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Question

A plane sound wave is travelling in a medium. In reference to a frame A, its equation is y=a cos (ωtkx). 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[(ω+kv)tkx]

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B
y=acos[(ωkv)tkx]
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C
y=acos[(ωkv)tkx]
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D
y=acos[(ωt+kv)t+kx]
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Solution

The correct option is C y=acos[(ωkv)tkx]

Suppose at an instant t, the x – coordinate of a point with reference to moving frame is x0. 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 cos[ωtk(vt+x0)]y=a cos[(ωkv)tx0)]

Hence, option (c) is correct.


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