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Homework Help: Interference of Sound Waves

  1. Nov 14, 2007 #1
    [SOLVED] Interference of Sound Waves

    Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 Hz. You are 8.00 m from speaker A. Take the speed of sound in air to be 344 m/s.
    What is the closest you can be to speaker B and be at a point of destructive interference?
    __________


    I am having the hardest time trying to visualize the problem. I know that destructive interference occurs when the difference in path lengths traveled by sound waves is a half integer number of wavelengths. So I need to know the wavelength of the sound which is just 2m.

    I also know that in general if d_a and d_b are paths traveled by two waves of equal frequency that are originally emitted in phase, the condition for destructive interference is d_a-d_b=n(wavelength)/2 where wavelength is what I calculated it to be (2m) and n=any nonzero odd integer. I think I need to know what the value of n is that corresponds to the shortest distance d_b to solve my prob. (is d_a=8m? then what is d_b?)

    I'm going around in circles and getting nowhere. Please help!
     
  2. jcsd
  3. Nov 14, 2007 #2

    Astronuc

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    d_a=8m is given.

    One has determined the wavelength of the sound, 2 m, so the distance 8 m is 4 wavelengths. The the distance to B must be out of phase by 180 degrees in order to destructively interfere.

    A half wavelength is 1 m.
     
    Last edited: Nov 14, 2007
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