# The amplitude of sound waves from two nearby speakers

1. The problem statement, all variables and given/known data
In the figure below, two speakers S1 and S2 emit sound waves of wavelength 2m, in phase with each other.

Attachment 67863

Let Ap be the amplitude of the resulting wave at point P, and Aq be he amplitude of the resultant wave at point Q. How does Ap compare to Aq?

a. Ap<Aq
b. Ap=Aq
c. Ap>Aq
d. Ap<0, Aq>0
e. Ap and Aq vary with time, so no comparison can be made

2. Relevant equations
Pythagorean Theorem

3. The attempt at a solution
My guess is that since amplitude varies with time, there would be times when Ap>Aq and vice versa, so the answer would be E. However, my textbook says that the answer is A because at Q sound waves from both speakers traveled 4m, so there would be constructive interference, but at point P sound waves from S1 traveled 4m whereas sound waves from S2 traveled 5m by the Pythagorean theorem, so there is destructive interference. Can you explain to me why there would be destructive interference at all in two waves that were said to be "in phase with each other?" Specifically, can you explain what that phrase and the phrase "out of phase" mean when we’re talking about waves?

Attached Images 20140321_114004.jpg (45.5 KB)

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