A harmonic wave is travelling in a stationary medium whose equation of this wave w.r.t. a frame which is moving along -ve x-axis with a constant speed v w.r.t. stationary medium. Also, find speed of wave in moving frame.

Explanation

Let in time `t`, wave gets displayed by `x w.r.t.` stationary medium, the displacement of wave `w.r.t.` moving frame is `x'=x+vt`.
so, equation of wave in moving frame is
`y=A sin [omegat-k(x'-vt)] [:.x=x'-vt]`
`y=A sin [(omega+kv) t-kx']`
speed of wave in moving frame
`V'=(dx')/(dt)=(omega+kv)/(k)=(omega)/(k)+v)`