The loudness of level of a sound can be expressed by comparingthe sound\'s inten

Question

The loudness of level of a sound can be expressed by comparingthe sound's intensity to the intensity of a sound barely audible tothe human ear. The formula a. Express the formula so that the expression in parenthesesis written as a single logarithm. b. Use the form of the formula from part (a) to answerthis question: If a sound has an intensity 100 times the intensityof a softer sound, how much larger on the decibel scale is theloudness level of the more intense sound?

Explanation / Answer

log rule: log(a) - log(b) = log(a/b) a) D = 10log10(I / I0) b) D = 10log10(100)     Since x = logb(y) --->bx = y, log10(100) = x means 10x =100 so x = 2     D = 10(2) = 20

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