Problem 17: Two small loudspeakers, L1 and L2, are oscillating in phase at a frequency of 516 Hz, sending out soundwave crests and troughs in synchrony. The speakers are spaced 4.1 m apart. The speed of sound propagation in air is 344 m/s. If you move a small microphone, M, slowly, along a straight line from L1 to L2, you will dectect maxima and minima of sound intensity, i.e., in the loudness of the sound. How such maxima and minima will you find between L1 and L2? many l2 – l1, where lz is the distance from L2 to Hints: Consider the pathlength difference, Al M and and li is the distance from L1 to M. (1) What is the range of Al-values covered as M is moved from Lị to L2? In other words: What is the initial value of Al when M starts from L1? What is the final value of Al when M arrives at L2? (2) An intensity maximum occurs whenever Al reaches the values Al 0, ±1A, ±2), (3) An intensity minimum .... occurs when Al +}1, ±}A, .... (A) 6 maxima, 5 minima (B) 6 maxima, 7 minima (C) 15 maxima, 14 minima (D) 13 maxima, 14 minima (E) 13 maxima, 12 minima

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Problem 17: Two small loudspeakers, L1 and L2, are oscillating in phase at a frequency
of 516 Hz, sending out soundwave crests and troughs in synchrony. The speakers are spaced
4.1 m apart. The speed of sound propagation in air is 344 m/s.
If you move a small microphone, M, slowly, along a straight line from L1 to L2, you will
dectect maxima and minima of sound intensity, i.e., in the loudness of the sound. How
such maxima and minima will you find between L1 and L2?
many
l2 – l1, where lz is the distance from L2 to
Hints: Consider the pathlength difference, Al
M and and li is the distance from L1 to M. (1) What is the range of Al-values covered as
M is moved from Lị to L2? In other words: What is the initial value of Al when M starts
from L1? What is the final value of Al when M arrives at L2? (2) An intensity maximum
occurs whenever Al reaches the values Al
0, ±1A, ±2),
(3) An intensity minimum
....
occurs when Al
+}1, ±}A,
....
(A) 6 maxima, 5 minima
(B) 6 maxima, 7 minima
(C) 15 maxima, 14 minima
(D) 13 maxima, 14 minima
(E) 13 maxima, 12 minima
Transcribed Image Text:Problem 17: Two small loudspeakers, L1 and L2, are oscillating in phase at a frequency of 516 Hz, sending out soundwave crests and troughs in synchrony. The speakers are spaced 4.1 m apart. The speed of sound propagation in air is 344 m/s. If you move a small microphone, M, slowly, along a straight line from L1 to L2, you will dectect maxima and minima of sound intensity, i.e., in the loudness of the sound. How such maxima and minima will you find between L1 and L2? many l2 – l1, where lz is the distance from L2 to Hints: Consider the pathlength difference, Al M and and li is the distance from L1 to M. (1) What is the range of Al-values covered as M is moved from Lị to L2? In other words: What is the initial value of Al when M starts from L1? What is the final value of Al when M arrives at L2? (2) An intensity maximum occurs whenever Al reaches the values Al 0, ±1A, ±2), (3) An intensity minimum .... occurs when Al +}1, ±}A, .... (A) 6 maxima, 5 minima (B) 6 maxima, 7 minima (C) 15 maxima, 14 minima (D) 13 maxima, 14 minima (E) 13 maxima, 12 minima
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