Audio Engineering

Measurement 43

The root mean square (rms) sound pressure P can be found by

PfAcrms 2 πρ, (2.20)

where Prms is in pascals, f is the frequency in Hertz (Hz), A is particle displacement in
meters (rms value), ρ is the density of air in kilograms per cubic meter (kg/m^3 ), c is
the velocity of sound in meters per second (m/s), ρc  406 RAYLS and is called the
characteristic acoustic resistance (this value can vary), or

L

P

P

 20 rms

20

log

μPa

. (2.21)

These are identical sound pressure levels bearing different labels. Sound pressure levels were
identifi ed as dB-SPL, and sound power levels were identifi ed as dB-PWL. Currently, LP is
preferred for sound pressure level and LW for sound power level. Sound intensity level is LI :

L

x

I^1010 

2

log 12 2

W/m

W/m

. (2.22)

At sea level, atmospheric pressure is equal to 2116 1 b/ft^2. Remember the old physics
laboratory stunt of partially fi lling an oil can with water, boiling the water, and then
quickly sealing the can and putting it under the cold water faucet to condense the steam
so that the atmospheric pressure would crush the can as the steam condensed, leaving a
partial vacuum?

1Atm  101,300 Pa

Therefore

LP



20

101 300

0 00002

194

log

,

.

dB.

This represents the complete modulation of atmospheric pressure and would be the
largest possible sinusoid. Note that the sound pressure ( SP ) is analogous to voltage.
AnLP of 200 dB is the pressure generated by 50 lb of TNT at 10 ft. Table 2.3 shows the
equivalents of sound pressure levels.

For additional insights into these basic relationships, the Handbook of Noise
Measurement by Peterson and Gross is thorough, accurate, and readable.