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A person sees a speaker at some initial distance and hears a tone with sound level...

A person sees a speaker at some initial distance and hears a tone with sound level 23.0dB. The person then walks 10.0m closer to the speaker and hears a sound level 87.0dB.

a. What is the initial distance?

b. What is the power of the speaker?

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Answer #1

a)

Sound Level in dB is given by

B=10Log(I/Io)

At B=23 dB

23 =10(I1/10-12)

I1=102.3*10-12 = 1.9953*10-10 W/m2

At B=87 dB

I2=108.7*10-12=5.012*10-4 w/m2

Since intensity is given by

I=P/4pir2

=>I1/I2 = (r2/r1)2

(1.9953*10-10/5.012*10-4) = (10/r1)2

r1=15848.93 m

b)

Power of the speaker

P=I*4pir2 =(1.9953*10-10)*(4pi*15848.932)

P=0.63 Watts

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