Question

Prove that the equation `y = a sin omegat` does not satisfy the wave equation and hence it does not represent a wave.

Answer 1

`(del^(2)y)/(delt^(2)) = -omega^(2) a sin omegat`
and `(del^(2)y)/(delx^(2)) = 0`
Since, `(del^(2)y)/(delt^(2)) != (del^(2)y)/(delx^(2))` (constant)
Hence, the given equation does not represent a wave equation.