Follow these steps to solve this problem: Two identical loudspeakers, speaker 1

Question

Follow these steps to solve this problem: Two identical loudspeakers, speaker 1 and speaker 2, are 2.0 m apart and are emitting 1700-Hz sound 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?

Compute the path-length difference ?r.

What is the wavelength ? of the sound waves emitted by the speakers?

Explanation / Answer

1. path difference delta = sqrt(4^2 + 2^2) - 4 = 0.472 m

2. wavelength ? = velocity/frequency = 340/1700 = 0.2 m

let n? = delta

n = 0.472/0.2 = 2.36 since nos not an integer it is not a point of maximum constructive interference

let (2n+1)?/2 = delta

n = 1.86 since n is not aninteger it is not a point of perfect destructive interference

so it is a point something in between the maximum constructive interference and perfect destructive interference

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