JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Waves & Sound

A travelling wave must contain position and time only in the combination $x\pm vt$, so that a given value of the disturbance moves bodily along the medium. Writing

shows exactly this form, the profile advancing along $+x$ at $\frac{2}{15}\mathrm{m}{\mathrm{s}}^{-1}$. The product of a function of $x$ with a function of $t$ has nodes fixed in space and describes a stationary wave, and the remaining expressions cannot be written as functions of $x\pm vt$ at all. The travelling wave is $y=A\sin (15x-2t)$.