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Some questions about sound(sine) waves.

  1. Feb 20, 2014 #1
    Hi all.

    I'm a music student and I've been trying to educate myself about acoustics lately.

    I'm exploring the correlations between two pure sound waves.
    This might be more of a mathemetical question rather than a physics one but anyways:

    I want to know how can I calculate when/how freuqently this function:
    will be zeroed.

    I wanna know this so I can now know frequent the pulses occur(by pulses I mean the fluctuating volume of the sound).

    Also, what is the proper way to define the sine function of , say, 440Hz?
    Sin(440) ?

    Thx in advance, hope I'm not too noobish :)
  2. jcsd
  3. Feb 20, 2014 #2


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    Gold Member

    Use the relation Sin(a) + Sin(b) = 2 Cos((a-b)/2) Sin((a+b)/2)

    If you have a sound at frequency f = 440Hz, the pressure varies in time (t) like

    Sin(2*∏*f* t) = Sin(ω* t)


    Sin(2*∏*f* t + shift) = Sin(ω* t + shift)

    Usually, one defines ω=2*∏*f.

    Concerning your signal and the beats, you will get from above:

    f(ω t) = Sin(ω t) + Sin(1.05 ω t) = 2 Cos(0.025 ω t) Sin(1.025 ω t)

    From this, you can see when the wave f(ω t) goes to zero.
    It does that at a high frequency because of the second factor Sin(1.025 ω t).
    But the whole high-frequency wave is modulated by the first factor Cos(0.025 ω t) which goes to zero at a lower frequency.
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