(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Satisfying wave equation

1. The problem statement, all variables and given/known data

Confirm that the following wave satisfies the wave equation and obtain an expression for the velocity of a wave

Y=Asin(2x-5t)*e^(-2t)

2. Relevant equations

the wave equation is

(d^2y/dt^2)=(V^2)*(d^2y/dx^2)

3. The attempt at a solution

I assumed that I had to differentiate Y with respect to 't' twice and the differentiate Y with respect to 'x' twice and then substitute these into the equation.

This left me with

-21Ae^(-2t)sin(2x-t)+20Ae^(-2t)cos(2x-5t)=(V^2)(-4Ae^(-2t)sin(2x-5t))

but this doesnt really prove that the wave satisfies the equation. Does it?

I can then rearrange to get V the wave velocity. Am I on the right track?

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# Homework Help: Satisfying wave equation

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