Rane AD22S "Environmental Effects on the Speed of Sound" Den - Page 6

and Relative Humidity

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BOHN PAPERS 2.5 Combined Effects of Temperature and Relative Humidity The results graphed in Figs. 3 and 4, and also tabulated in Tables 1and 2, can be added together to show the combined effects of temperature and relative humidity on the speed of sound. Doing so produces Table 3. Here the total percentage increase in sound speed is tabulated for easy reference. 3 EFFECT OF RELATIVE HUMIDITY ON THE ABSORPTION OF SOUND IN AIR 3.1 Introduction To a certain degree everything absorbs sound, es- pecially air. Wet air absorbs sound better than dry air. This section presents the latest findings on the absorption t=40 °C 1.2 1.1 1.0 % C 0.9 H A 0.8 N G E 0.7 I N 0.6 V E 0.5 L O 0.4 C I T 0.3 Y 0.2 0.1 t=30 °C t=20 °C t=l5 °C t=l0 °C t=60 °C 0.0 0 RH 100 RELATIVE HUMIDITY IN PERCENT Fig. 4. Relative humidity versus percentage change in speed of sound as a function of temperature. of sound in air. The data are summarized in tables and graphs to highlight the effect of changing relative humidity on air absorption. 3.2 Air Absorption Sound propagates through air as a wave in an elastic medium. Since air is not a perfectly elastic medium, this pulsating action causes several complex irreversible processes to occur. The wave action of air causes minute turbulence of the air molecules through which it passes. Each affected molecule robs the wave of some of its energy until eventually the wave dies completely. If this were not so, every sound generated would travel forever and we would live within a sonic shell of cacophony. Absorption works with divergence. Divergence of sound causes a reduction in the sound intensity due to spreading of the wave throughout the medium. The sound pressure level will decrease 6 dB for each doubling of the distance, that is, it is inversely proportional to the square of the distance. This well-known fact occurs simultaneously with absorption. Absorption describes the energy-exchanging mechanism occurring during divergence. So not only is the wave spreading, it is also dying. 3.3 Air Absorption Mathematics The strict confines of the ideal fluid-dynamic equa- tions cannot explain the attenuation of sound. Theoretical predictions must include bulk viscosity, thermal conduction, and molecular relaxation for agreement with measured results. Conservation of mass, entropy for the gas, and molecular vibrations all enter into the thermodynamic equilibrium equations. To truly understand all the mechanisms of sound absorption in air, the interested reader must be ready to study molecular Table 2. Percentage increase in speed of sound (re 0 °C) due to moisture in air only. Temperature effects not included except as they pertain to humidity. Temperature (°C) 5 10 15 20 30 40 10 0.014 0.020 0.027 0.037 0.068 0.118 20 0.028 0.039 0.054 0.075 0.135 0.236 30 0.042 0.059 0.082 0.112 0.203 0.355 40 0.056 0.078 0.109 0.149 0.272 0.474 Relative humidity (%) 50 60 70 0.070 0.098 0.136 0.187 0.340 0.594 0.083 0.118 0.163 0.224 0.408 0.714 0.097 0.137 0.191 0.262 0.477 0.835 80 0.111 0.157 0.218 0.299 0.546 0.957 90 0.125 0.176 0.245 0.337 0.615 1.08 100 0.139 0.196 0.273 0.375 0.684 1.20 Table 3. Total percentage increase in speed of sound (re 0 °C) due to temperature and humidity combined. Temperature (°C) 5 10 15 20 30 40 0 0.91 1.81 2.71 3.60 5.35 7.07 30 0.952 1.87 2.79 3.71 5.55 7.43 Relative humidity (%) 40 50 0.966 1.89 2.82 3.75 5.62 7.54 0.980 1.91 2.85 3.79 5.69 7.66 80 1.02 1.97 2.93 3.90 5.90 8.03 100 1.05 2.01 2.98 3.98 6.03 8.27 J. Audio Eng. Soc., Vol. 36, No. 4, 1988 April

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BOHN
PAPERS
2.5
Combined Effects
of
Temperature
and Relative Humidity
The results graphed in Figs.
3
and
4,
and also tab
-
ulated in Tables
1
and
2,
can be added together to show
the combined effects of temperature and relative hu
-
midity on the speed of sound. Doing
so
produces Table
3.
Here the total percentage increase in sound speed
is tabulated for easy reference.
3 EFFECT
OF
RELATIVE HUMIDITY
ON THE ABSORPTION
OF
SOUND
IN
AIR
3.1
Introduction
To a certain degree everything absorbs sound,
es
-
pecially air. Wet air absorbs sound better than dry air.
This section presents the latest findings on the absorption
t=40 °C
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
t=30 °C
t=20 °C
t=l5 °C
t=l0 °C
t=60 °C
0
RH
100
RELATIVE HUMIDITY IN PERCENT
Fig.
4.
Relative humidity versus percentage change in speed
of sound as a function of temperature.
of sound in air. The data are summarized in tables and
graphs to highlight the effect of changing relative hu
-
midity
on
air absorption.
3.2 Air Absorption
Sound propagates through air as a wave in an elastic
medium. Since air
is
not a perfectly elastic medium,
this pulsating action causes several complex irreversible
processes to occur. The wave action of air causes minute
turbulence of the air molecules through which it passes.
Each affected molecule robs the wave of some of its
energy until eventually the wave dies completely.
If
this were not
so,
every sound generated would travel
forever and we would live within a sonic shell of ca
-
cophony.
Absorption works with divergence. Divergence of
sound causes a reduction in the sound intensity due to
spreading of the wave throughout the medium. The
sound pressure level will decrease
6 dB
for each dou
-
bling of the distance, that is, it is inversely proportional
to the square of the distance. This well
-
known fact
occurs simultaneously with absorption. Absorption
describes the energy
-
exchanging mechanism occurring
during divergence.
So
not only is the wave spreading,
it is also dying.
3.3 Air Absorption Mathematics
The strict confines of the ideal fluid
-
dynamic equa
-
tions cannot explain the attenuation of sound. Theo
-
retical predictions must include bulk viscosity, thermal
conduction, and molecular relaxation for agreement
with measured results. Conservation of mass, entropy
for the gas, and molecular vibrations all enter into the
thermodynamic equilibrium equations. To truly un
-
derstand all the mechanisms of sound absorption in air,
the interested reader must be ready to study molecular
Table
2.
Percentage increase in speed of sound (re 0 °C) due to moisture in air only. Temperature effects not included
except as they pertain to humidity.
Temperature
Relative humidity
(%)
(°C)
10
20
30
40
50
60
70
80
90
100
5
0.014 0.028 0.042 0.056 0.070 0.083 0.097 0.111
0.125 0.139
10
0.020 0.039 0.059 0.078 0.098 0.118 0.137 0.157 0.176 0.196
15
0.027 0.054 0.082 0.109 0.136 0.163 0.191 0.218 0.245 0.273
20
0.037 0.075 0.112 0.149
0.187 0.224 0.262 0.299 0.337 0.375
30
0.068 0.135 0.203 0.272 0.340 0.408 0.477 0.546 0.615 0.684
40
0.118 0.236 0.355 0.474 0.594 0.714 0.835 0.957
1.08
1.20
Table
3.
Total percentage increase in speed
of
sound (re 0 °C) due to
temperature and humidity combined.
Relative humidity (%)
Temperature
(°C)
0
30
40
50
80
100
5
0.91
0.952
0.966
0.980
1.02
1.05
10
1.81
1.87
1.89
1.91
1.97
2.01
15
2.71
2.79
2.82
2.85
2.93
2.98
20
3.60
3.71
3.75
3.79
3.90
3.98
30
5.35
5.55
5.62
5.69
5.90
6.03
40
7.07
7.43
7.54
7.66
8.03
8.27
J.
Audio
Eng. Soc.,
Vol.
36,
No.
4, 1988
April
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