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Two loud speakers are separated by a distance AB=10 m. A listener which is at point C which is...

Question:

Two loud speakers are separated by a distance {eq}AB=10{/eq} m. A listener which is at point C which is colinear with AB (A,B,C are on a straight line). The two loud speakers are in phase with the wave length 20 m.

At point C,do you have constructive or destructive interference? Explain your answer.

Features of interference along the line on which the sound coherent sources are located.

The quality of interference of sound waves from two coherent sources, spaced at some point around them, depends on the difference in the distance of the sources to this point.

Along the straight line, passing through the sources, outside the segment AB bounded by them, the difference in distances from these sources remains unchanged and equal to the length of this segment.

Answer and Explanation:

Constructive interference is observed at the point if the difference between the distance from this point to the sources A and B equal to zero or even numbers of the half-length.

Destructive interference is observed at the point if the difference between the distance from this point to the sources A and B equal to odd numbers of the half-length.

In our case length of the segment between the sources (AB=10m) equal half of the wavelength (20m).

It means that we will observe only one point of constructive interference exactly in the middle of the segment AB.

The intensity of the interference field will decrease inside the segment AB as it approaches its edges.

As at points A, B and at all other points of the line ABC outside the segment AB,

the distance difference from the sound sources is equal to half the wavelength (10m) and, therefore, destructive interference will be observed.


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Interference Patterns of Sound Waves

from MTEL Physics (11): Practice & Study Guide

Chapter 16 / Lesson 5
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