Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013

9

( *

Equation 4.7 , abbreviated dBSIL

Neither power nor intensity is a convenient way of measuring the loudness of sound. We

give the definitions above primarily because they help to show how the definition of dBSPL was

derived historically. The easiest way to measure sound loudness is by means of air pressure

amplitude. When sound is transmitted, air pressure changes are detected by a microphone and

converted to voltages. If we consider the relationship between voltage and power, we can see

how the definition of was derived from the definition of . By

Equation 4.3, we know that power varies with the square of voltage. From this we get

( * (( * ) ( *

The relationship between power and voltage explains why there is

a factor of 20 is in Equation 4.4.

We can show how Equation 4.4 is applied to convert from air pressure amplitude to

dBSPL and vice versa. Let’s say we begin with the air pressure amplitude of a humming

refrigerator, which is about 0.002 Pa.

( *

Working in the opposite direction, you can convert the decibel level of normal

conversation (60 dBSPL) to air pressure amplitude:

( )

Thus, 60 dBSPL corresponds to air pressure amplitude of 0.02 Pa.

Rarely would you be called upon to do these conversions yourself. You’ll almost always

work with sound intensity as decibels. But now you know the mathematics on which the dBSPL

definition is based.

So when would you use these different applications of decibels? Most commonly you

use dBSPL to indicate how loud things seem relative to the threshold of hearing. In fact, you use

Aside:

If

then

Aside: