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

Options

A. `y =a cos[ omegat+kvt-kx]`
B. `y =-a cos[omegat-kvt-kx]`
C. `y=acos[omegat-kvt-kx]`
D. `y =acos[ omegat+ kv t +kx]`

Answer

c

Explanation

suppose at an instant t, the x-coordinate of a point with reference to moving frame is `x_(0)`. Since, at this moment, orgin of moving frame is at distance vt from origin of the fixed reference frame, therefore, putting this value of x in the given equation, we get
`y=a cos [omegat-k(vt+x_(0))]`
`y=a cos [omega-kv)t-x_(0)]`
Hence, option (c ) is correct.