# Diffraction Question

1. May 18, 2008

### equanox

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

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

L <center> d

3. 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.

2. May 18, 2008

### Hootenanny

Staff Emeritus
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. May 18, 2008

### equanox

If seperation is equal to 1/2 a wavelength plus a multiple of the wavelength there will be destructive interference, correct?

4. May 18, 2008

### Hootenanny

Staff Emeritus
Correct, that is constructive interference occurs if the path length (L) of the two waves differ by,

$$L = \left(n+\frac{1}{2}\right)\lambda\;\;\;\;\; n\in\mathbb{Z}$$

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: May 18, 2008
5. May 19, 2008

### equanox

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 :)