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!

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:
    f(x)=sin(x)+sin(1.05x)
    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

    maajdl

    User Avatar
    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)

    or

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Some questions about sound(sine) waves.
  1. Question about sounds (Replies: 2)

Loading...