While waiting for Stan Speedy to arrive on a late passenger train, Kathy Kool no

Question

While waiting for Stan Speedy to arrive on a late passenger train, Kathy Kool notices beats occurring as a result of two trains blowing their whistles simultaneously. One train is at rest and the other is approaching her at a speed of 20.3 km/h. Assume that both whistles have the same frequency and that the speed of sound is 344 m/s. If Kathy hears beat frequency at 2.69 Hz, what is the frequency of the whistles? Answer in units of Hz. While waiting for Stan Speedy to arrive on a late passenger train, Kathy Kool notices beats occurring as a result of two trains blowing their whistles simultaneously. One train is at rest and the other is approaching her at a speed of 20.3 km/h. Assume that both whistles have the same frequency and that the speed of sound is 344 m/s. If Kathy hears beat frequency at 2.69 Hz, what is the frequency of the whistles? Answer in units of Hz.

Explanation / Answer

beat frequency f = 2.69 Hz speed of sound v = 344 m / s Actual frequency = F Apperent frequency F ' = F + f                                     = F + 2.69 speed of observer v o = 0 m / s speed of source v ' = 20.3 k m / h                              = 20.3 * ( 5/ 18 ) m / s                             = 5.63888 m / s we know from doppler effect F ' = [ v / ( v - v ') ] F                                     F + 2.69 = [ ( 344 / ( 344-5.63888) ] F                                                   = 1.016666 F                                            2.69= 0.016666 F                                                 F = 161.413 Hz

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