Which of the following equations represents a travelling wave?

A travelling wave is characterized by a disturbance that propagates through space. Its mathematical form is a function of $$(kx - \omega t)$$ or $$(kx + \omega t)$$, where the spatial and temporal variables appear together in a single argument, maintaining a constant phase as the wave moves.

Examining each option: $$y = A\sin(15x - 2t)$$ is of the form $$A\sin(kx - \omega t)$$ with $$k = 15$$ and $$\omega = 2$$. This represents a wave travelling in the positive x-direction with a constant amplitude $$A$$. This is a valid travelling wave equation.

The second option $$y = Ae^x\cos(\omega t - \theta)$$ has an amplitude that grows exponentially with $$x$$, which does not represent a physical travelling wave. The third option $$y = Ae^{-x^2}(vt + \theta)$$ is not a sinusoidal wave function. The fourth option $$y = A\sin x\cos\omega t$$ is a product of a function of $$x$$ alone and a function of $$t$$ alone, which represents a standing wave, not a travelling wave.

The correct answer is $$y = A\sin(15x - 2t)$$.