A sound's noise level is measured in decibels (dB) by comparing the sound's intensity, [math], to a benchmark sound that has an intensity of [math] watts/cm[math]. In particular, [math]

A single jet engine that is 100 feet away from the listener has a noise level of 140dB.

a) Find the sound intensity of the jet engine in watts/cm[math].
watts/cm[math]

b) Suppose two jet engines are 100 feet away from a person, each with the same sound intensity as the jet engine from part (a). What is the combined noise level in decibels? [Hint: the combined sound intensity is the sum of the intensities of the two engines.]
dB

c) Suppose a source has sound intensity [math]. Using the definition of decibels, write an expression for the noise level in decibels if two sources with sound intensity [math] are present.
[math]

d) Using properties of logarithms, write the expression from part (c) as the sum of two logarithms.
[math]

Hint:

Solution: