Handbook for Sound Engineers

Fundamentals of Audio and Acoustics 27

the lowest audible frequency of 20 Hz and increase it by
a 2:1 ratio, the result is 40 Hz, an interval of one octave.
Doubling 40 Hz yields 80 Hz. This is also a one-octave
span, yet it contains twice the frequencies of the
previous octave. Each successive frequency doubling
yields another octave increase and each higher octave
will have twice the spectral content of the one below it.
This makes the logarithmic scale suitable for displaying
frequency. Figs. 2-7 and 2-8 show a logarithmic
frequency scale and some useful divisions. The
perceived midpoint of the spectrum for a human listener
is about 1 kHz. Some key frequency ratios exist:

• 10:1 ratio—decade.


• 2:1 ratio—octave.

The spectral or frequency response of a system

describes the frequencies that can pass through that

system. It must always be stated with an appropriate

tolerance, such as ±3 dB. This range of frequencies is

the bandwidth of the system. All system components

have a finite bandwidth. Sound systems are usually

bandwidth limited for reasons of stability and loud-

speaker protection. A spectrum analyzer can be used to

observe the spectral response of a system or system

component.

2.5 Wavelength

If the frequency f of a vibration is known, the time

period T for one cycle of vibration can be found by the

simple relationship

(2-6)

The time period T is the inverse of the frequency of

vibration. The period of a waveform is the time length

of one complete cycle, Fig. 2-9. Since most waves prop-

agate or travel, if the period of the wave is known, its

physical size can be determined with the following

equation if the speed of propagation is known:

(2-7)

(2-8)

Waves propagate at a speed that is dependent on the

nature of the wave and the medium that it is passing

through. The speed of the wave determines the physical

size of the wave, called its wavelength. The speed of

light in a vacuum is approximately 300,000,000 meters

per second (m/s). The speed of an electromagnetic wave

in copper wire is somewhat less, usually 90% to 95% of

the speed of light. The fast propagation speed of electro-

magnetic waves makes their wavelengths extremely

long at audio frequencies, Fig. 2-10.

Figure 2-6. Sound levels of interest to system designers and
operators. Courtesy Syn-Aud-Con.

Sound source

dB A

110

100

90

80

70

60

50

40

30

20

10

0

Appropriate levels

Leave the building!

(A-weighted slow)

Max music level using

sound system

(A-weighted slow)

Max speech level using

sound system

(A-weighted slow)

Face-to-face

communication

Maximum allowable

noise floor

Background noise

from HVAC

Threshold of hearing

T^1

f

---=

O=Tc

O c

f

= --

Figure 2-7. The audible spectrum divided into decades (a 10 to 1 frequency ratio). Courtesy Syn-Aud-Con.

Log Scale

1 10 100 1K 10K 100K

Audible Range

Low Mid High

Voice Range