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Homework Help: Destructive Interference Problem

  1. Jan 10, 2006 #1
    Hello. I'm having some trouble on the last of my homework problems for this week. The problem has to do with destructive interference and is as follows:
    Suppose that the separation between speakers A and B is 6.00 m and the speakers are vibrating in phase. They are playing identical 130 Hz tones, and the speed of sound is 343 m/s. What is the largest possible distance between speaker B and the observer at C, such that he observes destructive interference?
    http://img378.imageshack.us/img378/6470/1707alt5fr.th.gif [Broken]
    It is my understanding that for this problem, L*sqrt(2)-L=(n+lambda)/2 must be the case to get any kind of destructive interference. I think the reason I'm having trouble is that n could be any infinite value, and as n increases, so would length :uhh: ...though I have a feeling this way of thinking is totally backwards.
    If anyone has any thoughts, please share. Thanks in advance :cool:
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Jan 10, 2006 #2

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    no, the difference in path lengths is NOT (L*sqrt(2) - L) ...
    Pythagoras says that the length of the hypotenuse is sqrt(6^2 + L^2).

    The distance between speakers remains 6m no matter where the listener is.
     
  4. Jan 10, 2006 #3
    Bingo. Sqrt(L^2+36)-L=(n*lambda)/2

    1.319=Sqrt(L^2+36)-L; L=13! Thanks for the help.
     
  5. Jan 10, 2006 #4

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    For future problems with destructive interference, be sure to use
    (n + 1/2)*lambda . . . NOT (n + lambda)/2 <= it UNITS are even inconsistent!
     
  6. Feb 1, 2006 #5
    I have a question about this problem. how did you find L2?
     
  7. Feb 2, 2006 #6

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    By looking at the diagram!

    The sound path from speaker #1 travels in a straight line to the listener.
    The sound path from speaker #2 travels in a straight line to the listener,
    which is the hypotenuse (the diagonal) of a right triangle.

    Pythagoras says that c^2 = a^2 + b^2 , where our L = b .

    The path length difference is c - L .
     
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