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Let y=1/(1+x^(2)) at t=0 s be the amplit...

Let `y=1/(1+x^(2))` at t=0 s be the amplitude of the wave propogating in the positive x-direction. At t=2 s, the amplitude of the wave propogating becomes `y=1/(1+(x-2)^(2))`. Assume that the shape of the wave does not change during propogation. The velocity of the wave is

A

`0.5 ms^(-1)`

B

`1.0 ms^(-1)`

C

`1.5 ms^(-1)`

D

`2.0 ms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
`1.0 ms^(-1)`
The general expression y in terms of x
`y = (1)/(1 + (x - vt)^(2))`
The shape of the wave does not change: also wave move in 2 sec, 2m in positive .x. direction. So, wave moves 2m in 2 sec.
`therefore` The velocity of the wave = `("displacement")/("time") = (2)/(2) : v = 1 ms^(-1)`
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