Question

Both drawings show the same square, each of which has a side of length L =...

Both drawings show the same square, each of which has a side of length L = 0.92 m. An observer O is stationed at one corner of each square. Two loudspeakers are located at corners of the square, as in either drawing 1 or drawing 2. The speakers produce the same single-frequency tone in either drawing and are in phase. The speed of sound is 343 m/s. Find the single smallest frequency that will produce both constructive interference in drawing 1 and destructive interference in drawing 2.

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Answer #1

constructive interference

| L1 - L2 | = n lambda　

L1 = L2 = 0.92 m , n = 1

lambda = 0.92 m

f = v / lambda = 343 / 0.92 = 372.83 Hz

constructive interference

| L1 - L2 | = n lambda , L1 = 0.92 * sqrt 2 = 1.30 m , L2 = 0.92 m , n = 1

lambda = 1.30 - 0.92 = 0.38

f = v / lambda = 343 / 0.38

= 902.6 Hz

destructive interference

| L1 - L2 | = (n + 1/2) lambda , L1 = 1.30 m , L2 = 0.92 m , n = 0

0.38 = 1/2 * lambda

lambda = 0.76

f = v / lambda = 343 / 0.76 = 451 Hz

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