Destructive interference near two speakers

  • #1

Homework Statement:

Two acoustic speakers face each other at opposite ends of a 50.0 m walkway. The speakers broadcast an identical, 66 Hz sound wave in phase. Consider a person walking along x, the straight line from one speaker to the other.

Calculate the shortest distance from the face of either speaker to a position where destructive interference causes the sound to become weak. Show your work here, and then enter your final numeric answer in the next answer box.

Relevant Equations:

change in path distance=wave length*(m+0.5)
v sound=343 m/s
where x is the distance from one speaker
343=(66)(5.197)
wave length =5.197m
x-(50-x)=(5.197)(m+0.5)
I choose m=-10

2x-50=(5.197)(-9.5)

x=0.314m?

Prof says correct answer is 1.6m tho
 

Answers and Replies

  • #2
35,127
11,365
Working with units and formulas would make it easier to understand what you do.

x=0.314 m away from the speaker the distance difference is 50m-2*x = 49.382m, that is 9.502 times the wavelength. Looks good.

Was the speed of sound part of the problem statement? Assuming a different number here changes the result a lot. 325 m/s would lead to the answer of the professor. That value is a bit on the low side, but not impossible.
 

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