Among the following equations, which one describes a wave...

A traveling wave is represented by a function where the position and time variables appear together in the phase as $(kx \pm \omega t)$ or $(ky \pm \omega t)$.

Options (1) and (2) represent standing waves because the spatial and temporal variables are separated into a product of trigonometric functions.

Option (3) represents a wave propagating along the $X$-axis because the phase is $(kx - \omega t)$.

Option (4) represents a wave propagating along the $Y$-axis because the phase is $(ky - \omega t)$, with the displacement of particles occurring along the $X$-axis.