Conceptual question about longitudinal waves

  1. Saladsamurai

    Saladsamurai 3,016
    Gold Member

    So we are working on sound waves in my physics course now and I was doing some textbook reading. I have been following it pretty well, but I just came across a relationship that I am not quite following.

    It is with reference to wave interference. Let us say that two sound waves are emitted from two different point sources [tex]S_1[/tex] and [tex]S_2[/tex]. The waves have the same wavelength [tex]\lambda[/tex] and are in phase at their sources. They take paths of lengths [tex]L_1[/tex] and [tex]L_2[/tex] and pass through point P.

    The text says that their phase difference [tex]\phi[/tex] is dependent on [tex]\Delta L=|L_1-L_2|[/tex]

    Thus to relate the variables [tex]\Delta L[/tex] and [tex]\phi[/tex] we can use the proportion: [tex]\frac{\phi}{2\pi}=\frac{\Delta L}{\lambda}[/tex]

    I know that I should see it, but I don't exactly follow this proportion.

    Could somebody ellaborate on this a little for me? I sure would appreciate,
  2. jcsd
  3. learningphysics

    learningphysics 4,120
    Homework Helper

    Suppose the equation of both waves is: y = Acos(kx) (going along the direction the wave is travelling)

    The wavelength of this wave is 2*pi/k

    So at the point of interest, suppose wave 1 has travelled L1, and wave 2 has travelled L2:

    y1 = Acos(kL1)

    y2 = Acos(kL2)

    the phase of the first wave is kL1. the phase of the second is kL2.

    phase difference is: kL1 - kL2 = [2*pi/wavelength]*(L1 - L2)

    so from this we get the phase difference relationship.
  4. Saladsamurai

    Saladsamurai 3,016
    Gold Member

    Ah. I see that now. Thanks LP. It makes even more sense now that I wrote out what you did^^^...the phase difference is [tex]\phi[/tex]

    Last edited: Oct 13, 2007
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