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Musical instruments - beats phenomenon

  1. Jun 11, 2012 #1


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    Can anyone give me a description of the beats phenomenon associated with musical instruments (or in general, any waves with which beats are associated).
    I have looked at numerous textbooks however I feel I don't completely understand the concept still.
  2. jcsd
  3. Jun 11, 2012 #2
    Suppose you are hearing two sinusoid signals of slightly different frequencies f and f'. Say the phases are such that you are hearing the time-dependent waveform f(t) = sin(f*t)+sin(f'*t).

    Mathematically, this is the same as

    f(t) = 2 * sin(0.5*(f+f')*t) * cos(0.5*(f-f')*t)

    Since f-f' is small, the cos() will be a slowly varying function of time, while the sin() will vary quickly in time. The cos() will be heard as beats, i.e. a slowly varying amplitude of the quickly oscillating signal with frequency 0.5*(f+f') which is the average of f and f'.

    It will be very similar for real signals cantaining harmonics.
  4. Jun 11, 2012 #3


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    Just a small correction, if frequency is f, the waveform is sin(2π f t).
  5. Jun 11, 2012 #4
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