Wave Interference and speakers

Hank_Rearden

1. Homework Statement
You are standing 2.5m directly in front of one of two loudspeakers. they are 3m apart and both are playing a 686hz tone in phase. As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? Assume speed of sound of 343m/s

2. Homework Equations

3. The Attempt at a Solution

I've been trying to approach the problem using the idea that the minimum sound intensity will occur where the waves experience destructive interference, which will happen when they are a half-wavelength apart in phase.

so the wavelength can be calculated at .5m,

So r = phase difference.

r = wavelength*.5

r=(.5)*(.5m)

then, by the Pythagorean Theorem. r = (15.25 + 5x + 5x^2)^.5 -(2.5 + x)

where x is the distance from the starting point.

Is this the correct approach to take?

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vela

Staff Emeritus
Homework Helper
You have the basic idea, but you need to be a bit more careful and check some of your assumptions. For example, when x=0, there's already a path length difference that you need to account for. Destructive interference can happen not only when the difference is λ/2, but when it's 3λ/2, 5λ/2, and so on.

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