Essential University Physics

Richard Wolfson

Chapter 14

Wave Motion - all with Video Answers

Educators

Chapter Questions

Problem 1

What distinguishes a wave from an oscillation?

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 2

Red light has a longer wavelength than blue light. Compare their frequencies.

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 3

Consider a light wave and a sound wave with the same wavelength. Which has the higher frequency?

AS

Arka Sardar

Numerade Educator

Problem 4

If you doubled the tension in a string, what would happen to the speed of waves on the string?

AS

Arka Sardar

Numerade Educator

Problem 5

A heavy cable is hanging vertically, its bottom end free. How will the speed of transverse waves near the top and bottom of the cable compare? Why?

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 6

The intensity of light from a localized source decreases as the inverse square of the distance from the source. Does this mean that the light loses energy as it propagates?

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 7

Medical ultrasound uses frequencies around $10^{7} \mathrm{~Hz}$, far above the range of the human ear. In what sense are these waves "sound"?

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 8

If you double the pressure of a gas while keeping its density the same, what happens to the sound speed?

AS

Arka Sardar

Numerade Educator

Problem 9

If you place a perfectly clear piece of glass in perfectly clear water, you can still see the glass. Why?

AS

Arka Sardar

Numerade Educator

Problem 10

Why can a boat easily produce a shock wave on the water surface, while only a very high-speed aircraft can produce a sonic boom?

Shoukat Ali

Other Schools

Problem 11

Ocean waves with 18 -m wavelength travel at $5.3 \mathrm{~m} / \mathrm{s}$. What's the time interval between wave crests passing a boat moored at a fixed location?

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 12

Ripples in a shallow puddle propagate at $34 \mathrm{~cm} / \mathrm{s}$. If the wave frequency is $5.2 \mathrm{~Hz}$, find (a) the period and (b) the wavelength.

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 13

An 89.5-MHz FM radio wave propagates at the speed of light. What's its wavelength?

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 14

A seismograph located $1250 \mathrm{~km}$ from an earthquake detects seismic waves 5.12 min after the quake occurs. The seismograph oscillates in step with the waves, at $3.21 \mathrm{~Hz}$. Find the wavelength.

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 15

A seismograph located $1250 \mathrm{~km}$ from an earthquake detects seismic waves 5.12 min after the quake occurs. The seismograph oscillates in step with the waves, at $3.21 \mathrm{~Hz}$. Find the wavelength.

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 16

An ocean wave has period $4.1 \mathrm{~s}$ and wavelength $10.8 \mathrm{~m} .$ Find its (a) wave number and (b) angular frequency.

Manne Andergronde

Manne Andergronde

Numerade Educator

Problem 16

Ultrasound used in a medical imager has frequency $4.86 \mathrm{MHz}$ and wavelength $0.313 \mathrm{~mm}$. Find (a) the angular frequency, (b) the wave number, and (c) the wave speed.

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 17

Find the (a) amplitude, (b) wavelength, (c) period, and (d) speed of a wave whose displacement is given by $y=1.3 \cos (0.69 x+31 t),$ where $x$ and $y$ are in centimeters and $t$ in seconds. (e) In which direction is the wave propagating?

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 19

Figure 14.36 shows a simple harmonic wave at time $t=0$ and later at $t=2.6 \mathrm{~s}$. Write a mathematical description of this wave.

Shoukat Ali

Other Schools

Problem 20

Analysis of waves in shallow water (depth much less than wavelength) yields the following wave equation:
$$\frac{\partial^{2} y}{\partial x^{2}}=\frac{1}{g h} \frac{\partial^{2} y}{\partial t^{2}}$$
where $h$ is the water depth and $g$ the gravitational acceleration. Give an expression for the wave speed.

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 21

The main cables supporting New York's George Washington Bridge have a mass per unit length of $4100 \mathrm{~kg} / \mathrm{m}$ and are under 250-MN tension. At what speed would a transverse wave propagate on these cables?

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 22

A transverse wave $1.2 \mathrm{~cm}$ in amplitude propagates on a string; its frequency is $44 \mathrm{~Hz}$. The string is under 21 -N tension and has mass per unit length $15 \mathrm{~g} / \mathrm{m}$. Determine its speed.

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 23

Transverse waves propagate at $18 \mathrm{~m} / \mathrm{s}$ on a string under $14-\mathrm{N}$ tension. What will be the wave speed if the tension is increased to $40 \mathrm{~N} ?$

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 24

A rope is stretched between supports $18.3 \mathrm{~m}$ apart; its tension is $78.6 \mathrm{~N}$. If one end of the rope is tweaked, the resulting disturbance reaches the other end $585 \mathrm{~ms}$ later. Find the rope's mass.

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 25

A rope with $280 \mathrm{~g}$ of mass per meter is under $550-\mathrm{N}$ tension. Find the average power carried by a wave with frequency $3.3 \mathrm{~Hz}$

Shoukat Ali

Other Schools

Problem 26

Cell phones typically transmit with a power of $0.60 \mathrm{~W}$ when they're in urban areas with closely spaced cell towers. In rural areas, however, the power increases to $3.0 \mathrm{~W}$. By what factor does this power boost increase a phone's range $-$ that is, the distance at which the phone's signal has a given intensity?

Shoukat Ali

Other Schools

Problem 27

Find the sound speed in air under standard conditions with pressure $101 \mathrm{kN} / \mathrm{m}^{2}$ and density $1.20 \mathrm{~kg} / \mathrm{m}^{3}$.

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 28

Timers in sprint races start their watches when they see smoke from the starting gun, not when they hear the sound. Why? How much error would be introduced by timing a $100-\mathrm{m}$ race from the sound of the gun?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 29

The specific heat ratio $\gamma$ for nitrous oxide $\left(\mathrm{N}_{2} \mathrm{O}\right)$ is $1.31 .$ Find the sound speed in $\mathrm{N}_{2} \mathrm{O}$ at $1.95 \times 10^{4}-\mathrm{N} / \mathrm{m}^{2}$ pressure and $0.352-\mathrm{kg} / \mathrm{m}^{3}$
density.

Shoukat Ali

Other Schools

Problem 30

A gas with density $1.0 \mathrm{~kg} / \mathrm{m}^{3}$ and pressure $81 \mathrm{kN} / \mathrm{m}^{2}$ has sound speed $368 \mathrm{~m} / \mathrm{s}$. Are the gas molecules monatomic or diatomic?

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 31

Divers in an underwater habitat breathe a special mixture of oxygen and neon to prevent the possibly fatal effects of nitrogen in ordinary air. With pressure $6.2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ and density $4.5 \mathrm{~kg} / \mathrm{m}^{3},$ the effective $\gamma$ value for the mixture is $1.61 .$ Find the frequency in this mixture for a $50-\mathrm{cm}$ -wavelength sound wave, and compare with its frequency in air under normal conditions.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 32

You're flying in a twin-engine turboprop aircraft, with its two propellers turning at 985 and 993 rpm, respectively. How often to you hear a peak in the engine sound?

Vishal Gupta

Numerade Educator

Problem 33

What's the wavelength of the ocean waves in Example 14.5 if the calm water you encounter at $33 \mathrm{~m}$ is the second calm region on your voyage from the center line?

Shoukat Ali

Other Schools

Problem 34

A 2.0 -m-long string is clamped at both ends. (a) Find the longest-wavelength standing wave possible on this string. (b) If the wave speed is $56 \mathrm{~m} / \mathrm{s},$ what's the lowest standing-wave frequency?

Shoukat Ali

Other Schools

Problem 35

When a stretched string is clamped at both ends, its fundamental frequency is $140 \mathrm{~Hz}$. (a) What's the next higher frequency? If the same string, with the same tension, is now clamped at one end and free at the other, what are (b) the fundamental and (c) the next higher frequency?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 36

A string is clamped at both ends and tensioned until its fundamental frequency is $85 \mathrm{~Hz}$. If the string is then held rigidly at its midpoint, what's the lowest frequency at which it will vibrate?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 37

A crude model of the human vocal tract treats it as a pipe closed at one end. Find the effective length of a vocal tract whose fundamental tone is $620 \mathrm{~Hz}$. Take $V_{\text {sound }}=354 \mathrm{~m} / \mathrm{s}$ at body temperature.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 38

A car horn emits $380-\mathrm{Hz}$ sound. If the car moves at $17 \mathrm{~m} / \mathrm{s}$ with its horn blasting, what frequency will a person standing in front of the car hear?

Ajay Singhal

Numerade Educator

Problem 39

A fire station's siren is blaring at $85 \mathrm{~Hz}$. What's the frequency perceived by a firefighter racing toward the station at $120 \mathrm{~km} / \mathrm{h} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 40

A fire truck's siren at rest wails at $1400 \mathrm{~Hz}$; standing by the roadside as the truck approaches, you hear it at $1600 \mathrm{~Hz}$. How fast is the truck going?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 41

Red light emitted by hydrogen atoms at rest in the laboratory has wavelength $656 \mathrm{nm} .$ Light emitted in the same process on a distant galaxy is received at Earth with wavelength $708 \mathrm{nm}$. Describe the galaxy's motion relative to Earth.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 42

A surfer paddles out beyond the breaking surf towhere waves are sinusoidal in shape, with crests $59.6 \mathrm{~m}$ apart. The surfer bobs a vertical distance of $4.28 \mathrm{~m},$ taking $3.09 \mathrm{~s}$ to $\mathrm{go}$ from trough to crest. (a) Find the wave speed and
(b) describe the wave using Equation 14.3 .

Shoukat Ali

Other Schools

Problem 43

A surfer just misses catching a big wave. If the wavelength is $78.2 \mathrm{~m},$ and if she stays in the same place, how long will she have to wait for the next wave? Hint: You'll find Equation 14.11 useful.

Shoukat Ali

Other Schools

Problem 44

A Mars rover includes an experiment designed to explore Mars' atmosphere using sound waves. The experiment generates sound waves of a known frequency and measures their wavelength. For a frequency of $482 \mathrm{~Hz}$, the measured wavelength is $50.6 \mathrm{~cm} .$ Find the sound speed on Mars.

Shoukat Ali

Other Schools

Problem 45

The speed of sound in water is $1480 \mathrm{~m} / \mathrm{s}$. (a) Find the wavelength of sound waves emitted by a blue whale vocalizing at a frequency of $14.5 \mathrm{~Hz}$. (b) How does this compare with the wavelength in air of sound with the same frequency, assuming a sound speed of $343 \mathrm{~m} / \mathrm{s} ?$

Shoukat Ali

Other Schools

Problem 46

A car speeds down the highway with its stereo blasting. An observer with perfect pitch is standing by the roadside and, as the car approaches, notices that a musical note that should be $\mathrm{B}$ at a frequency of $494 \mathrm{~Hz}$ sounds like $\mathrm{D}$ at $523 \mathrm{~Hz}$ Find the car's speed, assuming a sound speed of $343 \mathrm{~m} / \mathrm{s}$.

Shoukat Ali

Other Schools

Problem 47

The speed limit on a highway is $95.0 \mathrm{~km} / \mathrm{h}$. A car whose horn emits 352 -Hz sound is approaching you. What frequency will you hear if the car is going at the speed limit, assuming a sound speed of $343 \mathrm{~m} / \mathrm{s} ?$

Shoukat Ali

Other Schools

Problem 48

The Sun undergoes oscillations with periods on the order of 5 min and amplitudes, measured as variations in the height of the solar surface, of a few $\mathrm{m}$. The corresponding velocity of the solar surface is on the order of $10 \mathrm{~cm} / \mathrm{s},$ and this can be measured by carefully observing the Doppler effect on light emitted at the solar surface. One space-based instrument observes light from singly ionized nickel atoms, emitted with a wavelength of $676.8 \mathrm{nm}$. If the instrument observes this light Doppler shifted by $3.52 \times 10^{-7} \mathrm{nm},$ what is the velocity at the Sun's surface?

Shoukat Ali

Other Schools

Problem 49

A star is orbiting the galactic center, and at a point in its orbit when it's heading in the direction toward Earth, it's moving at $64.8 \mathrm{~km} / \mathrm{s}$. An astronomer observes a spectral line emitted by hydrogen atoms in the star's atmosphere; the wavelength relative to the emitting atoms is $656.28 \mathrm{nm} .$ By how much will the astronomer observe this wavelength to be shifted?

Shoukat Ali

Other Schools

Problem 50

A uniform cable hangs vertically under its own weight. Show that the speed of waves on the cable is given by $v=\sqrt{y g},$ where $y$ is the distance from the bottom of the cable.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 51

Find the maximum speed for transmission of waves on a rope with $\mu=68.4 \mathrm{~g} / \mathrm{m}$ if the rope's breaking tension is $415 \mathrm{~N}$.

Shoukat Ali

Other Schools

Problem 52

A loudspeaker emits energy at the rate of $50 \mathrm{~W}$, spread in all directions. Find the intensity of sound $18 \mathrm{~m}$ from the speaker.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 53

Light intensity $3.3 \mathrm{~m}$ from a lamp is $0.73 \mathrm{~W} / \mathrm{m}^{2}$. Find the lamp's power output, assuming it radiates equally in all directions.

Shoukat Ali

Other Schools

Problem 54

An experiment based at New Mexico's Apache Point observatory uses a laser beam to measure the distance to the Moon with milli-
meter precision. The laser power is $120 \mathrm{GW}$, although it's pulsed on for only $90 \mathrm{ps}$. The beam emerges from the laser with a diameter of $7.0 \mathrm{~mm}$. It's then beamed into a telescope aimed at the Moon. When the beam leaves the telescope, it has the telescope's full 3.5 -m diameter. By the time it reaches the Moon, the beam has expanded to a diameter of $6.5 \mathrm{~km} .$ Find the intensity of the beam (a) as it leaves the laser, (b) as it leaves the telescope, and (c) as it reaches the Moon. Do any of these intensities exceed that of bright sunlight on Earth (about $\left.1000 \mathrm{~W} / \mathrm{m}^{2}\right) ?$

Shoukat Ali

Other Schools

Problem 55

Two waves have the same angular frequency $\omega,$ wave number $k$ and amplitude $A,$ but they differ in phase: $y_{1}=A \cos (k x-\omega t)$ and $y_{2}=A \cos (k x-\omega t+\phi) .$ Show that their superposition is also a simple harmonic wave, and determine its amplitude as a function of the phase difference $\phi$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 56

A wire is under 32.8 - $\mathrm{N}$ tension, carrying a wave described by $y=1.75 \sin (0.211 x-466 t),$ where $x$ and $y$ are in centimeters and $t$ is in seconds. What are (a) the wave amplitude, (b) the wavelength, (c) the wave period, (d) the wave speed, and
(e) the power carried by the wave?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 57

A spring of mass $m$ and spring constant $k$ has an unstretched length $L_{0} .$ Find an expression for the speed of transverse waves on this spring when it's been stretched to a length $L$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 58

When a 340 -g spring is stretched to a total length of $40 \mathrm{~cm},$ it supports transverse waves propagating at $4.5 \mathrm{~m} / \mathrm{s}$. When it's stretched to $60 \mathrm{~cm},$ the waves propagate at $12 \mathrm{~m} / \mathrm{s} .$ Find (a) the spring's unstretched length and (b) its spring constant.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 59

At a point $15 \mathrm{~m}$ from a source of spherical sound waves, you measure the intensity $750 \mathrm{~mW} / \mathrm{m}^{2}$. How far do you need to walk, directly away from the source, until the intensity is $270 \mathrm{~mW} / \mathrm{m}^{2} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 60

Figure 14.37 shows two observers $20 \mathrm{~m}$ apart on a line that connects them to a spherical light source. If the observer nearer the source measures a light intensity $50 \%$ greater than the other observer, how far is the nearer observer from the source?

Shoukat Ali

Other Schools

Problem 61

An ideal spring is stretched to a total length $L_{1} .$ When that length is doubled, the speed of transverse waves on the spring triples. Find an expression for the unstretched length of the spring.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 62

Show that the time it takes a wave to propagate up the cable in Problem 50 is $t=2 \sqrt{L / g},$ where $L$ is the cable length.

Shoukat Ali

Other Schools

Problem 63

You see an airplane $5.2 \mathrm{~km}$ straight overhead. Sound from the plane, however, seems to be coming from a point back along the plane's path at $35^{\circ}$ to the vertical. What's the plane's speed, assuming an average sound speed of $330 \mathrm{~ms} ?$

Vipender Yadav

Numerade Educator

Problem 64

What are the intensities in $\mathrm{W} / \mathrm{m}^{2}$ of sound with intensity levels of (a) $65 \mathrm{~dB}$ and $(\mathrm{b})-5 \mathrm{~dB}$ ?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 65

Show that a doubling of sound intensity corresponds to approximately a 3 -dB increase in the decibel level.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 66

Sound intensity from a localized source decreases as the inverse square of the distance, according to Equation $14.8 .$ If the distance from the source doubles, what happens to (a) the intensity and (b) the decibel level?

Villiam Zelinsky

Villiam Zelinsky

Numerade Educator

Problem 67

At $2.0 \mathrm{~m}$ from a localized sound source you measure the intensity level as $75 \mathrm{~dB}$. How far away must you be for the perceived loudness to drop in half (i.e., to an intensity level of $65 \mathrm{~dB}$ )?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 68

The A-string $(440 \mathrm{~Hz})$ on a piano is $38.9 \mathrm{~cm}$ long and is clamped at both ends. If the string tension is $667 \mathrm{~N},$ what's its mass?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 69

Show that the standing-wave condition of Equation 14.13 is equivalent to the requirement that the time it takes a wave to make a round trip from one end of the medium to the other and back be an integer multiple of the wave period.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 70

You're designing an organ for a new concert hall; the lowest note is to be $22 \mathrm{~Hz}$. The architects have asked you to minimize the lengths of the organ pipes. How long will the longest pipe be if it's
(a) closed at one end and
(b) open at both ends?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 71

Show by differentiation and substitution that a wave described by Equation 14.3 satisfies the wave equation (Equation 14.5 ), with wave speed $v=\omega / k$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 72

Show by differentiation and substitution that $a n y$ function of the form $y=f(x \pm v t)$ satisfies the wave equation (Equation 14.5 ).

Shoukat Ali

Other Schools

Problem 73

You're a marine biologist concerned with the effect of sonic booms on plankton, and you need to estimate the altitude of a supersonic aircraft flying directly over you at 2.2 times the speed of sound. You hear its sonic boom $19 \mathrm{~s}$ later. Assuming a constant $340 \mathrm{~m} / \mathrm{s}$ sound speed, find the plane's altitude.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 74

A $2.25-\mathrm{m}$ -long pipe has one end open. Among its possible standing-wave frequencies is $345 \mathrm{~Hz}$; the next higher frequency is $483 \mathrm{~Hz}$. Find (a) the fundamental frequency and (b) the sound speed.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 75

Gravitational waves were first detected in 2015 , using the LIGO detectors at Livingston, Louisiana, and Hanford, Washington. The gravitational waves, propagating as plane waves, reached the Livingston detector $7.0 \mathrm{~ms}$ before they reached Hanford. (a) Did the waves come from the southern or northern hemisphere of the sky? (b) Estimate the straight-line distance between Livingston and Hanford and, using the fact that gravitational waves propagate at the speed of light, find the approximate angle between the direction of the waves' propagation and the Livingston-Hanford line. Knowing this angle helped LIGO scientists to determine an approximate location of the source.

Shoukat Ali

Other Schools

Problem 76

Obstetricians use ultrasound to monitor fetal heartbeat. If $5.0-\mathrm{MHz}$ ultrasound reflects off the moving heart wall with a $100-\mathrm{Hz}$ frequency shift, what's the speed of the heart wall? (Hint: You have two shifts to consider.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 77

You're in court, trying to argue your way out of a speeding ticket. You were stopped going $120 \mathrm{~km} / \mathrm{h}$ in a $90-\mathrm{km} / \mathrm{h}$ zone. A technical expert testifies that the 70 -GHz police radar signal underwent a $15.6-\mathrm{kHz}$ frequency shift when it reflected off your car. You claim that corresponds to an impossible $240 \mathrm{~km} / \mathrm{h},$ so the radar must be defective. How should the judge rule?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 78

You move at speed $u$ toward a wave source that's stationary with respect to the medium in which waves of wavelength $\lambda$ propagate with speed $v$. Your speed relative to the wave crests is therefore $v+u .$ Show that for you, the time between wave crests is $T^{\prime}=\lambda /(v+u),$ and from this show that you perceive a frequency given by Equation $14.16,$ with the $+$ sign.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 79

You're a meteorologist specifying a new Doppler radar system that determines the velocity of distant raindrops by reflecting radar signals (which travel at the speed of light) off them and measuring the Doppler shift. You need a system that will measure speeds as low as $2.5 \mathrm{~km} / \mathrm{h} .$ A vendor offers a $5.0-\mathrm{GHz}$ radar that can detect a frequency shift of only $50 \mathrm{~Hz}$. Is that sufficient?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 80

Use a computer to form the sum implied in the caption of Figure $14.17,$ taking $\omega=1 \mathrm{~s}^{-1}$ and using (a) the three terms shown and (b) 10 terms (note that only odd harmonics appear in the sum). Plot your result over one cycle $(t$ from 0 to $2 \pi)$ and compare with the square wave shown in the figure.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 81

Two loudspeakers are mounted $2.85 \mathrm{~m}$ apart, pointing in the same direction and producing identical sound waves of a fixed frequency. You're standing $10.0 \mathrm{~m}$ from the speakers, on the perpendicular bisector of the line between them. You move in direction parallel to the line between the speakers and find that the sound intensity diminishes, reaching a minimum when you've moved $2.44 \mathrm{~m}$. If the sound speed is $343 \mathrm{~m} / \mathrm{s},$ what is the frequency of the sound waves?

Shoukat Ali

Other Schools

Problem 82

An airport neighborhood is concerned about the basing of the new F-35 jet fighter. They've got the following data for the sound intensity level measured at different distances from the plane as it takes off. They'd like to know the total sound power emitted by the plane. As a physics student, you're called to help. First, convert the sound intensity levels to actual intensity. Then find a quantity which, when you plot intensity against it, should give a straight line. Make your plot, determine the best-fit line, and use its slope to report the total sound power.
$$
\begin{array}{|l|l|l|l|l|l|l|}
\hline \text { Distance }(\mathrm{m}) & 1000 & 1200 & 1500 & 2000 & 3000 & 4000 \\
\hline \begin{array}{l}
\text { Sound intensity } \\
\text { level (dB) }
\end{array} & 80.7 & 79.4 & 76.9 & 74.2 & 71.6 & 68.8 \\
\hline
\end{array}
$$

Shoukat Ali

Other Schools

Problem 83

As a tsunami approaches shore, it
a. speeds up.
b. slows down.
c. maintains its speed.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 84

For a tsunami to behave as a shallow-water wave, its wavelength
a. must be comparable to or longer than the ocean depth.
b. must be shorter than the ocean depth.
c. can have any value.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 85

A tsunami is traveling at $450 \mathrm{~km} / \mathrm{h}$ when the ocean depth abruptly doubles. Its new speed is roughly
a. $225 \mathrm{~km} / \mathrm{h}$
b. $320 \mathrm{~km} / \mathrm{h}$
c. $640 \mathrm{~km} / \mathrm{h}$
d. $900 \mathrm{~km} / \mathrm{h}$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 86

On the open ocean, a tsunami has relatively small amplitudetypically $1 \mathrm{~m}$ or less. As the tsunami approaches shore, its amplitude increases and its wavelength decreases. As a result,
a. its total energy increases.
b. the rate at which it carries energy shoreward increases.
c. the wave frequency increases.
d. none of these quantities changes.

Shoukat Ali

Other Schools