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A microphone is located on the line connecting two speakers that are 0.600 m apart and...

Question:

A microphone is located on the line connecting two speakers that are {eq}0.600 \ m {/eq} apart and oscillating {eq}180^\circ {/eq} out of phase. The microphone is {eq}2.25 \ m {/eq} from the midpoint of the two speakers.

(a) What are the lowest two frequencies that produce an interference maximum at the microphone's location?

Superposition of acoustic waves along a straight line connecting sound sources.

The microphone is located on the line connecting two speakers, outside the segment that connects the sound sources.

At a selected frequency (wavelength) of sound, the intensity of the total field from two sources depends only on difference in the distances from the sources to the selected point.

Answer and Explanation:

For any point, located on the line connecting two speakers outside the selected segment, the difference in the distances from sources to the point will be constant and equal the distance between sources d=0.6m.

The intensity of the total field, in this case, may vary with the change of frequency (wavelength).

Taking into account the fact that sound sources radiate out of phase, to obtain maximum field intensity, the distance d between the sources should be equal to an odd number of half-waves.

{eq}d=\lambda*(1/2+n)=v/f*(1/2+n) {/eq} (1)

{eq}\lambda,v,f -\text{wavelength,speed and frequency of the sound waves} {/eq}

n=0,1,2,3...

Therefore from the relation (1)

f=v/d*(1/2+n)

Assume sound's speed

v=340m/s,

f=340/0.6*(1/2+n)Hz=566.7*(1/2+n)Hz.

a)It means the lowest two frequencies that produce an interference maximum (n=0, n=1)

{eq}f_1=283.3Hz, f_2=850Hz {/eq}


Learn more about this topic:

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Interference Patterns of Sound Waves

from MTEL Physics (11): Practice & Study Guide

Chapter 16 / Lesson 5
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