic motion with periodic time $\pi / \omega$
(D) A periodic motion with period $2 \pi / \omega$

Akshaya Rs

Numerade Educator

Problem 1442

If two almost identical waves having frequencies $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$, produced one after the other superposes then the time interval to obtain a beat of maximum intensity is $\ldots \ldots \ldots .$
(A) $\left\{1 /\left(\mathrm{n}_{1}-\mathrm{n}_{2}\right)\right\}$
(B) $\left(1 / \mathrm{n}_{1}\right)-\left(1 / \mathrm{n}_{2}\right)$
(C) $\left(1 / \mathrm{n}_{1}\right)+\left(1 / \mathrm{n}_{2}\right)$
(D) $\left\{1 /\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right)\right\}$

Akshaya Rs

Numerade Educator

Problem 1443

When two sound waves having amplitude A, angular frequency $\omega$ and a phase difference of $\pi / 2$ superposes, the maximum amplitude and angular frequency of the resultant wave is $\ldots \ldots \ldots \ldots$
(A) $\sqrt{2} \mathrm{~A}, \omega$
(B) $(\mathrm{A} / \sqrt{2}),(\omega / 2)$
(C) $(\mathrm{A} / \sqrt{2}), \omega$
(D) $\sqrt{2} \mathrm{~A},(\omega / 2)$

Akshaya Rs

Numerade Educator

Problem 1444

The amplitude of a wave in a string is $2 \mathrm{~cm}$. This wave is propagating along the $\mathrm{x}$ -direction with a speed of $128 \mathrm{~m} / \mathrm{s}$. Five such waves are accommodated in $4 \mathrm{~m}$ length of the string. The equation for this wave is
(A) $\mathrm{y}=0.02 \sin (15.7 \mathrm{x}-2010 \mathrm{t}) \mathrm{m}$
(B) $\mathrm{y}=0.02 \sin (15.7 \mathrm{x}+2010 \mathrm{t}) \mathrm{m}$
(C) $\mathrm{y}=0.02 \sin (7.85 \mathrm{x}-1005 \mathrm{t}) \mathrm{m}$
(D) $\mathrm{y}=0.02 \sin (7.85 \mathrm{x}+1005 \mathrm{t}) \mathrm{m}$

Akshaya Rs

Numerade Educator

Problem 1445

A string of length $70 \mathrm{~cm}$ is stretched between two rigid supports. The resonant frequency for this string is found to be $420 \mathrm{~Hz}$ and $315 \mathrm{~Hz}$. If there are no resonant frequencies between these two values, then what would be the minimum resonant frequency of this string ?
(A) $10.5 \mathrm{~Hz}$
(B) $1.05 \mathrm{~Hz}$
(C) $105 \mathrm{~Hz}$
(D) $1050 \mathrm{~Hz}$

Akshaya Rs

Numerade Educator

Problem 1446

Sound waves propagates with a speed of $350 \mathrm{~m} / \mathrm{s}$ through air and with a speed of $3500 \mathrm{~m} / \mathrm{s}$ through brass. If a sound wave having frequency $700 \mathrm{~Hz}$ passes from air to brass, then its wavelength .........
(A) decreases by a fraction of 10
(B) increases 20 times
(C) increases 10 times
(D) decreases by a fraction of 20

Akshaya Rs

Numerade Educator

Problem 1447

A transverse wave is represented by $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$. For what value of its wavelength will the wave velocity be equal to the maximum velocity of the particle taking part in the wave propagation?
(A) $2 \pi \mathrm{A}$
(B) A
(C) $\pi \mathrm{A}$
(D) $\pi \mathrm{A} / 2$

Akshaya Rs

Numerade Educator

Problem 1448

Two monoatomic ideal gases 1 and 2 has molecular weights $\mathrm{m}_{1}$ and $\mathrm{m}_{2}$. Both are kept in two different containers at the same temperature. The ratio of velocity of sound wave in gas 1 and 2 is $\ldots \ldots \ldots$
(A) $\sqrt{\left(m_{2} / m_{1}\right)}$
(B) $\sqrt{\left(m_{1} / m_{2}\right)}$
(C) $\left(\mathrm{m}_{1} / \mathrm{m}_{2}\right)$
(D) $\left(\mathrm{m}_{2} / \mathrm{m}_{1}\right)$

Akshaya Rs

Numerade Educator

Problem 1449

A wire having length $\mathrm{L}$ is kept under tension between $\mathrm{x}=0$ and $\mathrm{x}=\mathrm{L}$. In one experiment, the equation of the wave and energy is given by $\mathrm{y}_{1}=\mathrm{A} \sin (\pi \mathrm{x} / \mathrm{L}) \sin \omega \mathrm{t}$ and $\mathrm{E}_{1}$
respectively. In another experiment, it is $\mathrm{y}_{2}=\mathrm{A} \sin$ $\{(2 \pi \mathrm{x}) / \mathrm{L}\} \sin 2 \omega \mathrm{t}$ and $\mathrm{E}_{2}$. Then........
(A) $E_{2}=E_{1}$
(B) $E_{2}=2 \mathrm{E}_{1}$
(C) $\mathrm{E}_{2}=4 \mathrm{E}_{1}$
(D) $E_{2}=16 \mathrm{E}_{1}$

Akshaya Rs

Numerade Educator

Problem 1450

Twenty four tuning forks are arranged in such a way that each fork produces 6 beats/s with the preceding fork. If the frequency of the last tuning fork is double than the first fork, then the frequency of the second tuning fork is $\ldots \ldots$
(A) 132
(B) 138
(C) 276
(D) 144

Akshaya Rs

Numerade Educator

Problem 1451

If two SHM's are given by the equation $\mathrm{y}_{1}=0.1 \sin [\pi \mathrm{t}+(\pi / 3)]$ and $\mathrm{y}_{2}=0.1 \cos \pi \mathrm{t}$, then the phase
difference between the velocity of particle 1 and 2 is $\ldots \ldots \ldots$
(A) $\pi / 6$
(B) $-\pi / 3$
(C) $\pi / 3$
(D) $-\pi / 6$

Akshaya Rs

Numerade Educator

Problem 1452

The wave number for a wave having wavelength $0.005 \mathrm{~m}$
is $\ldots \ldots \mathrm{m}^{-1}$
(A) 5
(B) 50
(C) 100
(D) 200

Akshaya Rs

Numerade Educator

Problem 1453

An listener is moving towards a stationary source of sound with a speed (1/4) times the speed of sound. What will be the percentage increase in the frequency of sound heard by the listener?
(A) $20 \%$
(B) $25 \%$
(C) $2.5 \%$
(D) $5 \%$

Akshaya Rs

Numerade Educator

Problem 1454

When the resonance tube experiment, to measure speed of sound is performed in winter, the first harmonic is obtained for $16 \mathrm{~cm}$ length of air column. If the same experiment is performed in summer, the second harmonic is obtained for $\mathrm{x}$ length of air column. Then $\ldots \ldots$
(A) $32>\mathrm{x}>16$
(B) $16>\mathrm{x}$
(C) $\mathrm{x}>48$
(D) $48>\mathrm{x}>32$

Akshaya Rs

Numerade Educator

Problem 1455

What should be the speed of a source of sound moving towards a stationary listener, so that the frequency of sound heard by the listener is double the frequency of sound produced by the source? \{Speed of sound wave is $\mathrm{v}\}$
(A) $\mathrm{v}$
(B) $2 \mathrm{v}$
(C) $\mathrm{v} / 2$
(D) $\mathrm{v} / 4$

Akshaya Rs

Numerade Educator

Problem 1456

A metal wire having linear mass density $10 \mathrm{~g} / \mathrm{m}$ is passed over two supports separated by a distance of $1 \mathrm{~m}$. The wire is kept in tension by suspending a $10 \mathrm{~kg}$ mass. The mid point of the wire passes through a magnetic field provided by magnets and an a. c. supply having frequency $\mathrm{n}$ is passed through the wire. If the wire starts vibrating with its resonant frequency, what is the frequency of a. c. supply?
(A) $50 \mathrm{~Hz}$
(B) $100 \mathrm{~Hz}$
(C) $200 \mathrm{~Hz}$
(D) $25 \mathrm{~Hz}$

Akshaya Rs

Numerade Educator

Problem 1457

If the listener and the source of sound moves along the same direction with the same speed, then.........
(A) $\left(\mathrm{f}_{\mathrm{L}} / \mathrm{f}_{\mathrm{s}}\right)<1$
(B) $\left(\mathrm{f}_{\mathrm{L}} / \mathrm{f}_{\mathrm{s}}\right)=0$
(C) $\left(\mathrm{f}_{\mathrm{L}} / \mathrm{f}_{\mathrm{3}}\right)=1$
(D) $\left(\mathrm{f}_{\mathrm{L}} / \mathrm{f}_{\mathrm{s}}\right)>1$

Akshaya Rs

Numerade Educator

Problem 1458

A wire of length $10 \mathrm{~m}$ and mass $3 \mathrm{~kg}$ is suspended from a rigid support. The wire has uniform cross sectional area. Now a block of mass $1 \mathrm{~kg}$ is suspended at the free end of the wire and a wave having wavelength $0.05 \mathrm{~m}$ is produced at the lower end of the wire. What will be the wavelength of this wave when it reached the upper end of the wire?
(A) $0.12 \mathrm{~m}$
(B) $0.18 \mathrm{~m}$
(C) $0.14 \mathrm{~m}$
(D) $0.10 \mathrm{~m}$

Akshaya Rs

Numerade Educator

Problem 1459

If the mass of 1 mole of air is $29 \times 10^{-3} \mathrm{~kg}$, then the speed of sound in it at STP is $(\gamma=7 / 5) .\left\{\mathrm{T}=273 \mathrm{~K}, \mathrm{P}=1.01 \times 10^{5} \mathrm{~Pa}\right\}$
(A) $270 \mathrm{~m} / \mathrm{s}$
(B) $290 \mathrm{~m} / \mathrm{s}$
(C) $330 \mathrm{~m} / \mathrm{s}$
(D) $350 \mathrm{~m} / \mathrm{s}$

Akshaya Rs

Numerade Educator

Problem 1460

A wave travelling along a string is described by $\mathrm{y}=0.005 \sin (40 \mathrm{x}-2 \mathrm{t})$ in SI units. The wavelength and
frequency of the wave are $\ldots \ldots \ldots$
(A) $(\pi / 5) \mathrm{m} ; 0.12 \mathrm{~Hz}$
(B) $(\pi / 10) \mathrm{m} ; 0.24 \mathrm{~Hz}$
(C) $(\pi / 40) \mathrm{m} ; 0.48 \mathrm{~Hz}$
(D) $(\pi / 20) \mathrm{m} ; 0.32 \mathrm{~Hz}$

Akshaya Rs

Numerade Educator

Problem 1461

Two sitar strings $\mathrm{A}$ and $\mathrm{B}$ playing the note "Dha" are slightly out of time and produce beats of frequency $5 \mathrm{~Hz}$. The tension of the string B is slightly increased and the beat frequency is found to decrease to $3 \mathrm{~Hz}$. What is the original frequency of $\mathrm{B}$ if the frequency of $\mathrm{A}$ is $427 \mathrm{~Hz}$ ?
(A) 432
(B) 422
(C) 437
(D) 417

Akshaya Rs

Numerade Educator

Problem 1462

A rocket is moving at a speed of $130 \mathrm{~m} / \mathrm{s}$ towards a stationary target. While moving, it emits a wave of frequency $800 \mathrm{~Hz}$. Calculate the frequency of the sound as detected by the target. (Speed of wave $=330 \mathrm{~m} / \mathrm{s}$ )
(A) $1320 \mathrm{~Hz}$
(B) $2540 \mathrm{~Hz}$ (C) $1270 \mathrm{~Hz}$
(D) $660 \mathrm{~Hz}$

Akshaya Rs

Numerade Educator

Problem 1463

Length of a steel wire is $11 \mathrm{~m}$ and its mass is $2.2 \mathrm{~kg}$. What should be the tension in the wire so that the speed of a transverse wave in it is equal to the speed of sound in dry air at $20^{\circ} \mathrm{C}$ temperature?
(A) $2.31 \times 10^{4} \mathrm{~N}$
(B) $2.25 \times 10^{4} \mathrm{~N}$
(C) $2.06 \times 10^{4} \mathrm{~N}$
(D) $2.56 \times 10^{4} \mathrm{~N}$

Akshaya Rs

Numerade Educator

Problem 1464

A wire stretched between two rigid supports vibrates with a frequency of $45 \mathrm{~Hz}$. If the mass of the wire is $3.5 \times 10^{-2} \mathrm{~kg}$ and its linear mass density is $4.0 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$, what will be the tension in the wire?
(A) $212 \mathrm{~N}$
(B) $236 \mathrm{~N}$
(C) $248 \mathrm{~N}$
(D) $254 \mathrm{~N}$

Akshaya Rs

Numerade Educator

Problem 1465

Tube $A$ has both ends open while tube $B$ has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube $\mathrm{A}$ and $\mathrm{B}$ is $\ldots \ldots \ldots$
(A) $1: 2$
(B) $1: 4$
(C) $2: 1$
(D) $4: 1$

Akshaya Rs

Numerade Educator

Problem 1466

A tuning fork arrangement produces 4 beats/second with one fork of frequency $288 \mathrm{~Hz}$. A little wax is applied on the unknown fork and it then produces 2 beats/s. The frequency of the unknown fork is $\ldots \ldots \ldots . \mathrm{Hz}$.
(A) 286
(B) 292
(C) 294
(D) 288

Akshaya Rs

Numerade Educator

Problem 1467

A wave $\mathrm{y}=\mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$ on a string meets with another
wave producing a node at $\mathrm{x}=0 .$ Then the equation of the unknown wave is $\ldots \ldots \ldots$
(A) $y=a \sin (\omega t+k x)$
(B) $\mathrm{y}=-\mathrm{a} \sin (\omega \mathrm{t}+\mathrm{kx})$
(C) $\mathrm{y}=\mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$
(D) $\mathrm{y}=-\mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$

Akshaya Rs

Numerade Educator

Problem 1468

When temperature increases, the frequency of a tuning fork
(A) Increases
(B) Decreases
(C) remains same
(D) Increases or decreases depending on the material.

Akshaya Rs

Numerade Educator

Problem 1472

In a longitudinal wave, pressure variation and displacement variation are
(A) In phase
(B) $90^{\circ}$ out of phase
(C) $45^{\circ}$ out of phase
(D) $180^{\circ}$ out of phase

Akshaya Rs

Numerade Educator

Problem 1473

A tuning fork of frequency $480 \mathrm{~Hz}$ produces 10 beats/s when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces fewer beats per second than before?
(A) $480 \mathrm{~Hz}$
(B) $490 \mathrm{~Hz}$
(C) $460 \mathrm{~Hz}$
(D) $470 \mathrm{~Hz}$

Akshaya Rs

Numerade Educator

Problem 1474

Which of the following functions represents a travelling wave?
(A) $(\mathrm{x}-\mathrm{vt})^{2}$
(B) in $(\mathrm{x}+\mathrm{vt})$
(C) $\mathrm{e}^{-(\mathrm{x}+\mathrm{vt}) 2}$
(D) $\{1 /(\mathrm{x}+\mathrm{vt})\}$

Akshaya Rs

Numerade Educator

Problem 1475

Two sound waves are represented by $\mathrm{y}=\mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$ and $\mathrm{y}=\mathrm{a} \cos (\omega \mathrm{t}-\mathrm{kx})$. The phase difference between the waves
in water is $\ldots \ldots \ldots$
(A) $(\pi / 2)$
(B) $(\pi / 4)$
(C) $\pi$
(D) $(3 \pi / 4)$

Akshaya Rs

Numerade Educator

Problem 1476

A string of linear density $0.2 \mathrm{~kg} / \mathrm{m}$ is stretched with a force of $500 \mathrm{~N}$. A transverse wave of length $4.0 \mathrm{~m}$ and amplitude $1 / 1$ meter is travelling along the string. The speed of the wave is $\ldots \ldots \ldots \ldots \mathrm{m} / \mathrm{s}$
(A) 50
(B) $62.5$
(C) 2500
(D) $12.5$

Akshaya Rs

Numerade Educator

Problem 1477

Two wires made up of same material are of equal lengths but their radii are in the ratio $1: 2$. On stretching each of these two strings by the same tension, the ratio between their fundamental frequency is $\ldots \ldots \ldots .$
(A) $1: 2$
(B) $2: 1$
(C) $1: 4$
(D) $4: 1$

Akshaya Rs

Numerade Educator

Problem 1478

The tension in a wire is decreased by $19 \%$, then the percentage decrease in frequency will be.......
(A) $19 \%$
(B) $10 \%$
(C) $0.19 \%$
(D) None of these

Akshaya Rs

Numerade Educator

Problem 1479

An open organ pipe has fundamental frequency $100 \mathrm{~Hz}$. What frequency will be produced if its one end is closed?
(A) $100,200,300, \ldots$
(B) $50,150,250 \ldots .$
(C) $50,100,200,300 \ldots \ldots$
(D) $50,100,150,200 \ldots \ldots$

Akshaya Rs

Numerade Educator

Problem 1480

A closed organ pipe has fundamental frequency $100 \mathrm{~Hz}$. What frequencies will be produced if its other end is also opened?
(A) $200,400,600,800 \ldots \ldots$
(B) $200,300,400,500 \ldots \ldots$
(C) $100,300,500,700 \ldots \ldots$
(D) $100,200,300,400 \ldots \ldots$

Akshaya Rs

Numerade Educator

Problem 1481

A column of air of length $50 \mathrm{~cm}$ resonates with a stretched string of length $40 \mathrm{~cm}$. The length of the same air column which will resonate with $60 \mathrm{~cm}$ of the same string at the same tension is $\ldots \ldots \ldots$
(A) $100 \mathrm{~cm}$
(B) $75 \mathrm{~cm}$
(C) $50 \mathrm{~cm}$
(D) $25 \mathrm{~cm}$

Akshaya Rs

Numerade Educator

Problem 1482

Two forks $\mathrm{A}$ and $\mathrm{B}$ when sounded together produce 4 beats $/ \mathrm{s}$. The fork A is in unison with $30 \mathrm{~cm}$ length of a sonometer wire and $B$ is in unison with $25 \mathrm{~cm}$ length of the same wire at the same tension. The frequencies of the fork are
(A) $24 \mathrm{~Hz}, 28 \mathrm{~Hz}$
(B) $20 \mathrm{~Hz}, 24 \mathrm{~Hz}$
(C) $16 \mathrm{~Hz}, 20 \mathrm{~Hz}$
(D) $26 \mathrm{~Hz}, 30 \mathrm{~Hz}$

Akshaya Rs

Numerade Educator

Problem 1483

A tuning fork of frequency $200 \mathrm{~Hz}$ is in unison with a sonometer wire. The number of beats heard per second when the tension is increased by $1 \%$ is $\ldots \ldots \ldots .$
(A) 1
(B) 2
(C) 4
(D) $0.5$

Akshaya Rs

Numerade Educator

Problem 1484

A bus is moving with a velocity of $5 \mathrm{~m} / \mathrm{s}$ towards a huge wall. The driver sounds a horn off frequency $165 \mathrm{~Hz}$. If the speed of sound in air is $335 \mathrm{~m} / \mathrm{s}$, the number of beats heard per second by the passengers in the bus will be........
(A) 3
(B) 4
(C) 5
(D) 6 A vehicle with a horn of frequency $\mathrm{n}$ is moving with a velocity

Akshaya Rs

Numerade Educator

Problem 1485

A vehicle with a horn of frequency $\mathrm{n}$ is moving with a velocity
of $30 \mathrm{~m} / \mathrm{s}$ in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency $\left(\mathrm{n}+\mathrm{n}_{1}\right) .$ If the sound velocity in air is $300 \mathrm{~m} / \mathrm{s}$, then $\ldots \ldots . .$
(A) $\mathrm{n}_{1}=10 \mathrm{n}$
(B) $\mathrm{n}_{1}=0$
(C) $\mathrm{n}_{1}=0.1 \mathrm{n}$
(D) $\mathrm{n}_{1}=-0 . \ln$

Akshaya Rs

Numerade Educator

Problem 1486

In a sine wave, position of different particles at time $\mathrm{t}=0$ is shown in figure. The equation for this wave travelling along the positive $\mathrm{x}$ - direction can be $\ldots \ldots$
(A) $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$
(B) $\mathrm{y}=\mathrm{A} \cos (\mathrm{kx}-\omega \mathrm{t})$
(C) $\mathrm{y}=\mathrm{A} \cos (\omega \mathrm{t}-\mathrm{kx})$
(D) $\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}-\omega \mathrm{t})$

Akshaya Rs

Numerade Educator

Problem 1487

Which of the following changes at an antinode in a stationary wave?
(A) Density only
(B) Pressure only
(C) Both pressure and density
(D) Neither pressure nor density

Akshaya Rs

Numerade Educator

Problem 1488

A sonometer wire supports a $4 \mathrm{~kg}$ load and vibrates in fundamental mode with a tuning fork of frequency $416 \mathrm{~Hz}$. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to $\ldots \ldots \ldots$
(A) $1 \mathrm{~kg}$
(B) $2 \mathrm{~kg}$
(C) $8 \mathrm{~kg}$
(D) $16 \mathrm{~kg}$

Akshaya Rs

Numerade Educator

Problem 1489

In brass, the velocity of a longitudinal wave is 100 times the velocity of a transverse wave. If $\mathrm{Y}=1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, then stress in the wire is $\ldots \ldots$
(A) $1 \times 10^{13} \mathrm{~N} / \mathrm{m}^{2}$
(B) $1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
(C) $1 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
(D) $1 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$

Akshaya Rs

Numerade Educator

Problem 1490

The frequency of tuning fork $\mathrm{A}$ is $2 \%$ more than the frequency of a standard fork. Frequency of tuning fork $B$ is $3 \%$ less than the frequency of the standard fork. If 6 beats per second are heard when the two forks $\mathrm{A}$ and $\mathrm{B}$ are excited, then frequency of $A$ is $\ldots \ldots \ldots . H z$
(A) 120
(B) $122.4$
(C) $116.4$
(D) 130

Akshaya Rs

Numerade Educator

Problem 1491

Fundamental frequency of a sonometer wire is $\mathrm{n}$. If the length and diameter of the wire are doubled keeping the tension same, the new fundamental frequency is......
(A) $(2 \mathrm{n} / \sqrt{2})$
(B) $\{\mathrm{n} /(2 \sqrt{2})$
(C) $\sqrt{2 n}$
(D) $(\mathrm{n} / 4)$

Akshaya Rs

Numerade Educator

Problem 1492

A car blowing its horn at $480 \mathrm{~Hz}$ moves towards a high wall at a speed of $20 \mathrm{~m} / \mathrm{s}$. If the speed of sound is $340 \mathrm{~m} / \mathrm{s}$, the frequency of the reflected sound heard by the driver sitting in the car will be closest to $\ldots \ldots \ldots . \mathrm{Hz}$
(A) 510
(B) 524
(C) 568
(D) 480

Akshaya Rs

Numerade Educator

Problem 1493

A cylindrical tube open at both ends has a fundamental frequency $\mathrm{f}$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now........
(A) $\mathrm{f} / 2$
(B) $\mathrm{f}$
(C) $3 \mathrm{f} / 4$
(D) $2 \mathrm{f}$

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Numerade Educator

Problem 1494

Three sound waves of equal amplitudes have frequencies $(\mathrm{v}-1), \mathrm{v},(\mathrm{v}+1)$. They superpose to give beats. The number of beats produced per second will be
(A) 3
(B) 2
(C) 1
(D) 4

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Problem 1495

A wave travelling along the $\mathrm{x}$ -axis is described by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=0.005 \operatorname{Cos}(\propto \mathrm{x}-\beta \mathrm{t}) .$ If the wavelength and
the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$ respectively, then $\propto$ and $\beta$ in appropriate units are $\ldots \ldots$
(A) $\propto=12.50 \pi, \beta=\mathrm{p} / 2.0$
(B) $\propto=25 \pi, \beta=\pi$
(C) $\propto=0.08 / \pi, \beta=2.0 / \pi$
(D) $\propto=0.04 / \pi, \mathrm{a}=1.0 / \pi$

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Problem 1496

A wave travelling along a string is described by the equation $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx}) .$ The maximum particle velocity is $\ldots \ldots$
(A) A\omega
(B) $\omega / \mathrm{k}$
(C) $\mathrm{d} \omega / \mathrm{dk}$
(D) $\mathrm{x}$

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Problem 1497

A string is stretched between fixed points separated by 75 $\mathrm{cm} .$ It is observed to have a resonant frequencies of $420 \mathrm{~Hz}$ and $315 \mathrm{~Hz}$. There are other resonant frequencies between these two. Then the lowest frequency for this string is $\ldots \ldots \ldots \ldots . . . h z$
(A) $1.05$
(B) 1050
(C) $10.5$
(D) 105

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Problem 1498

Two tuning forks $P$ and $Q$ when set vibrating gives 4 beats/ second. If the prong of fork $P$ is filed, the beats are reduced to $2 / \mathrm{s}$. What is the frequency of $\mathrm{P}$, if that of $\mathrm{Q}$ is $250 \mathrm{~Hz}$ ?
(A) $246 \mathrm{~Hz}$
(B) $250 \mathrm{~Hz}$
(C) $254 \mathrm{~Hz}$
(D) $252 \mathrm{~Hz}$

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Problem 1499

The length of a string tied across two rigid supports is $40 \mathrm{~cm}$. The maximum wavelength of a stationary wave that can be produced in it is $\ldots \ldots \ldots \mathrm{cm}$.
(A) 20
(B) 40
(C) 80
(D) 120

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Problem 1500

A stationary wave of frequency $200 \mathrm{~Hz}$ are formed in air. If the velocity of the wave is $360 \mathrm{~m} / \mathrm{s}$, the shortest distance between two antinodes is $\ldots \ldots \ldots \ldots \mathrm{m}$
(A) $1.8$
(B) $3.6$
(C) $0.9$
(D) $0.45$

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Problem 1501

A tuning fork produces 4 beats per second with both $49 \mathrm{~cm}$ and $50 \mathrm{~cm}$ of stretched wire of a sonometer. Frequency of the fork is $\ldots \ldots \ldots . \mathrm{Hz}$.
(A) 396
(B) 196
(C) 296
(D) 693

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Numerade Educator

Problem 1502

An open pipe is in resonance in $2^{\text {nd }}$ harmonic with frequency
$\mathrm{f}_{1}$. Now one end of the tube is closed and frequency is increased to $\mathrm{f}_{2}$, such that the resonance again occurs in the nth harmonic. Choose the correct option.
(A) $n=3, f_{3}=(3 / 4) f$
(B) $n=3, f_{2}=(5 / 4) f_{1}$
(C) $\mathrm{n}=5, \mathrm{f}_{2}=(5 / 4) \mathrm{f}$
(D) $\mathrm{n}=5, \mathrm{f}_{2}=(3 / 4) \mathrm{f}_{1}$

Akshaya Rs

Numerade Educator

Problem 1503

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
Statement $-1:$ Two waves moving in a uniform string having uniform tension cannot have different velocities. Statement $-2:$ Elastic and inertial properties of string are same for all waves in same string. Moreover speed of wave in a string depends on its elastic and inertial properties only.
(A) a
(B) $b$
(C) $c$
(D) $\mathrm{d}$

Akshaya Rs

Numerade Educator

Problem 1504

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement
$-2$ is not the correct explanation of statement $-1$
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
Statement $-1:$ When a sound source moves towards observer, then frequency of sound increases. Statement $-2:$ Wavelength of sound in a medium moving towards the observer decreases.
(A) a
(B) $\mathrm{b}$
(C) $c$
(D) $\mathrm{d}$

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Numerade Educator

Problem 1505

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement
$-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
Statement $-1:$ Newton's equation for speed of sound was found wrong because he assumed the process to be isothermal. Statement $-2:$ When sound propagates, the compressions and rarefactions happen so rapidly that there is not enough time for heat to be distributed.
(A) a
(B) $b$
(C) $c$
(D) $\mathrm{d}$

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Numerade Educator

Problem 1506

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
Statement $-1:$ When pressure in a gas changes, velocity of sound in gas may change. Statement $-2:$ Velocity of sound is directly proportional to square root of pressure.
(A) a
(B) $b$
(C) $\mathrm{c}$
(D) $\mathrm{d}$

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Numerade Educator

Problem 1507

For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option.
(a) Statement $-1$ is true, statement $-2$ is true; statement $-2$ is the correct explanation of statement $-1$.
(b) Statement $-1$ is true, statement $-2$ is true but statement $-2$ is not the correct explanation of statement $-1$.
(c) Statement $-1$ is true, statement $-2$ is false
(d) Statement $-1$ is false, statement $-2$ is true
Statement $-1:$ If wave enters from one medium to another medium then sum of amplitudes of reflected wave and transmitted wave is equal to the amplitude of incident wave. Statement $-2:$ If wave enters from one medium to another medium some part of energy is transmitted and rest of the energy is reflected back.
(A) a
(B) $\mathrm{b}$
(C) c
(D) $\mathrm{d}$

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Numerade Educator

Problem 1508

A string $25 \mathrm{~cm}$ long and having a mass of $2.5 \mathrm{~g}$ is under tension. A pipe closed at one end is $40 \mathrm{~cm}$ long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second is heard. It is observed that decreasing the tension in the string decreases the beat frequency. The speed of sound in air is $320 \mathrm{~ms}^{-1}$
The frequency of the fundamental mode of the closed pipe is $\ldots \ldots \ldots . h z$
(A) 100
(B) 200
(C) 300
(D) 400

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Numerade Educator

Problem 1509

A string $25 \mathrm{~cm}$ long and having a mass of $2.5 \mathrm{~g}$ is under tension. A pipe closed at one end is $40 \mathrm{~cm}$ long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second is heard. It is observed that decreasing the tension in the string decreases the beat frequency. The speed of sound in air is $320 \mathrm{~ms}^{-1}$
The frequency of the string vibrating in its $1^{\text {st }}$ overtone is $\ldots \ldots \ldots . \mathrm{Hz}$
(A) 92
(B) 108
(C) 192
(D) 208 .

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Numerade Educator

Problem 1510

A string $25 \mathrm{~cm}$ long and having a mass of $2.5 \mathrm{~g}$ is under tension. A pipe closed at one end is $40 \mathrm{~cm}$ long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second is heard. It is observed that decreasing the tension in the string decreases the beat frequency. The speed of sound in air is $320 \mathrm{~ms}^{-1}$
The tension in the string is very nearly equal to $\ldots \ldots \ldots$
(A) $25 \mathrm{~N}$
(B) $27 \mathrm{~N}$
(C) $28 \mathrm{~N}$
(D) $30 \mathrm{~N}$

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Numerade Educator

Problem 1511

Standing waves are produced by the superposition of two waves $y_{1}=0.05 \sin (3 \pi t-2 x)$ and $y_{2}=0.05 \sin (3 \pi t+2 x)$
where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ is in seconds.
The speed (in $\mathrm{ms}-1$ ) of each wave is $\ldots \ldots$
(A) $1.5$
(B) $3.0$
(C) $3 \pi / 2$
(D) $3 \pi$

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Numerade Educator

Problem 1512

Standing waves are produced by the superposition of two waves $y_{1}=0.05 \sin (3 \pi t-2 x)$ and $y_{2}=0.05 \sin (3 \pi t+2 x)$
where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ is in seconds.
The distance (in meters) between two consecutive nodes is
(A) $\pi / 2$
(B) $\pi$
(C) $0.5$
(D) $1.0$

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Numerade Educator

Problem 1513

Standing waves are produced by the superposition of two waves $\mathrm{y}_{1}=0.05 \sin (3 \pi \mathrm{t}-2 \mathrm{x})$ and $\mathrm{y}_{2}=0.05 \sin (3 \pi \mathrm{t}+2 \mathrm{x})$
where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ is in seconds.
The amplitude of a particle at $\mathrm{x}=0.5 \mathrm{~m}$ is $\ldots \ldots$
(A) $1.08 \times 10^{-1} \mathrm{~m}$
(B) $5.4 \times 10^{-2} \mathrm{~m}$
(C) $(\pi / 2) \times 10^{-1} \mathrm{~m}$
(D) $\pi \times 10^{-1} \mathrm{~m}$

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Numerade Educator

Problem 1514

Standing waves are produced by the superposition of two waves $y_{1}=0.05 \sin (3 \pi t-2 x)$ and $y_{2}=0.05 \sin (3 \pi t+2 x)$
where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ is in seconds.

The velocity (in $\mathrm{ms}^{-1}$ ) of a particle at $\mathrm{x}=0.25 \mathrm{~m}$ at $\mathrm{t}=0.5 \mathrm{~s}$ is $\ldots \ldots$
(A) $0.1 \pi$
(B) $0.3 \pi$
(C) zero
(D) $0.3$

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Numerade Educator

Problem 1515

When two sound waves travel in the same direction in a medium, the displacement of a particle located at $\mathrm{x}$ at time $\mathrm{t}$ is given by $\mathrm{y}_{1}=0.05 \cos (0.50 \mathrm{px}-100 \mathrm{pt}) \&$
$\mathrm{y}_{2}=0.05 \cos (0.46 \mathrm{px}-92 \mathrm{pt})$, where $\mathrm{y}_{1}, \mathrm{y}_{2}$ and $\mathrm{x}$ are in meter
and $t$ is in seconds.
What is the speed of sound in the medium ?
(A) $332 \mathrm{~m} / \mathrm{s}$
(B) $100 \mathrm{~m} / \mathrm{s}$
(C) $92 \mathrm{~m} / \mathrm{s}$
(D) $200 \mathrm{~m} / \mathrm{s}$

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Numerade Educator

Problem 1516

When two sound waves travel in the same direction in a medium, the displacement of a particle located at $\mathrm{x}$ at time $\mathrm{t}$ is given by $\mathrm{y}_{1}=0.05 \cos (0.50 \mathrm{p} \mathrm{x}-100 \mathrm{pt}) \&$
$y_{2}=0.05 \cos (0.46 p x-92 p t)$, where $y_{1}, y_{2}$ and $x$ are in meter and $t$ is in seconds.
How many times per second does an observer hear the sound of maximum intensity ?
(A) 4
(B) 8
(C) 12
(D) 16

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Numerade Educator

Problem 1517

When two sound waves travel in the same direction in a medium, the displacement of a particle located at $\mathrm{x}$ at time $\mathrm{t}$ is given by $\mathrm{y}_{1}=0.05 \cos (0.50 \mathrm{px}-100 \mathrm{pt}) \&$
$\mathrm{y}_{2}=0.05 \cos (0.46 \mathrm{px}-92 \mathrm{pt})$, where $\mathrm{y}_{1}, \mathrm{y}_{2}$ and $\mathrm{x}$ are in meter
and $\mathrm{t}$ is in seconds.
At $\mathrm{x}=0$, how many times between $\mathrm{t}=0$ and $\mathrm{t}=1 \mathrm{~s}$ does the resultant displacement become zero ?
(A) 46
(B) 50
(C) 92
(D) 100

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Numerade Educator

Problem 1518

The equation $\mathrm{y}=10 \sin (\pi \mathrm{x} / 4) \cos 10 \pi t$ represents a
stationary wave where $\mathrm{x}$ and $\mathrm{y}$ are in centimeter and $\mathrm{t}$ is in seconds.
The amplitude of each component wave is $\ldots \ldots .$
(A) $5 \mathrm{~cm}$
(B) $10 \mathrm{~cm}$
(C) $20 \mathrm{~cm}$
(D) between $5 \mathrm{~cm}$ and $10 \mathrm{~cm} .$

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Problem 1519

The equation $\mathrm{y}=10 \sin (\pi \mathrm{x} / 4) \cos 10 \pi t$ represents a
stationary wave where $\mathrm{x}$ and $\mathrm{y}$ are in centimeter and $\mathrm{t}$ is in seconds. The separation between two consecutive nodes is
(A) $2 \mathrm{~cm}$
(B) $4 \mathrm{~cm}$
(C) $5 \mathrm{~cm}$
(D) $8 \mathrm{~cm}$
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