# 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 S

_{1}and S

_{2}emit sound waves of wavelength 2m, in phase with each other.

Let A_{p} be the amplitude of the resulting wave at point P, and A_{q} be he amplitude of the resultant wave at point Q. How does A_{p} compare to A_{q}?

a. A_{p}<A_{q}

b. A_{p}=A_{q}

c. A_{p}>A_{q}

d. A_{p}<0, A_{q}>0

e. A_{p} and A_{q} 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 A_{p}>A_{q} 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 S_{1} traveled 4m whereas sound waves from S_{2} 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?

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