Handbook for Sound Engineers

204 Chapter 8

appears to be modulated as the wind gust rises and falls,
a layman’s description being “it fades in and out.”

Sound speed is influenced by air temperature with
higher temperatures corresponding to increased sound
speed. This relationship is given by

(8-1)

where,

c is the sound speed in meters per second,

T is the absolute temperature in degrees Kelvin.

A fixed air temperature has no influence on propaga-
tion direction, but thermal gradients can be a source of
further diffraction effects. Normal thermal gradients
correspond to a temperature decrease with increasing
elevation. Such a condition diffracts sound waves
upward such that the apparent direction of propagation
is elevated. A temperature inversion gradient has just
the opposite effect producing an apparent depressed
direction of propagation. The severity of these effects
obviously depends on the size of the thermal gradients.
Typically encountered stadium situations can result in
shifts of 5q or more over a distance of 200 m (650 ft).
These effects are illustrated in Fig. 8-2.

Atmospheric absorption of acoustical energy ulti-

mately amounts to the conversion of the energy associ-

ated with a sound wave into heat energy associated with

the random thermal motion of the molecular constitu-

ents of the air. Air is basically a gaseous mixture of

nitrogen, oxygen, and argon with trace amounts of

carbon dioxide, the noble gases, and water vapor. With

the exception of argon and the other noble gases all of

the constituent molecules are polyatomic and thus have

complicated internal structures. There are three mecha-

nisms contributing to the sound energy absorption

process. Two of these, viscosity and thermal conduc-

tivity, are smooth functions of frequency and constitute

what is called the classical absorption. The third or

molecular effect involves transfer of acoustic energy

into internal energy of vibration and rotation of poly-

atomic molecules and into the dissociation of molecular

clusters. This third effect is by far the most dominant at

audio frequencies and explains the complicated influ-

ence of water vapor on atmospheric absorption. The

detailed behavior given in Fig. 8-3 is illustrative of

these effects at a temperature of 20°C whereas the

approximate behavior given in Fig. 8-4 is more useful

for general calculations.

Table 8-1 is extracted from Fig. 8-3 and illustrates

the severity of the absorption effects.

Below 1 kHz the attenuation is not significant even

for a 200 m (650 ft) path length. The relative humidi-

ties encountered in practice usually lie in the 10% to

100% range and it can be seen that for frequencies

below 5 kHz that wetter air is preferable to drier air.

High-frequency equalization to compensate for air

losses is usually possible up to about 4 kHz with the

amount of equalization required being dependent on the

path length. Note that on a dry fall afternoon, the attenu-

ation at 5 kHz over a 200 m path length is about 22 dB.

No wonder that a marching brass band on such a day

loses its sparkle. As a consequence, long throws in a

single source outdoor system are limited to about a

4 kHz bandwidth.

Figure 8-2. The effects of wind and thermal gradients on
sound propagation.

c=20.06 T

B. Warm air on the bottom causes sound to

curve upward.

C. Cool air on the bottom causes sound to

curve toward the ground.

Sound source Warm air

Cool air

Sound source

Sound source

Warm air

Cool air

A. Wind mixes layers of air, losing effect

of the thermal layers.

Wind direction

wind velocity slow

Wind velocity fast

Table 8-1. The Entries Are Attenuation Values in

dB/m for Various Values of Relative Humidity at 20°C

RH 0.1 kHz 1 kHz 2 kHz 5 kHz 10 kHz 20 kHz

0% 0.0012 0.0014 0.002 0.0052 0.019 0.07

10% 0.00053 0.018 0.053 0.11 0.13 0.20

100% 0.0003 0.0042 0.010 0.045 0.15 0.50