Question

Prove that the equation y = a sin $\omega t$ does not satisfy the wave equation and hence it does not represent a wave.

Answer 1

A sinusoidal wave must be in the form of

$y=Asin(kx-wt)$

But here $kx=0$

so,

$k$ is zero which is not possible

$V=\frac{w}{k}$

Velocity will become infinite which is not possible.