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19 August, 17:06

The equation for the Doppler shift of a sound wave of speed v, reaching a moving detector, is where vd is the speed of the detector; vs is the speed of the source; f is the frequency of the source; f' is the frequency at the detector. If the detector moves toward the source, vd is positive; if the source moves toward the detector, vs if positive. A train moving toward a detector at 35 m/s blows a 303-Hz horn. What frequency is detected by a (a) stationary train

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  1. 19 August, 18:40
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    Given Information:

    Speed of train = vs = 35 m/s

    Frequency of horn = fs = 303 Hz

    Speed of sound = v = 340 m/s

    Required Information:

    Frequency detected = fd = ?

    Answer:

    Frequency detected = fd ≈ 338 Hz

    Explanation:

    The Doppler effect is the increase or decrease in the observed frequency of a wave when the source or the observer move relative to each other.

    The equation of Doppler effect is given by

    fd = fs * (v ± vd) / (v ± vs)

    Where fs is the frequency of horn, vs is the speed of train and v is the speed of light.

    Since the source is moving towards the detector, vs will be negative and detector is stationary therefore, vd = 0

    fd = fs * (v - 0) / (v - vs)

    fd = 303 * (340/340-35)

    fd ≈ 337.77 Hz

    fd ≈ 338 Hz

    Therefore, the frequency detected by stationary detector is 338 Hz.
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