Both drawings show the same square, each of which has a side of length L = 0.80
ID: 1376975 • Letter: B
Question
Both drawings show the same square, each of which has a side of length L = 0.80 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.
Both drawings show the same square, each of which has a side of length L = 0.80 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.Explanation / Answer
constructive interference
f = v / lambda = 343 / 0.80 = 429 Hz
drawing 2:
L1 = 0.80 * sqrt 2 = 1.13 m , L2 = 0.80 m ,n = 1
lambda = 1.13 - 0.80 = 0.33
f = v / lambda = 343 / 0.33 = 1039 Hz
destructive interference
L1 - L2 = (n + 1/2) lambda?
L1 = 0.80 * sqrt 2 = 1.13 m , L2 = 0.80 m ,n = 0
0.33 = 1/2 * lambda
lambda = 0.66
f = v / lambda = 343 / 0.66 = 519.7 Hz
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