Loudspeaker Interference Both drawings show the same square, at one corner of wh
ID: 2111713 • Letter: L
Question
Loudspeaker Interference
Both drawings show the same square, at one corner of which an observer O is stationed. Two loudspeakers are located at corners of the square, either as in drawing 1 or as in drawing 2. The speakers produce the same single-frequency tone in either drawing and are in phase. Constructive interference occurs in drawing 1, but destructive interference occurs in drawing 2.
(a) Will only certain frequencies lead to the constructive interference in drawing 1, or will it occur for any frequency at all? There is no frequency that can produce constructive interference in drawing 1. Only sufficiently high frequencies will lead to constructive interference in drawing 1. Only sufficiently low frequencies will lead to constructive interference in drawing 1. Constructive interference will occur in drawing 1 for any frequency at all.
(b) Will only certain frequencies lead to the destructive interference in drawing 2, or will it occur for any frequency at all? All frequencies higher than a certain value will lead to destructive interference in drawing 2. There is no frequency that can produce destructive interference in drawing 2. All frequencies lower than a certain value will lead to destructive interference in drawing 2. Destructive interference will occur in drawing 2 for any frequency at all. Only certain frequencies will lead to destructive interference in drawing 2, and they occur throughout a large frequency range, from moderate to the very high.
One side of the square has a length of 0.80 m. The speed of sound is 343 m/s.
(c) What is the algebraic expression for the difference in path lengths traveled by the sound waves in drawing 2? Express your answer in terms of the length L of one side of the square.
Difference in path lengths =
(d) What is the algebraic expression for the magnitude of the difference in path lengths traveled by the sound waves in drawing 2 when destructive interference occurs? Express your answer in terms of the speed v of sound, the frequency f of the sound, and the integer variable n that can have the values 1, 3, 5, ....
Difference in path lengths =
(e) What is the single smallest frequency f that will produce both constructive interference in drawing 1 and destructive interference in drawing 2?
Number Unit f = ---Select---kgNHzPaJm/s
Explanation / Answer
a)
ANSWER: Constructive interference will occur in drawing 1 for any frequency at all.
b)
ANSWER: All frequencies higher than a certain value will lead to destructive interference in drawing 2.
c)
path difference = (sqrt(2) - 1) L
d)
lamda = v/f
path difference = (n/2) * (v/f)
e)
(sqrt(2) - 1) L = (1/2) * (v/f)
(1.4142 - 1) * 0.8 = 1/2 * 343/f
==> f = 518 Hz
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