Rane AD22S "Environmental Effects on the Speed of Sound" Den - Page 5

Papers, Environmental Effects Of Speed Of Sound, J. Audio Eng. Soc., Vol. 36, No. 4, 1988 April

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PAPERS expression to Humphreys's equation as used in thermodynamics.] The average molecular weight of air decreases with added moisture. To see this, M is calculated first for dry air. Dry air composition is ENVIRONMENTAL EFFECTS OF SPEED OF SOUND h. Relative humidity RH (expressed as a percentage) is defined such that 78% nitrogen 21% oxygen 1% argon (molecular weight = 28) (molecular weight = 32) (molecular weight = 40) for a total molecular weight equal to M = (0.78)(28) + (0.21)(32) + (0.01)(40) = 29 where p equals ambient pressure (1.013 X l05 Pa for 1 atm reference pressure) and e(t) is the vapor pressure of water at temperature t. For temperature values in degrees Celsius, representative values of e(t) are e (5) = 872 Pa e (l0) = 1228 Pa e (l5) = 1705 Pa e (20) = 2338 Pa e (30) = 4243 Pa e (40) = 7376 Pa The presence of water (with a molecular weight of 18) causes the total average molecular weight to decrease to 29 - (29 - 18) h, or MW := 29 - ll h (11) Eqs. (10) and (11) modify the two terms from Eq. (5) affected by the addition of water vapor to air. Both are a function of the introduced water molecule fraction To express the percentage increase in the speed of sound due to relative humidity all that remains is to take the ratio of the wet and dry speeds, subtract 1, and multiply by 100. Since both wet and dry speed terms involve the same constant terms (R and T), their ratio will cause these to cancel, leaving Table 1. Velocity of sound in dry air versus temperature. Temperature (°"C) Temperature ("°F) Velocity (m/s) Velocity (ft/s) Subtracting 1 and multiplying by 100 yields - 100 Eq. (14) is plotted in Fig. 4 as a function of relative humidity for six temperature values. Fig. 4 shows the percentage increase in sound speed due to relative humidity only; the temperature values are for accurately specifying the relative humidity. Table 2 gives calculated results for Eq. (14). J. Audio Eng. Soc., Vol. 36, No. 4, 1988 April Fig. 3. Temperature versus percentage change in speed of sound (re 0°C) in dry air.

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PAPERS
ENVIRONMENTAL EFFECTS OF SPEED OF SOUND
expression to Humphreys’s equation as used in ther-
modynamics.]
The average molecular weight of air decreases with
added moisture. To see this,
M
is calculated first for
dry air. Dry air composition is
78% nitrogen
(molecular weight = 28)
21% oxygen
(molecular weight = 32)
1% argon
(molecular weight = 40)
for a total molecular weight equal to
M
= (0.78)(28) + (0.21)(32) + (0.01)(40) = 29
The presence of water (with a molecular weight of 18)
causes the total average molecular weight to decrease
to 29 – (29 – 18)
h,
or
M
W
:= 29 – ll
h
(11)
Eqs. (10) and (11) modify the two terms from Eq.
(5) affected by the addition of water vapor to air. Both
are a function of the introduced water molecule fraction
Table 1. Velocity of sound in dry air versus temperature.
Temperature
(“C)
(°C)
Temperature
Temperature
(“F)
(°F)
Velocity
Velocity
Velocity
Velocity
(m/s)
(m/s)
(ft/s)
(ft/s)
h.
Relative humidity RH (expressed as a percentage)
is defined such that
where
p
equals ambient pressure (1.013 X l0
5
Pa for
1 atm reference pressure) and
e(t)
is the vapor pressure
of water at temperature
t.
For temperature values in
degrees Celsius, representative values of
e(t)
are
e
(5) = 872 Pa
e
(20) = 2338 Pa
e
(l0) = 1228 Pa
e
(30) = 4243 Pa
e
(l5) = 1705 Pa
e
(40) = 7376 Pa
To express the percentage increase in the speed of sound
due to relative humidity all that remains is to take the
ratio of the wet and dry speeds, subtract 1, and multiply
by 100. Since both wet and dry speed terms involve
the same constant terms
(R
and
T),
their ratio will
cause these to cancel, leaving
Subtracting 1 and multiplying by 100 yields
– 100
Eq. (14) is plotted in Fig. 4 as a function of relative
humidity for six temperature values. Fig. 4 shows the
percentage increase in sound speed due to relative hu-
midity only; the temperature values are for accurately
specifying the relative humidity. Table 2 gives cal-
culated results for Eq. (14).
Fig. 3. Temperature versus percentage change in speed of
sound (re 0°C) in dry air.
J. Audio Eng. Soc., Vol. 36, No. 4, 1988 April