A stationary source emits 500 Hz. An observer moves at 34 m/s, and the observer's velocity makes an angle 60° with the line from the observer towards the source. The velocity component along the line is towards the source. The speed of sound is 340 m/s. If the apparent frequency is N Hz, find N.
Physics · Wave Motion · doppler effect
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Question

A stationary source emits 500 Hz. An observer moves at 34 m/s, and the observer's velocity makes an angle 60° with the line from the observer towards the source. The velocity component along the line is towards the source. The speed of sound is 340 m/s. If the apparent frequency is N Hz, find N.

Physics · Wave Motion · doppler effect

G1 Physics · Accepted Answer

The radial component of observer velocity towards the source is uᵣ = 34cos60° = 17 m/s. For a moving observer approaching a stationary source, f' = f×(v+uᵣ)/v. Thus, f' = 500×(340+17)/340 = 500×357/340. Since 357/340 = 1.05, f' = 525 Hz. Hence, N = 525.