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A train is moving parallel to a highway with a constant speed of 16.0 m/s. A car is traveling in the same direction as the train with a speed of 36.0 m/s. The car horn sounds at a frequency of 504 Hz, and the train whistle sounds at a frequency of 314 Hz.
(a) When the car is behind the train, what frequency does an occupant of the car observe for the train whistle?
Hz
(b) After the car passes and is in front of the train, what frequency does a train passenger observe for the car horn?
Hz

  • physics -

    when the car is behind the train, the listener in the car is approaching the sound source in the train at 36-16 = 20 m/s
    The listener will hear a higher frequency.


    when the car is ahead of the train, the listener in the train is departing from the sound source in the car at 20 m/s and will hear a lower frequency.

    In general:
    Fl = frequency listener
    Fs = frequency source
    v = sound speed assume 340 m/s

    vl is velocity of listener toward source. It is negative if in direction away from source.
    (in part a it is +)
    (in part b it is +)

    vs is velocity of source. It is negative if opposite to the direction of the listener toward the source
    (in part a it is +)
    (in part b it is +)

    Fl = Fs(v + vl)/(v + vs)
    part a
    Fcar = Ftrain whistle (340+36)/(340+16)
    Fcar = 1.056 Fwhistle

    pert b
    Ftrain passenger= Fcar (340+16)/(340+36)
    Ftrain passenger = .947 F car horn

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