Two train whistles have identical frequencies of 1.54 102 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 8.00 beats/s when the whistles operate together. What are the two possible speeds that the moving train can have? moving away from the station m/s moving towards the station m/s

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Two train whistles have identical frequencies of 154 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 8.00 beats/s when the whistles operate together. What are the two possible speeds that the moving train can have? moving away from the station m/s moving towards the station m/s

Answer:

vs=16.93 m/s when approach the station

vs=18.79 m/s when away from the station

Explanation:

154+8 = 162Hz (when approach the station)

fd=f (v+vr) / (v-vs), (fd=162Hz, f=154Hz, vr=0, as v (speed of sound) = 343m/s)

162=154 (343+0) / (343-vs)

162 (343-vs) = 52822

162vs = 2744

vs = 16.93 = 16.93 m/s

154-8 = 146Hz (when away from the station)

fd=f (v+vr) / (v+vs), (fd=146Hz, f=154Hz, vr=0, as v (speed of sound) = 343m/s)

146=154 (343+0) / (343+vs)

146vs+50078=52822

vs = 18.79 = 18.79 m/s