The loudness level of a sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible to the human ear. The formula D = 10 ( log I − log I 0 ) describes the loudness level of a sound, D , in decibels, where I is the intensity of the sound, in watts per meter 2 , and I 0 is the intensity of a sound barely audible to the human ear. a. Express the formula so that the expression in parentheses is written as a single logarithm. b. Use the form of the formula from part (a) to answer this question; If a sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
The loudness level of a sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible to the human ear. The formula D = 10 ( log I − log I 0 ) describes the loudness level of a sound, D , in decibels, where I is the intensity of the sound, in watts per meter 2 , and I 0 is the intensity of a sound barely audible to the human ear. a. Express the formula so that the expression in parentheses is written as a single logarithm. b. Use the form of the formula from part (a) to answer this question; If a sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
Solution Summary: The author explains how the loudness level of a sound is obtained by formula underset_D=mathrmlog(m
The loudness level of a sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible to the human ear. The formula
D
=
10
(
log
I
−
log
I
0
)
describes the loudness level of a sound, D, in decibels, where I is the intensity of the sound, in watts per meter2, and I0 is the intensity of a sound barely audible to the human ear.
a. Express the formula so that the expression in parentheses is written as a single logarithm.
b. Use the form of the formula from part (a) to answer this question; If a sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
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