Destructive Interference Problem

[nutster]

Hello. I'm having some trouble on the last of my homework problems for this week. The problem has to do with destructive interference and is as follows:
Suppose that the separation between speakers A and B is 6.00 m and the speakers are vibrating in phase. They are playing identical 130 Hz tones, and the speed of sound is 343 m/s. What is the largest possible distance between speaker B and the observer at C, such that he observes destructive interference?
http://img378.imageshack.us/img378/6470/1707alt5fr.th.gif
It is my understanding that for this problem, L*sqrt(2)-L=(n+lambda)/2 must be the case to get any kind of destructive interference. I think the reason I'm having trouble is that n could be any infinite value, and as n increases, so would length ...though I have a feeling this way of thinking is totally backwards.
If anyone has any thoughts, please share. Thanks in advance

 

[lightgrav]

no, the difference in path lengths is NOT (L*sqrt(2) - L) ...
Pythagoras says that the length of the hypotenuse is sqrt(6^2 + L^2).

The distance between speakers remains 6m no matter where the listener is.

 

[nutster]

Bingo. Sqrt(L^2+36)-L=(n*lambda)/2

1.319=Sqrt(L^2+36)-L; L=13! Thanks for the help.

 

[lightgrav]

For future problems with destructive interference, be sure to use
(n + 1/2)*lambda . . . NOT (n + lambda)/2 <= it UNITS are even inconsistent!

 

[kris24tf]

I have a question about this problem. how did you find L2?

 

[lightgrav]

By looking at the diagram!

The sound path from speaker #1 travels in a straight line to the listener.
The sound path from speaker #2 travels in a straight line to the listener,
which is the hypotenuse (the diagonal) of a right triangle.

Pythagoras says that c^2 = a^2 + b^2 , where our L = b .

The path length difference is c - L .