Simple single-slit sound diffraction

[Ownaginatious]

Homework Statement

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. "

Homework 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

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

 

[rl.bhat]

What is the condition for destructive interference in terms of path difference?

 

[Ownaginatious]

What is the condition for destructive interference in terms of path difference?

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?

 

[rl.bhat]

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

 

[Ownaginatious]

Well, I'm guessing it's a single speaker because it doesn't really specify a second one in the question.