Solve Diffraction Question: 2 Speakers 4.0m Apart, 325Hz, 343m/s, 4.5m Away

[equanox]

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.

 

[Hootenanny]

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.

 

[equanox]

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

 

[Hootenanny]

If separation 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,

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

Therefore, you need to find the shortest distance by which the two waves for the two speakers differ by a half-integer wavelength.

 

[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 :)