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Diffraction Question

  • Thread starter equanox
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  • #1
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Homework Statement


I am having difficulty with this problem because I am not quite sure where to start.

A lecturer is demonstrating two-slit interference with sound waves. Two speakers are used 4.0 meters apart. The sound frequency is 325 Hz and the speed of sound is 343 m/s. Students sit in seats 4.5 meters away. What is the spacing between the location where no sound is heard because of destructive interference?



Homework Equations



x <center>lamda
_ = <center>____ ????????????? (sorry these didn't line up too well)

L <center> d

The Attempt at a Solution



I know full well that I'm supposed to show work, but the problem is that I don't know how to get started. I tried using the equation that I showed above, using 4.0 as d and 4.5 as L, but then that leaves frequency and speed of sound, which don't fit in. I then tried v=f(lamda), which works partially, except they aren't asking for wave length in this problem as far as I know. I can't figure out if there's too much information in the problem, or if I'm just looking at the wrong equations. Any help would be appreciated. Thanks.
 

Answers and Replies

  • #2
Hootenanny
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Let's start from the top. What is the condition for destructive interference between two waves?

As an aside, this question has nothing to do with diffraction.
 
  • #3
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If seperation is equal to 1/2 a wavelength plus a multiple of the wavelength there will be destructive interference, correct?
 
  • #4
Hootenanny
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If seperation is equal to 1/2 a wavelength plus a multiple of the wavelength there will be destructive interference, correct?
Correct, that is constructive interference occurs if the path length (L) of the two waves differ by,

[tex]L = \left(n+\frac{1}{2}\right)\lambda\;\;\;\;\; n\in\mathbb{Z}[/tex]

Therefore, you need to find the shortest distance by which the two waves for the two speakers differ by a half-integer wavelength.
 
Last edited:
  • #5
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Okay...now I have a better idea of what I should do. If I have trouble I'll ask again. Thanks a lot for helping me :)
 

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