Two train whistles have identical frequencies of 1.75 102 Hz. When one train is

Question

Two train whistles have identical frequencies of 1.75 102 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 6.00 beats/s when the whistles operate together. What are the two possible speeds that the moving train can have? m/s moving towards the station 11.3 Incorrect: Your answer is incorrect. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s moving away from the station

Explanation / Answer

161+6= 167Hz (when approach the station)
fd=f(v+vr)/(v-vs) , (fd=167Hz,f=161Hz,vr=0, as v=343m/s)
167=161(343+0)/(343-vs)
167(343-vs)=55223
167vs= 2058
vs= 12.3233= 12.3[m/s]

161-6= 155Hz (when away from the station)
fd=f(v+vr)/(v+vs) , (fd=155Hz,f=161Hz,vr=0, as v=343m/s)
155=161(343+0)/(343+vs)
155vs+53165=55223
vs= 13.2774= 13.3[m/s]

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