Il The three identical Loudspeakers in FIGURE P 21.73 play a...

Il The three identical Loudspeakers in FIGURE $\mathrm{P} 21.73$ play a $170 \mathrm{Hz}$ tone in a room where the speed of sound is $340 \mathrm{m} / \mathrm{s} .$ You are standing $4.0 \mathrm{m}$ in front of the middle speaker. At this point, the amplitude of the wave from cach speaker is $a$. a. What is the amplitude at this point? b. How far must speaker 2 be moved to the left to produce a maximum amplitude at the point where you are standing? c. When the amplitude is maximum, by what factor is the sound intensity greater than the sound intensity from a single speaker?

Il The three identical Loudspeakers in FIGURE $\mathrm{P} 21.73$ play a $170 \mathrm{Hz}$ tone in a room where the speed of sound is $340 \mathrm{m} / \mathrm{s} .$ You are standing $4.0 \mathrm{m}$ in front of the middle speaker. At this point, the amplitude of the wave from cach speaker is $a$. a. What is the amplitude at this
point?
b. How far must speaker 2 be moved to the left to produce a maximum amplitude at the point where you are standing?
c. When the amplitude is maximum, by what factor is the sound intensity greater than the sound intensity from a single speaker?

Key Concepts

Amplitude and Intensity Relationship

In acoustics, the sound intensity is proportional to the square of the amplitude of the sound wave. Therefore, when multiple waves add constructively, the increase in amplitude leads to a quadratic increase in intensity, which is a key concept in understanding how maximum sound intensity is achieved from several coherent sources.

Path Difference and Phase Difference

Differences in the distances (path differences) from each sound source to an observation point lead to differences in the phase of the arriving waves. These phase differences determine whether the interference at that point will be constructive or destructive, influencing both the amplitude and the overall sound intensity.

Wave Superposition

This is the principle that when multiple waves meet at a point, their displacements add together to yield a net displacement. For sound waves, when waves from separate sources arrive at the same time, the resulting amplitude at a point is the sum of the individual amplitudes, which is crucial for analyzing interference patterns.

Interference

Interference occurs when waves from different sources combine, causing constructive interference (where wave crests align, enhancing the amplitude) or destructive interference (where crests and troughs cancel each other, reducing the amplitude). Understanding interference is fundamental when examining how multiple sound sources interact at a given point.

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