Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 m apart and are emi

Question

Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 m apart and are emitting 1700-Hzsound waves into a room where the speed of sound is 340 m/s. Consider a point 4.0 m in front of speaker 1, which lies along a line from speaker 1, that is perpendicular to a line between the two speakers. Is this a point of maximum constructive interference, a point of perfect destructive interference, or something in between?

PART a.Compute the path-length difference

?r

part b. What is the wavelength

of the sound waves emitted by the speakers?  

Explanation / Answer

The other speaker is a distance of
d^2 = 2^2 + 4^2
d = sqrt(20) = 2sqrt(5) m

Path difference from the two spwakers to the point is

2sqrt(5) - 4 = 4.47 - 4 = 0.47 m
If this path difference is a whole number of wavelengths we get constructive interference and if it is a whole number of half wavelengths we get descructive interference.
wavelength = v/f = 340/1700 = 0.2 m
0.47/0.2 = 2.35
0.47/0.094 = 5
so it is destructive interference.

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