   Chapter 14, Problem 71AP

Chapter
Section
Textbook Problem

Assume a 150 W loudspeaker broadcasts sound equally in all directions and produces sound with a level of 103 dB at a distance of 1.60 m from its center. (a) Find its sound power output. If a salesperson claims the speaker is rated at 150. W, he is referring to the maximum electrical power input to the speaker. (b) Find the efficiency of the speaker, that is, the fraction of input power that is converted into useful output power.

(a)

To determine
The maximum electrical power input to the speaker.

Explanation

Given Info: The loudspeaker broadcast sound with a level of 103 dB and distance of the speaker from its centre is 1.60m .

Formula to calculate the intensity of the sound from the speaker is,

β=10log(II0)

• β is the sound level ,
• I is the intensity of the sound,
• I0 is the reference intensity,

Rewrite the above relation in terms of I.

I=I010β/10

Substitute 1.00×1012W/m2 for I0 and 103dB for β .

I=(1.00×1012W/m2)10103dB/10=(1.00×1012W/m2)1010

(b)

To determine
The efficiency of the speaker.

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