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Prove that the equation y = a sin omegat...

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

Text Solution

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`(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.
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