Physics: Sound Intensity?
A person is standing in the middle of a large circle. At different locations on the perimeter of the circle 16 identical radios are playing at identical intensities. This person experiences a sound level of 63 decibels. What would be the sound level (decibels) if 13 of the 16 radios would be turned off? What is the intensity (watts/m^2) of one radio? The threshold of hearing (Io) has an Intensity of 1.0x10^-12 watts/m^2.
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Verified answer
10 log [I1/ I0] = 63 dB.
When only 3 of them is on
I2 = [3/16] [I1]
I2 /I0 = [3/16] [I1/I0]
Log [I2 /I0] = log [3/16] + log [I1/I0]
Log [I2 /I0] = -0.727+ 6.3
Log [I2 /I0] = 5.573
10 log [I2 /I0] = 55.7 dB
Sound level, if 13 of the 16 radios would be turned off is
55.7 dB
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Log [I1/ I0] = 6.3
Log I1 = 6.3 + log I0
Log I1 = 6.3 + log 1x10^ [-12] = -5.7
I1 = 1.995 x10^-6 W/m^2
The intensity (watts/m^2) of one radio is
[1/16] of1.995 x10^-6 W/m^2
=1.25e-7 W/m^2
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