(C) The wave velocity $V$ is given by $V = f\lambda$,where $f$ is the frequency.The maximum particle velocity $v$ for a sine wave is given by $v = A\o

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$V = v$ if $A = \frac{\lambda}{2\pi}$

(C) The wave velocity $V$ is given by $V = f\lambda$,where $f$ is the frequency.The maximum particle velocity $v$ for a sine wave is given by $v = A\omega$,where $\omega = 2\pi f$ is the angular frequency.Equating the two velocities: $V = v$$f\lambda = A(2\pi f)$Dividing both sides by $f$ (assuming $f \neq 0$):$\lambda = 2\pi A$Rearranging for $A$:$A = \frac{\lambda}{2\pi}$Thus,the correct condition is $A = \frac{\lambda}{2\pi}$.

Class 11 Physics Waves and Sound Wave Equation and Characteristics of Waves

Easy

$A$ sine wave has an amplitude $A$ and wavelength $\lambda$. Let $V$ be the wave velocity and $v$ be the maximum velocity of a particle in the medium. Then:

A
$V = v$ if $\lambda = \frac{3A}{2\pi}$
B
$V = v$ if $A = 2\pi\lambda$
C
$V = v$ if $A = \frac{\lambda}{2\pi}$
D
$V$ can not be equal to $v$

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Waves and Sound

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Wave Equation and Characteristics of Waves

The equation of a wave is given by $Y = 10^{-2} \sin 2 \pi (160 t - 0.5 x + \frac{\pi}{4})$,where $x$ and $Y$ are in $m$ and $t$ is in $s$. The speed of the wave is $..... \, km \, h^{-1}$.

EasyJEE MAIN 2023

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$A$ plane wave is represented by $x = 1.2 \sin(314t + 12.56y)$,where $x$ and $y$ are distances measured in meters and $t$ is time in seconds. This wave has:

Medium

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The equation of a transverse wave travelling on a rope is given by $y = 10\sin \pi (0.01x - 2.00t)$ where $y$ and $x$ are in $cm$ and $t$ is in $seconds$. The maximum transverse speed of a particle in the rope is about .... $cm/s$.

MediumAIIMS 2000

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What is the phase difference between consecutive crest and trough?

Medium

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$A$ transverse wave is represented by the equation $y = y_0 \sin \frac{2\pi}{\lambda} (vt - x)$. For what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?

DifficultAIPMT 1998

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$A$ sine wave has an amplitude $A$ and wavelength $\lambda$. Let $V$ be the wave velocity and $v$ be the maximum velocity of a particle in the medium. Then:

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The equation of a wave is given by $Y = 10^{-2} \sin 2 \pi (160 t - 0.5 x + \frac{\pi}{4})$,where $x$ and $Y$ are in $m$ and $t$ is in $s$. The speed of the wave is $..... \, km \, h^{-1}$.

$A$ plane wave is represented by $x = 1.2 \sin(314t + 12.56y)$,where $x$ and $y$ are distances measured in meters and $t$ is time in seconds. This wave has:

The equation of a transverse wave travelling on a rope is given by $y = 10\sin \pi (0.01x - 2.00t)$ where $y$ and $x$ are in $cm$ and $t$ is in $seconds$. The maximum transverse speed of a particle in the rope is about .... $cm/s$.

What is the phase difference between consecutive crest and trough?

$A$ transverse wave is represented by the equation $y = y_0 \sin \frac{2\pi}{\lambda} (vt - x)$. For what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?

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