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Verify that wave function (y=(2)/(x-3t...

Verify that wave function
`(y=(2)/(x-3t)^(2)+1)`
is a solution to the linear wave equation, x and y are in centimetres.

Text Solution

Verified by Experts

By taking paritcal derivatives of this funcation `w.r.t. x` and to `t`
`(del^(2)y)/(delx^(2))=(12(x-3t)^(2)-4)/([(x-3t)^(2)+1]^(3))`, and
`(del^(2)y)/(delt^(2)) = (108(x-3t)^(2)-36)/([(x-3t)^(2)+1]^(3))`
or `(del^(2)y)/(delx^(2)) = (1)/(9)(del^(2)x)/(delt^(2))`
Comparing with linear wave equation, we see that the wave funcation is a solution to the linear wave equation if the speed at which the pulse moves is `3 cm//s`. It is apparent from wave funcation therefore it is a solution to the linear wave equation.
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