# Homework Help: Destructive interference problem

1. Jan 31, 2008

### vkrock

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

Speaker A and B are separated by 5.00m. A listener, C, stands a distance directly in front of speaker B. What is the largest possible distance between speaker B and the listener so that he observes destructive interference? The two speakers vibrate in phase and play identical 125Hz tones, the speed of sound is 343m/s.

The figure is a right triangle with the distance from A to C (AC) as the hypt.

2. Relevant equations

|Path Diff| = AC - BC

3. The attempt at a solution
I know that for destructive interference, the path difference needs to be n($$\lambda$$/2). The problem is I am not sure how to set up an equation that solves for the maximum distance, rather than just one distance that gives the destructive interference. Can anyone help me figure out how to set this up properly to find a maximum distance?

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