Two ships in a heavy fog are blowing their horns, both of which produce sound wi

Question

Two ships in a heavy fog are blowing their horns, both of which produce sound with a frequency of 160.0 Hz (see the figure (Figure 1)). One ship is at rest; the other moves on a straight line that passes through the one at rest.() If people on the stationary ship hear a beat frequency of 3.5 Hz, what is the speed of the approaching ship? Express your answer using two significant figures. If people on the stationary ship hear a beat frequency of 3.5 Hz, what is the speed of the receding ship? Express your answer using two significant figures.

Explanation / Answer

f = 160.0 Hz
f' = 160.0 + 3.5 Hz = 163.5 Hz
v = 343 m/s

(a)
f' = f * (v +/- vo) / (v -/+ vs )
163.5 = 160 * ( 343 + 0) / ( 343 - vs)
vs = 7.34 m/s

(b)
f' = f * (v +/- vo) / (v -/+ vs )
157.5 = 160 * ( 343 + 0) / ( 343 + vs)
vs = 5.44 m/s

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