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28 December, 21:25

A car's horn has a frequency of 1000 Hz. An observer hears the

horn at a pitch of 1.10 kHz. If the speed of sound in air is 345

m/s, the speed that the car was travelling, relative to the

observer, is ___ m/s.

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Answers (1)
  1. 28 December, 23:11
    0
    31.4 m/s

    Explanation:

    The Doppler equation describes how sound frequency depends on relative velocities:

    fr = fs (c + vr) / (c + vs),

    where fr is the frequency heard by the receiver,

    fs is the frequency emitted at the source,

    c is the speed of sound,

    vr is the velocity of the receiver,

    and vs is the velocity of the source.

    Note: vr is positive if the receiver is moving towards the source, negative if away.

    Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.

    Given:

    fs = 1000 Hz

    fr = 1100 Hz

    c = 345 m/s

    vr = 0 m/s

    Find: vs

    1100 = 1000 (345 + 0) / (345 + vs)

    vs = - 31.4

    The speed of the car is 31.4 m/s.
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