SOLUTION: 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-logI^0) desc

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 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-logI^0) desc      Log On


   

Question 86088: 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-logI^0) describes the loudness level of a sound, D, in decibels, where I in 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 form part (A) to answer this question: If a sound has 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?
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
a. D = 10logI%2FIo
b. D1 = 10logI1%2FIo
D2 = 10log100I1%2FIo = 10(log 100I1 - log Io) = 10(log 100 + log I1 - log Io) = 10(2 + log I1 - log Io) = 20 + 10log+I1%2Flog+Io ; 20 decibels greater.