In the figure, two loudspeakers, separated by a distance of d; = 2.74 m, are in phase. Assume the amplitudes of the sound from the speakers are approximately the same at the position of a listener, who is d, = 3.81 m directly in front of one of the speakers. Consider the audible range for normal hearing, 20 Hz to 20 kHz. (a) What is the lowest frequency that gives the minimum signal (destructive interference) at the listener's ear? (b) What is the lowest frequency that gives the maximum signal (constructive interference) at the listener's ear? (Take the speed of sound to be 343 m/s.) di Speakers Listener (a) Number Units (b) Number Units >

University Physics Volume 1
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Chapter16: Waves
Section: Chapter Questions
Problem 147CP: Consider two wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kx+t+) . What is the wave function...
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In the figure, two loudspeakers, separated by a distance of d;
at the position of a listener, who is d, = 3.81 m directly in front of one of the speakers. Consider the audible range for normal hearing, 20 Hz to 20 kHz. (a) What is the
lowest frequency that gives the minimum signal (destructive interference) at the listener's ear? (b) What is the lowest frequency that gives the maximum signal
(constructive interference) at the listener's ear? (Take the speed of sound to be 343 m/s.)
2.74 m, are in phase. Assume the amplitudes of the sound from the speakers are approximately the same
%D
di
Speakers
Listener
(a) Number
Units
(b) Number
Units
Transcribed Image Text:In the figure, two loudspeakers, separated by a distance of d; at the position of a listener, who is d, = 3.81 m directly in front of one of the speakers. Consider the audible range for normal hearing, 20 Hz to 20 kHz. (a) What is the lowest frequency that gives the minimum signal (destructive interference) at the listener's ear? (b) What is the lowest frequency that gives the maximum signal (constructive interference) at the listener's ear? (Take the speed of sound to be 343 m/s.) 2.74 m, are in phase. Assume the amplitudes of the sound from the speakers are approximately the same %D di Speakers Listener (a) Number Units (b) Number Units
Expert Solution
Step 1

Given:

d1=2.74 md2=3.81 mv=343 m/s

Distance between speaker and listener be d3:

d3=d12+d22    =2.742+3.812    =7.5+14.5    =22    =4.7 m

L=d3-d2      =4.7-3.81      =0.89 m

vsound=fλ

(a)

For destructive interference,

Lλ=0.5,1.5,2.5Lvsound/fmin=0.5,1.5,2.5fmin=vsoundL×0.5,1.5,2.5       =3430.89×0.5, 1.5, 2.5

Lowest frequency that gives minimum signal at listener ear;

fmin,1=3430.89×0.5       =192.7 Hz

 

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