Question

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

• A. $y=acos\left[\right(\omega +kv)t–kx]$
• B. $y=-acos\left[\right(\omega -kv)t-kx]$
• C. $y=acos\left[\right(\omega -kv)t-kx]$
• D. $y=acos\left[\right(\omega t+kv)t+kx]$

Answer 1

The correct option is C $y=acos\left[\right(\omega -kv)t-kx]$

Suppose at an instant t, the x – coordinate of a point with reference to moving frame is $x_0$. Since, at this moment, origin 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

$y=acos[\omega t-k(vt+x_0\left)\right]y=acos\left[\right(\omega -kv)t-x_0)]$

Hence, option (c) is correct.