(B) The given wave equation is $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$.Comparing this with the standard wave equation $y = a \sin (\omega t - kx)

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(B) The given wave equation is $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$.Comparing this with the standard wave equation $y = a \sin (\omega t - kx)$,we have $\omega = \frac{\pi}{2}$ and $k = \frac{\pi}{4}$.The wave velocity $v$ is given by $v = \frac{\omega}{k} = \frac{\pi/2}{\pi/4} = 2 \ m/s$.The distance $d$ traveled by the wave in time $t = 8 \ s$ is $d = v \times t$.$d = 2 \ m/s \times 8 \ s = 16 \ m$.

Class 11 Physics Waves and Sound Progressive Waves

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The equation of a progressive wave is given by $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$,where $t$ is in seconds and $x$ is in meters. The distance through which the wave moves in $8 \ s$ is .... $(m)$

A
$8$
B
$16$
C
$2$
D
$4$

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Waves and Sound

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Progressive Waves

$A$ progressive wave is given by $Y = 12 \sin (5t - 4x)$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

MediumMHT CET 2023

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$A$ progressive wave of frequency $500 \,Hz$ is travelling with a velocity of $360 \,ms^{-1}$. The distance between two points, having a phase difference of $60^{\circ}$, is ............. (in $\,m$)

EasyAP EAMCET 2018

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$A$ wave is represented by $x = 0.4 \cos \left(8t - \frac{y}{2}\right)$ where $x$ and $y$ are in meters and $t$ is in seconds. The speed of the wave is

EasyAP EAMCET 2020

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Which of the following expressions represents a simple harmonic progressive wave?

EasyKCET 2012

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In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:
$(a)$ Amplitude
$(b)$ Wavelength
$(c)$ Frequency
$(d)$ Wave velocity
$(e)$ Particle velocity amplitude.

Medium

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The equation of a progressive wave is given by $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$,where $t$ is in seconds and $x$ is in meters. The distance through which the wave moves in $8 \ s$ is .... $(m)$

Similar Questions

$A$ progressive wave is given by $Y = 12 \sin (5t - 4x)$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

$A$ progressive wave of frequency $500 \,Hz$ is travelling with a velocity of $360 \,ms^{-1}$. The distance between two points, having a phase difference of $60^{\circ}$, is ............. (in $\,m$)

$A$ wave is represented by $x = 0.4 \cos \left(8t - \frac{y}{2}\right)$ where $x$ and $y$ are in meters and $t$ is in seconds. The speed of the wave is

Which of the following expressions represents a simple harmonic progressive wave?

In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:$(a)$ Amplitude$(b)$ Wavelength$(c)$ Frequency$(d)$ Wave velocity$(e)$ Particle velocity amplitude.

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In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:
$(a)$ Amplitude
$(b)$ Wavelength
$(c)$ Frequency
$(d)$ Wave velocity
$(e)$ Particle velocity amplitude.