A stationary observer hears a moving source at 360 Hz while it approaches and at 300 Hz after it has passed and is receding. The speed of sound is 330 m/s. If the source speed is N m/s, find N.
Physics · Wave Motion · doppler effect
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Question

A stationary observer hears a moving source at 360 Hz while it approaches and at 300 Hz after it has passed and is receding. The speed of sound is 330 m/s. If the source speed is N m/s, find N.

G1 Physics · Accepted Answer

For a stationary observer, fₐ = f×v/(v−u), fᵣ = f×v/(v+u). Take the ratio: 360/300 = (v+u)/(v−u). Thus, 6/5 = (330+u)/(330−u). Cross-multiply: 6(330−u) = 5(330+u). 1980−6u = 1650+5u. 330 = 11u. Therefore, u = 30 m/s. Hence, N = 30.