Simple single-slit sound diffraction

  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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    What is the condition for destructive interference in terms of path difference?
     
  4. 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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    Sorry. I am thinking about the stereo speaker. Whether it is a single source problem or the double source?
     
  6. 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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