   Chapter 14, Problem 75AP

Chapter
Section
Textbook Problem

A stereo speaker is placed between two observers who are 36.0 m apart, along the line connecting them. If one observer records an intensity level of 60.0 dB, and the other records an intensity level of 80.0 dB, how far is the speaker from each observer?

To determine
The distance of the speaker from each observer.

Explanation

Given Info: The intensity of the sound from the first and second observer

Formula for the intensity of sound from first observer is,

I1=P4πr12 (1)

• P is the pressure.
• I1 is the intensity of sound from the first observer.
• r1 is the distance from the first observer.

Formula for the intensity of sound from second observer is,

I2=P4πr22 (2)

• P is the pressure.
• I2 is the intensity of sound from the second observer.
• r2 is the distance from second the observer.

The difference in the decibel levels for the two observers is,

β1β2=10log10(I1I0)10log10(I2I0)

• β1 and β2 is the decibel level for the first and second observer.
• I1 and I2 is the intensity of the sound from first and second observer.
• I0 is the reference intensity.

Rewrite the above equation.

β1β2=10log10(I2I1) (3)

Use equation (1) and (2) to rewrite the equation (3).

β1β2=10log10(P4πr22P4πr12)=10log10(r2r1)2=20log10(r2r1) (4)

Use the equation (4) we get r2

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