You are standing 2.5 m directly in front of one of the two loudspeakers shown in

Question

You are standing 2.5 m directly in front of one of the two loudspeakers shown in the figure. They are 3.0 m apart and both are playing a 686 Hz tone in phase. (Figure 1) You may assume that the room is 20C in this example such that the speed of sound is 343 m/s.

A) What is the largest distance from the top speaker at which you would hear a minimum sound intensity?

B) In the previous part, you figured out that the difference in path length between the two speakers must be a multiple of a half wavelength to get destructive interference. A path length difference of exactly half of a wavelength gave you the answer above. What distance will result if the path difference is 1.5 ?

Explanation / Answer

Wavelength = speed / frequency = 343/686 = 0.5 m

a) For minimum intensity, destructive interference of the two sound waves coming from each speaker must occur at the distance X from the line joining the speakers. For destructive interference, path difference = d * sin(theta) = 0.5 (Wavelength)   

d = 3m

3*sin(theta) = 0.5 * 0.5

3*3/sqrt(3^2 + X^2) = 0.25

X = 35.875 m

b) 3*sin(theta) = 1.5 * 0.5

3*3/sqrt(3^2 + X^2) = 0.75

X = 11.62 m

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