Math, physics: decibels: a practical example

Tutoring math, everyday situations come up. The tutor mentions a construction application: noise dampening.

Today I was at a hardware store and noticed some ear protection rated as reducing noise by 27 decibels (aka 27 dB). What amount of noise dampening is that, really?

Decibels measure a ratio of power between two sources. The formula is

dB=10*log(S2/S1), where S2 and S1 are the two sources.

In this case, S2 is the dampened S1, and the formula reads

-27=10*log(S2/S1)

which gives, by dividing both sides by 10,

-2.7=log(S2/S1)

The log is base 10, so we have

10^(-2.7)=S2/S1

which gives

0.002=S2/S1

Therefore, a reduction of 27 dB dampens the noise to 0.002 times what it originally was.

Interesting, eh?

Source:

courses.lumenlearning.com