Interference of Sound Waves

  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. Take n=1 for shortest distance from speaker B.
  4. Chi Meson

    Chi Meson 1,772
    Science Advisor
    Homework Helper

    Usually, it is important to know the distance between the two speakers. Is this not given?

    Then you can move B wherever you like. If you are 8 m from A, and wavelength is 2 m, the sound form A has traveled 4 full integer multiples of the wavelength. You must place B at a location such that the sound will arrive 1/2 wavelength out of phase. One full wavelength? or less? how much less?
  5. apparently n=1 is not the right answer.

    all info has been given.

    gahh. i need help. Yes, sound from A has traveled 4X the wavelength of sound emitted by the loud speakers. Sound from B must be moved so that the sound arrives 1/2 wavelength out of phase (d_a-d_b=n(wavelength)/2) so are you telling me the same thing that Vijay told me, that n=1?
  6. am i approaching this the wrong way???? ..Nobody??
  7. Re: [SOLVED] Interference of Sound Waves

    The correct answer is 1.00m.
    Hint: The closest you can be to B. (lamda/2)
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