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

Explanation

By taking partial derivatives of this function w.r.t x and to t.
`(del^2y)/(delx^2)=(12(x-3t)^2-4)/[(x-3t)^2+1]^3, and (del^2y)/(delt^2)=(108(x-3t)^2-36)/[(x-3t)^2+1]^3`
or `(del^2y)/(delx^2)=(1del^2x)/(9delt^2)`
Comparing with linear wave equation, we see that the wave function 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 function therefore it is a solution to the linear wave equation