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The amplitude of a wave disturbance prop...

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`, `x and y` are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ............... m//s`.

A

`1ms^(-1)`

B

`0.5ms^(-1)`

C

`1.5ms^(-1)`

D

`2ms^(-1)`

Text Solution

Verified by Experts

Writing the general expression for `y` in terms of `x` as
`y=(1)/(1+(x-vt)^(2))`. At `t=0`, `y=1//(1+x^(2))`. At `t=2s`, `y=(1)/(1+[x-v(2)]^(2))`
Comparing with the given equation we get `2v=1` and `v=0.5m//s`.
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