   Chapter 14, Problem 23P

Chapter
Section
Textbook Problem

Show that the difference in decibel levels β1 and β2 of a sound source is related to the ratio of its distances r1 and r2 from the receivers by the formula β 2 − β 1 = 20  log ( r 1 r 2 )

To determine
The expression for difference in decibel levels is related to ration of distances.

Explanation

Given Info: the ratio of distance r1 and r2

Formula for sound intensity,

β=10log(II0)

• I0 is intensity constant,
• I is the total intensity,

Formula for difference in intensity level,

β2β1=10log(I2I0)10log(I1I0)

Simplify the above expression,

β2β1=10log(I2I0I0I1)=10log(I2I1

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