Question
A wave is represented by the equation $y=A \sin (10 \pi x+15 \pi t+\pi / 3)$ where $x$ is in metre and $t$ is in second. The expression represents(a) a wave travelling in the positive $x$-direction with a velocity $1.5 \mathrm{~m} / \mathrm{s}$(b) a wave travelling in the negative $x$-direction with a velocity $1.5 \mathrm{~m} / \mathrm{s}$(c) a wave travelling in the negative $x$-direction having a wavelength $0.2 \mathrm{~m}$(d) a wave travelling in the positive $x$-direction having a wavelength $0.2 \mathrm{~m}$
Step 1
We can compare this with the standard wave equation $y=A \sin (\omega t + kx + \phi)$, where $\omega$ is the angular frequency, $k$ is the wave number, and $\phi$ is the phase constant. Show more…
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A wave is represented by the equation $$ y=A \sin [10 \pi x-15 \pi t+(\pi / 3)] $$ where $x$ is in metre and $t$ is in second. The expression represents (a) a wave travelling in positive $x$-direction with velocity $1.5 \mathrm{~ms}^{-1}$ (b) a wave travelling in negative $x$-direction with velocity $1.5 \mathrm{~ms}^{-1}$ (c) a wave travelling in negative $x$-direction with wavelength $2.0 \mathrm{~m}$ (d) a wave travelling in positive $x$-direction with wavelength $0.2 \mathrm{~m}$
Waves
Round 2
A wave represented by the given equation $y=A \sin \left(10 \pi x+15 \pi t+\frac{\pi}{3}\right)$ where $x$ is in meter and $t$ is in second. The expression represents (a) A wave travelling in the positive $x$-direction with a velocity of $1.5 \mathrm{~m} / \mathrm{sec}$ (b) A wave travelling in the negative $x$-direction with a velocity of $1.5 \mathrm{~m} / \mathrm{sec}$ (c) A wave travelling in the negative $x$-direction with a wavelength of o.2 $m$ (d) A wave travelling in the positive $x$-direction with a wavelength of $0.2 \mathrm{~m}$
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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