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Two loudspeakers are placed side by side a distance d = 4.00 m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is 1 = 5.00 m. One of the loudspeakers is then moved directly away from the other. Once the speaker is moved a distance r = 60.0 cm from its original position, the listener, who is not moving, observes destructive interference for the first time. Find the speed of sound in the air if both speakers emit a tone of frequency 700 Hz.

Two loudspeakers are placed side by side a distance d = 4.00 m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is 1 = 5.00 m. One of the loudspeakers is then moved directly away from the other. Once the speaker is moved a distance r = 60.0 cm from its original position, the listener, who is not moving, observes destructive interference for the first time. Find the speed of sound in the air if both speakers emit a tone of frequency 700 Hz.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Find v, the speed of the sound waves in air 

express in meters per second to three significant figures

Two loudspeakers are placed side by side a distance d = 4.00 m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is 1 = 5.00 m. One of the loudspeakers is then moved directly away from the other. Once the speaker is moved a distance r = 60.0 cm from its original position, the listener, who is not moving, observes destructive interference for the first time. Find the speed of sound in the air if both speakers emit a tone of frequency 700 Hz. Figure d/2 d/2 12 " 1 of 1
Transcribed Image Text:Two loudspeakers are placed side by side a distance d = 4.00 m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is 1 = 5.00 m. One of the loudspeakers is then moved directly away from the other. Once the speaker is moved a distance r = 60.0 cm from its original position, the listener, who is not moving, observes destructive interference for the first time. Find the speed of sound in the air if both speakers emit a tone of frequency 700 Hz. Figure d/2 d/2 12 " 1 of 1
MODEL: Model the waves as linear, circular, or spherical. VISUALIZE: Draw a picture showing the sources of the waves and the point where the waves interfere. Give relevant dimensions. Identify the distances ₁ and ₂ from the sources to the interference point. Note any phase difference Ap between the two sources. SOLVE: The interference depends on the path-length difference Ar = r2 and for destructive interference, T₁ and the source phase difference Apo. For constructive interference, A6 = 2π + Ado = 2mπ (m = 0, 1, 2,…..) A6 = 2π + A = 2 (m + ½) π (m = 0, 1, 2, …). For identical sources (Ado=0), the interference is maximum constructive if Ar=mλ and perfect destructive if Ar = (m + 1/2)). REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Viqualizo Model The two loudspeakers are sources of circular waves. The overlap of these waves causes interference. For simplicity, let us assume that these waves have equal amplitude.
Transcribed Image Text:MODEL: Model the waves as linear, circular, or spherical. VISUALIZE: Draw a picture showing the sources of the waves and the point where the waves interfere. Give relevant dimensions. Identify the distances ₁ and ₂ from the sources to the interference point. Note any phase difference Ap between the two sources. SOLVE: The interference depends on the path-length difference Ar = r2 and for destructive interference, T₁ and the source phase difference Apo. For constructive interference, A6 = 2π + Ado = 2mπ (m = 0, 1, 2,…..) A6 = 2π + A = 2 (m + ½) π (m = 0, 1, 2, …). For identical sources (Ado=0), the interference is maximum constructive if Ar=mλ and perfect destructive if Ar = (m + 1/2)). REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Viqualizo Model The two loudspeakers are sources of circular waves. The overlap of these waves causes interference. For simplicity, let us assume that these waves have equal amplitude.
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