Solving the Wave Equation with D=A sin kx cos \omegat

[physicsnewb7]

1. Homework Statement [/b

Determine whether the function D=A sin kx cos $$\omega$$t
is a solution of the wave equation.

Homework Equations

D=Asin (kx-$$\omega$$t)

The Attempt at a Solution

sorry completely lost please help

 

[Gear300]

This is the (linear) wave equation:
http://hyperphysics.phy-astr.gsu.edu/HBASE/Waves/waveq.html
The one you're focusing on is the top one.

You'll have to find the second partial derivative of D with respect to x and of D with respect to t. The velocity is given by v = w/k. To check whether the given wave is a solution to the wave equation, you just have to plug things in and see if it works out. The linear wave equation is a general property of linear waves. I forgot what the key characteristics of linear waves were, but if the wave does follow this wave equation, then it holds these characteristics.