x=280m Problem 2: On atab8hree speakers. The fist speaker produces a sound with

Question

x=280m Problem 2: On atab8hree speakers. The fist speaker produces a sound with sound level of 64.0dB. The second speaker produces a sound with a sound level of 66.0dB and the third speaker produces a sound with a sound level of 69.0dB. a) What is the combined decibel level of all three speakers? b) How far away from the table would you need to be for the combined decibel level to be 70.0dB? Assume that the sound produced by all three speakers combined results in a spherical wave. (10 points) B10 -12

Explanation / Answer

I0 = threshold frequency = 10^-12 W/m^2

for speaker 1

intensity level B1 = 10*log(I1/I0)

64 = 10*log(I1/10^-12)

I1 = 2.51*10^-6 W/m^2

for speaker 2

intensity level B2 = 10*log(I2/I0)

66 = 10*log(I2/10^-12)

I2 = 3.98*10^-6 W/m^2

for speaker 3

intensity level B3 = 10*log(I3/I0)

69 = 10*log(I3/10^-12)

I3 = 7.94*10^-6 W/m^2

a)

combined Intensity I = I1 + I2 + I3 = 14.43*10^-6 W/m^2

intensity level B = 10*log(I/I0)

intensity level B = 10*log(14.43*10^-6/10^-12) = 71.6 dB

====================

(b)

for decible level B' = 70 dB = 10*log(I'/I0)

I' = 10^-5 W/m^2

I'/I = r^2/r'^2

10^-5/(14.43*10^-6) = 2.8^2/r'^2

r' =

10^-5/(14.43*10^-6) = 2.8^2/r^2

r = 3.36 m <<<----------ANSWER

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