The loudness level of a sound can be exposed 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) (the zero is beneath the I, like a downward exponent).

Describes the loudness level of sound, d, in decibels, where I is the intensity of the sound, and watts per meter ^2, and I is the intensity of a sound barely audible to the human ear.

A. Express the formula so that the expression in the parenthesis is written as a single logarithm.

B. Use the form of the formula for part a) to answer the question. If a sound has an intensity of 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:

(A)

The formula is

d=10 log(I/I0)

(B)

d=10 log(I/I0) = 10 log(100)= 20 dB

So it's 20 dB larger