Simple single-slit sound diffraction

  1. Apr 6, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm having trouble solving this problem and I'm unsure why,

    "A stereo speaker is located inside a speaker cabinet with an opening 30.9 cm wide. The speaker emits a sound with a frequency of 2620 Hz. Assuming that the speed of sound in air is 343 m/s, find the location along a wall 97.7 m away where a listener will hear the first diffraction minimum. Give this location as a distance from the central axis. "

    2. Relevant equations

    I believe the relevant equation for this is the equation for the diffraction of waves through a single slit:

    wavelength = r
    Distance to wall = L
    Distance between slits: d
    diffraction minimum/maximum: m

    With the equation, y = (mrL)/d

    3. The attempt at a solution

    r = (speed of sound)/(frequency)
    r = (343 m/s)/(2620 Hz)
    r = 0.131 m

    Now since this is the first diffraction minimum, m = 1.

    y = (mrL)/d
    y = (0.131 m * 97.7 m) / (0.309 m)
    y = 41.4 m

    This answer is apparently wrong. Can anyone please show me where I went wrong?

    Thanks!

    - Dillon
     
  2. jcsd
  3. Apr 6, 2009 #2

    rl.bhat

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    What is the condition for destructive interference in terms of path difference?
     
  4. Apr 6, 2009 #3
    I'm sorry, I'm not sure I follow. Are you giving me a hint, or asking me something in regards to the problem?

    If the former, doesn't one sound wave have to be out of phase with the other by pi?
     
  5. Apr 7, 2009 #4

    rl.bhat

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    Sorry. I am thinking about the stereo speaker. Whether it is a single source problem or the double source?
     
  6. Apr 7, 2009 #5
    Well, I'm guessing it's a single speaker because it doesn't really specify a second one in the question.
     
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