The loudness L(x), measured in decibels, of a sound of intensity x, measured in

Question

The loudness L(x), measured in decibels, of a sound of intensity x, measured in watts per square meter, is defined as
L(x) = 10log ( x/I0), where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect.
Determine the loudness, in decibels, of the sound.
At a recent Phish rock concert, sound intensity reached a level of 0.50 watt per square meter. To the nearest
whole number, calculate the loudness of this sound in decibels.
a. 112 decibels
b. 123 decibels
c. 117 decibels
d. 107 decibels

Explanation / Answer

L(x) = 10log ( x/I0), where I0 = 10-12 watt per square meter

x = 0.50 watt per square meter

Then L(x) = 10*log(0.5/10^-12) = 116.9897 ~ 117 dB

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