SOLUTION: The loudness level of sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible tot he human ear. The formula D = 10(log I

SOLUTION: The loudness level of sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible tot he human ear. The formula D = 10(log I - log I<sub>0

Question 215485This question is from textbook College Mathematics II
: The loudness level of sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible tot he 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 patentheses 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?}} This question is from textbook College Mathematics II

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The loudness level of sound can be expressed by comparing the sound's intensity to the intensity of a sound barely audible tot he human ear. The formula D = 10(log I - log I0) describes the loudness level of a sound. D, in decibels, where I is the intensity of the sound, in watts per meter^2, and I0 is the intensity of a sound barely audible to the human ear.
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(a.) Express the formula so that the expression in patentheses is written as a single logarithm.
D = 10log(I/Io)
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(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?
D = 10log(100Io/Io)
D = 10log(100)
D = 10*2
D = 20 dB
=========================
Cheers,
Stan H.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
(a) Express: as a single logarithm: Applying the quotient rule for logarithms, we get:
For part (b), substitute and
(b)

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