A plane wave `zeta= A cos (omega t-kx)` propagates in the reference frame S. find the equation of this wave in a refreence frame S' moving in the +ve direction of x-axis with a constant velocity V relative to S.

Answer

`[A cos [omega(1-(V)/(v)) t -kx']]`

Explanation

In frame k wave equation is
`y = Acos(omegat - kx)`
In frame k' waves velocity is v- V so motion equation for a point P is
`y' = A cos [omegat - k(x' + Vt)]`
`y' = A cos [omegat - kx' -k Vt)]`
`y' = A cos[omega(1-(V)/(v)) t - kx']`