1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Musical instruments - beats phenomenon

  1. Jun 11, 2012 #1


    User Avatar
    Gold Member

    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


    User Avatar
    Science Advisor

    Just a small correction, if frequency is f, the waveform is sin(2Ï€ f t).
  5. Jun 11, 2012 #4
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook