Physics 222 Homework 4 (Chapter 16) Problem 16.71 A loudspeaker, mounted on a ta

Question

Physics 222 Homework 4 (Chapter 16) Problem 16.71 A loudspeaker, mounted on a tall pole, is engineered to emit 75% of its sound energy into the forward hemisphere, 25% toward the back. You measure an 85 dB sound intensity level when standing 1.0 m in front of and 2.5 m below the speaker Part A What is the speaker's power output? Express your answer with the appropriate units. P 0.0288 Watt Submit Incorrect: Try Again; 5 attempts remaining; no points deducted One or more of the units you entered is not recognized. Click help to view a list of re Provide Feedback

Explanation / Answer

Distance from speeker to the given point, r = sqrt(1^2 +2.5^2)

= 2.692 m

let I is the Intensity at the given point.

we know,

sound intensity level, beta = 10*log(I/Io)

85 = 10*log(I/10^-12)

8.5 = log(I/10^-12)

10^8.5 = I/10^-12

I = 10^(8.5 - 12)

I = 0.000316 W/m^2

we know, I = Power/Area

I = 75% of P/(Area of hemisphere)

I = 0.75*P/(2*pi*r^2)

P = I*2*pi*r^2/0.75

= 0.000316*2*pi*2.692^2/0.75

= 0.0192 W

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