Amplitude of a wave disturbance propagating in positive X- direction is given by y = 1/(1 + x^2) at

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14.Waves and Sound

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The amplitude of a wave disturbance propagating in the positive $X-$ direction is given by $y = 1/(1 + x^2)$ at time $t = 0$ and by $y = 1/[1 + (x -1)^2]$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ..... $ms^{-1}$

A

$1$

B

$0.5$

C

$1.5$

D

$2$

Solution

Writing the general expression for $y$ in terms of $\mathrm{x}$ as

$y=\frac{1}{1+(x-v t)^{2}}$

at $t=0: \quad y=\frac{1}{1+x^{2}}$

at $t=2$ $s \,:$ $\quad y=\frac{1}{1+(x-2 v)^{2}}$

Comparing with the given equation we get,

$2 v=1$ Or $v=0.5 \mathrm{\,m} / \mathrm{s}$

Standard 11

Physics

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