Progressive Wave Equation question from NEET 1994 (AIPMT)

Answer: (a)

1. A travelling wave must be a function of $(\omega t \pm kx)$, depending on both $x$ and $t$.
2. $y = A\sin(\omega t - kx)$ is the standard progressive wave.
3. $A\sin kx$ has no time dependence and $A\sin\omega t$ has no space dependence, so they are not waves.
4. So the answer is (a) $y = A\sin(\omega t - kx)$.