A plane sound wave is travelling in a medium. In reference to a frame A, its equation is $y = a c o s (ω t - k x)$ . 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

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Solution

The correct option is C
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

$y = a c o s [ω t - k (v t + x_{0})] y = a c o s [(ω - k v) t - x_{0})]$

Hence, option (c) is correct.

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