Handbook for Sound Engineers

26 Chapter 2

This means that the amplifier can be 20 dB louder than
a 1 watt amplifier. A mixer that can output 10 volts
prior to clipping can be rated at

(2-3)

If the same mixer outputs 1 volt rms at meter zero,
then the mixer has 20 dB of peak room above meter zero.
If a loudspeaker can produce a sound level at 1 meter
of 90 dB ref. 20μPa (micro-Pascals), then at 10 meters
its level will be

(2-4)

In short, the decibel says, “The level difference
caused by changing a quantity will depend upon the
initial value of the quantity and the percentage that it is
changed.”
The applications of the decibel are endless, and the
utility of the decibel is self-evident. It forms a bridge
between the amount of change of a physical parameter
and the loudness change that is perceived by the human
listener. The decibel is the language of audio, Fig. 2-5.

2.3 Loudness and Level

The perceived loudness of a sound event is related to its

acoustical level, which is in turn related to the electrical

level driving the loudspeaker. Levels are electrical or

acoustical pressures or powers expressed in decibels. In

its linear range of operation, the human hearing system

will perceive an increase in level as an increase in loud-

ness. Since the eardrum is a pressure sensitive mecha-

nism, there exists a threshold below which the signal is

distinguishable from the noise floor. This threshold is

about 20μPa of pressure deviation from ambient at

midrange frequencies. Using this number as a reference

and converting to decibels yields

(2-5)

This is widely accepted as the threshold of hearing

for humans at mid-frequencies. Acoustic pressure levels

are always stated in dB ref. 0.00002 Pa. Acoustic power

levels are always stated in dB ref. 1 pW (picowatt or

10 ^12 W). Since it is usually the pressure level that is of

interest, we must square the Pascals term in the decibel

conversion to make it proportional to power. Sound

pressure levels are measured using sound level meters

with appropriate ballistics and weighting to emulate

human hearing. Fig. 2-6 shows some typical sound pres-

sure levels that are of interest to audio practitioners.

2.4 Frequency

Audio practitioners are in the wave business. A wave is

produced when a medium is disturbed. The medium can

be air, water, steel, the earth, etc. The disturbance

produces a fluctuation in the ambient condition of the

medium that propagates as a wave that radiates outward

from the source of the disturbance. If one second is used

as a reference time span, the number of fluctuations

above and below the ambient condition per second is

the frequency of the event, and is expressed in cycles

per second, or Hertz. Humans can hear frequencies as

low as 20 Hz and as high as 20,000 Hz (20 kHz). In an

audio circuit the quantity of interest is usually the elec-

trical voltage. In an acoustical circuit it is the air pres-

sure deviation from ambient atmospheric pressure.

When the air pressure fluctuations have a frequency

between 20 Hz and 20 kHz they are audible to humans.

As stated in the decibel section, humans are sensitive

to proportional changes in power, voltage, pressure, and

distance. This is also true for frequency. If we start at

Figure 2-5. Summary of decibel formulas for general audio
work. Courtesy Syn-Aud-Con.

Lout= 20 logE

= 20 log 10

= 20 dBV

Lp 90 20 1

10

+= log----- -

90 += 20–

=70 dB

Lp 20 0.00002

0.00002

= log-------------------

=0 dB (or 0 dB SPL)