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13 August, 03:53

While sitting in your car by the side of a country road, you see your friend, who happens to have an identical car with an identical horn, approaching you. You blow your horn, which has a frequency of 260 Hz; your friend begins to blow his horn as well, and you hear a beat frequency of 5.0 Hz. Part A How fast is your friend approaching you

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  1. 13 August, 04:00
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    -6.49 m/s

    Explanation:

    This is doppler effect.

    The equation is;

    F_l = [ (v + v_l) / (v + v_s) ]F_s

    Where;

    F_l is frequency observed by the listener

    v is speed of sound

    v_l is speed of listener

    v_s is speed of source of the sound

    F_s is frequency of the source of the sound

    In this question, the source of the sound is the moving vehicle.

    Thus;

    F_l = F_beat + F_s

    We are given beat frequency (f_beat) as 5 Hz while source frequency (F_s) as 260 Hz.

    So,

    F_l = 5 + 260

    F_l = 265 Hz

    Since listener is sitting by car, thus; v_l = 0 m/s

    Thus, from our doppler effect equation, let's make v_s the subject;

    v_s = F_s[ (v + v_l) / F_l] - v

    Speed of sound has a value of v = 344 m/s

    Thus;

    v_s = 260[ (344 + 0) / 265] - 344

    v_s = - 6.49 m/s

    This value is negative because the source is moving towards the listener
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