A plane sound wave is travelling in a medium. In reference to a frame A, its equation is y=a cos `(omegat-kx)`. Which refrence to frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will be

Explanation

The wave equation propagating in the direction of `+vex` axis in medium `K` is give as
`xi=a cos ( omegat- kx)`
So,` xi=a cos k ( v t - x), ` where` k=(omega)/(k)` and `v` is the wave velocity
In the refrence frame `K^(')` , the wave velocity will be `(v-V)` propagating in the direction of ` + ve x` axis and `x` will be `x^(')` the sought wave equation .
`xi=a cos k [(v-V)t-x^(')]`
or, `xi=a cos [(omega-(omega)/(v)V)t-kx^(')]=a cos [omegat(1-(V)/(v))-kx^(')]`