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10 December, 13:02

Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward the first at 10 m/s, the driver at rest hears a beat frequency of 5.0 Hz.

What is the frequency the horns emit?

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  1. 10 December, 13:18
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    f = 4.85 Hz

    Explanation:

    This question is an example of the Doppler's effect

    We are given that;

    The source velocity; v_s = 10 m/s

    The apparent frequency f' = 5 Hz

    We will also need the speed of sound in air and it has a constant value of 340 m/s. Thus, v = 340 m/s

    Now, the true frequency is given by the formula;

    f = [ (v - v_s) / v]•f'

    Where;

    v is speed of sound in air

    v_s is speed of source

    f' is apparent frequency

    Thus, plugging in the relevant values, we have;

    f = [ (340 - 10) / 340]•5

    f = (330/340) •5

    f = 4.85 Hz
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