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Chapter 16: Q. 32 (page 452)

A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners at x = -7.0 m and x = +3.0 m. a. What is the x-coordinate of the source? b. A third listener is positioned along the positive y-axis. What is her y-coordinate if the same wave front reaches her at the same instant it does the first two listeners?

Short Answer

Expert verified

Part a

X- coordinate of the source is x=-2.0m.

Part b

Y-coordinate of the third listener is y=4.6m.

Step by step solution

01

Given information

Wavefront simultaneously reaches atx=-7.0mandx=+3.0m.

02

Part a

As the same wavefront simultaneously reaches listeners at x=-7.0mand x=+3.0m, role="math" localid="1649951372478" ∆ϕ=0radwhich implies that

2πλr2-r1=0r2=r1

Thus, the source is at x=-2.0mso that it is equidistant from the two listeners.

03

Part b

The third person is also 5.0maway from the source.

Her y-coordinate is thus

y=52-22=25-4=21=4.6m

Therefore, the y-coordinate of the third listener is4.6m.

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