The fabrication of parts for the acoustic ground impedance meter was completed, and the instrument tested. Acoustic ground impedance meter, automatic data processing system, cooling system for the resonant tube, and final results of sound absorption in N2-H2O gas mixtures at elevated temperatures are described

Becher, J.

Meredith, R. W.

Zuckerwar, A. J.

English

NASA Technical Reports Server

  
 
 
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DEPARTMENT OF PHYSICS
SCHOOL OF SCISNCE^ AND HEALTH PROFESSIONS
4
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F— NORFOLK; VIRGINIA
Technical Report PTR-81; 4
 ;^^" _ PROPAGATION OF SOUND THROUGH THE EARTH S.
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Harlan K. Holmes, Technical Monit	 v	 ^,
4yInstrument. Research Division	 '"`-.°
January 1981
DEPARTDiENT OF PHYSICS
SCHOOL OF SCIENCES AND HEALTH PROFESSIONS
OLD DOMtINION UNIVERSITY
NORFOLK, VIRGINIA
Technical Report PTR-81-4
PROPAGATION OF SOUND THROUGH THE EARTH'S
ATMOSPHERE:
It MEASUREMENT OF SOUND ABSORPTION IN THE
AIR AND
IIi MEASUREMENT OF GROUND IMPEDANCE
By
Jacob Becher
and
Ruger IV. Meredith
Principal Investigator: Allan J, Zuckertvar
(from January 1 to September 28, 1980)
Final Report
For the period July 1, 1980 - June 30, 1981
Prepared for the
National Aeronautics and Space Administration
Langley Research Center
Hampton, Virginia 23665
Under
Research Grant NAG1-l5
Harlan K, Holmes, Technical Monitor
Instrument Research D;.,ision
Submitted by the
Old Dominion University Research Foundation
P.O.  Bose 6369
Norfolk, Virginia 23508
January 1981
a
PROPAGATION OF SOUND THROUGH THE EARTH'S ATMOSPHERE:
I. MEASURDIENT OF SOUND ABSORPTION IN AIR AND
II. MEASUREMENT OF GROUND IMPEDANCE
By
Jacob Becher l
 and Roger N, Meredith
SM04ARY
This report summarizes work accomplished under NASA grant NAG1-15 since
July 1, 1980. This work is described under four major subject headings:
(1) acoustic ground impedance meter, (2) automatic data-processing system,
(3) cooling system for the resonant tube, and (4) final results of sound
absorption in Nu-H ., O gas mixtures at elevated temperatures.
ACOUSTIC GROUND IMPEDANCE NICTER
The fabrication of parts for the acoustic ground impedance meter has
been completed, and the instrument has been tested. The volume velocity
source, using the five-lobed cam and the LED-photodiode monitor, functioned
as expected. However, mechanical vibrations from the volume velocity
source produced chatter to such an extent as to overwhelm the microphone
signal. This problem was eliminated by unscrewing the resonator neck
from the chamber and reconnecting the two parts by means of a rubber hose
to suppress vibration. The neck is currently being modified for mounting
on the center post of a camera tripod. It can then be lowered to a
Favorable height above the chamber and connected with the rubber hose,
lAssociate Professor, Department of Physics, told Dominion University, Norfolk,
Virginia 23508.
"Research Associate, Old. Dominion University Research Foundat;',on, P.O. Box
6369, Norfolk, Y'_rgina 25508.
YAUTOMATIC DATA-PROCESSING SYSTEM
The Datel Interstl A./D converter model ADC-HC12B has been successfully
integrated into the Apple II Computer detection system. $oftware for
controlling the A/D conversion rate and data storage is currently being
developed and tested. Software for graphics and evaluation of the free
decay curves has been initiated.
COOLING SYSTEM FOR THE RESONANT TUBE
When the initial cooling system proved ineffective in cooling the
resonant tube to 0° C (32' F), the cooling system piping was insulated.
Even with the added insulation; the cooling system was ineffective. The
cooling system was modified to use liquid nitrogen coolant by passing
liquid nitrogen from a nearby trailer, The liquid proved to ))e sufficient
to cool the resonant tube to the required temperature; however, the
temperature gradient 
within 
each of t he fo U.L. tube sections reached unac-
ceptable levels. Figure 1 shows the results of the cooling test and the
resulting temperature gradient for one tube section. Modifications to the
cooling system are presently being designed and implemented so that each
tube section can be cooled more uniformly.
FINAL RESUI;rS OF SOUND ABSORPTION IN No-HqO GAS MIXTURES
AT ELEVATED TEMPERATURES
Final measurements of deexcitation of nitrogen by water vapor were
reported at the 100th Meeting of the Acoustical Society of America
in the fall of 1980. The results indicate that the physical process
responsible for the deexritation is not the direct vibration-translation
energy transfer, but is a vibration-vibration energy transfer. The
results also indicate that ANSI Standard S1.26/ASA 23-1978 predicts an
excessive shift of the nitrogen relaxation frequency with humidity.
This paper is reproduced in the Appendix.
11
i
0
	
25	 50	 75
120
tJ
50
15
5
TIME (HOURS)
Figure 1. Temperature gradient in one tube section. The large temperature
gradient results from liquid N ,, going in one end and gaseous N,
coming out the other end of the tube section.
3
APPENDIX
SOUND ABSORPTION IN N ,,-HiO GAS MIXTURES AT
ELEVATED TEMPERATURES
By
Allan J. '"AuckerwaT and Roger W. Meredith
Presented at the 100th Meeting of the Acoustical
Society of tWerica, fall 1980,
4
SOUND ABSORPTION IN N Z-H20 GAS MIXTURES AT
ELEVATED TDIPERATURES
By
Allan J. 7.uckerwar and Roger W. Meredith
The purpose of our measurements is to make a decisive determination of
the physical process responsible for the deexcitation of nitrogen by water
vapor, and to compare the measured temperature dependence of the sound
absorption with that of the new ^W51 standard, "America National Standard
Method for the Calculation of the Absorption of Sound by the Atmosphere"
(51.26/ASA 23-1978).
The first slide shows the results of sound absorption measurements in
a typical mixture of nitrogen and water vapor at three different temperatures.
The water vapor content for this particular composition is 3500 parts per
million. The sound absorption u, in nepers/wavelength, is plotted against
frequency/pressure (£/P) ratio. The data define a pronounced peak - the
vibrational relaxation peak of nitrogen - at each temperature. Tile value
of f/P at the crest of the peak is called the "relaxation f/P" or "(f/P)
mate" and lios at about 60 liz/atm for this mixture.
The data appear in a more or less uniform band about a baud curve,
owing to the random nature of the background damping. With increasing
temperature the accuracy of the measurement improves considerably as the
peak soars above the background. The solid lines represent the best fit
to the Debye relaxation curve, (f/P) max being the only adjustable para-
meter, The peak height was computed with the aid of the Planck-Einstein
formula. Eight such sets of data were taken at humidities ranging from
10 ppm to a maximum of 3 mole o.
Slide 2. Here (f/P) max is plotted against humidity for 21 of the 24
measured relaxation peaks. The data for the lowest value of humidity fall
beyond the range (*f the graph and are not shown. At low humidities all the
data lie on the same straight line, having a slope of 184 liz/atm • mole 15,
which is independent of temperature. This agrees well with Griffin's room-
temperature slope of 200 Hz/atm • mole	 reported at the Cambridge meeting
last year (ref. 1). At high humidities the data deviate from the linear
5
Ifit. At 298* K the deviation, falls within the experimental error. At the
higher temperatures the deviation lies well beyond the error and is con-
F'	 sidered a real phya;cal effect.
Slide 3. On this slide the relationship between relaxation frequency,
referred to 1 atm, and humidity is compared with past results. At law
humidities our slope shows good agreement with that obtained by Evans (ref. 2).
The data of Chang, Shields, and Bass (CiSB) (ref. 3), taken at much higher
humidities (starting at 4 mole %), yield the somewhat greater slope of 260
Hw/atm^mole	 The problem is to reconcile the existence of two different
slopes at low and high humidities. Fortunately, theory enables us to do this.
Slide 4. The nitrogen -water vapor system is an example of a two-component
system, where both components are excitable. Deexcitation of the vibrational
degrees of freedom takes place by means of five reactions. The reaction rate
kjo for the deexcitation of nitrogen by itself is extremely slow and will
be neglected. The second reaction rate ko represents the deexcitation
of nitrogen by water through direct vibrational-translational transfer.
Traditionally this reaction has been assumed to be dominant and leads to a
strictly linear relationship between (f/P) max and humidity, that is, to a
single slope. In the model that we propose here k 2o is considered small,
and the deexcitation process takes place through the last three reactions.
Rate k3 o represents vibrational-vibrational transfer between the nitrogen
and water molecules, kpo the deexcitation of water by itself, and k50
the deexcitation of water by nitrogen.
Slide 5. The Tuesday-Boudart analysis yields the following expression
for the slope of the 21r(f/P) max vs. h relationship in terms of the
reaction rate constants. It should be noted that the matrix formulation by
Bauer for this particular system yields identical results, but the Tuesday-
Boudart analysis is chosen because it lends itself more readily to physical
interpretation. The reaction rates k, 0 and k j o are neglected. Now
consider the remaining fraction. At low humidities only the leading terms
in the numerator and demoninator are important, and these determine the
low-humidity slope S 1 . At high humidities the latter terms in the
numerator and denominator become dominant; and when only these are retained,
we obtain a different slope—the high-humidity slope S 2 . Thus, the
theory leads to one value of slope at low humidities and another value of
6
slope at high humidities. The situation is quite different in the oxygen-
water vapor system, where the reaction k Q 3 is so large that the second
term in the denominator never really becomes dominant for values of humidity
normally encountered.
Slide 6, The function S(h) is plotted against humidity on a log-
arithmic scale. The circles are Griffin's data points at room temperature.
The triangles are the data of the CSB group (ref. 3). The solid line is
the best fit of the Tuesday-Boudart formula to both sets of data with k4o
as the only adjustable parameter. Thus the V-V model not only rccounts for
the existence of two slopes, but also fits bath sets of data, There are
two possible objections to the V-V interpretation. First, the rate constant
k c}o for the deexcitation of water by itself is smaller than the values
obtained from past experiments. The dash lines are similar plots using
other values of kayo derived from the literature. Actually, a value of
k;,p as high as 5 x 10 7 is consistent with the data. Secondly, it might
be argued that a single straight line, with a slope somewhat less than 1.5
^5	 .C..t 7	 'yL1.^ tL^. -
	
L	 7.+ F •. n 1. It- f +U_ ntn	 Th1V-, would -Ea.11 Wr 47i1t1 he error uounds o4 ;.he 	 ^i T .,..v ^- —	 ^^
is true for the room-temperature data and is our primary motivation for
obtaining the more accurate data at elevated temperatures.
Slide 7. Here we see slope versus log humidity for all three tempera-
tures. As before the solid lines are best fits of the Tuesday-Boudart
formula. At room temperature the existence of two slopes is barely notice-
able and concealed within the experimental error. The situation changes
at higher temperatures, where the change of slope at high humidity lies
well beyond the experimental error. A triangle represents a CSB point
at the closest corresponding temperature. Agreement is quite good.
Slide 3, This is a Landau-Teller plot for the V-V process. The
solid circles are derived from the low-humidity slope. The rate constant
represents a series combination of k3 o and kco and is independent of
temperature. The remaining data belong to the high-humidity slope k3o.
The solid line is the best fit to our own and past data, The data chosen
to determine the line are those points whose error: bars intersect the line,
these include Henderson's point (ref, 4), three CSB points, Evan's point,
and three of our own, Each point is weighted according to how many
humidity values were used to establish the slope. The shock tube data
7
of Huber and Kantrowit (ref. 5) show too touch scatter and are not included.
Once we get above room temperature the error assigned to the various data
points demonstrates the existence of two slopes beyond any doubt.
Slide 9. We analyzed our own data and accountail for the 78 percent
dilution in air to compare our measured relaxation frequencies with Chose
specified by the new ANSI Standard, The values chosen correspond to the
extremes of temperature and humidity specified in the standard.,. The first
thing to notice is that the standard predicts tar too great a shift of the
nitrogen relaxation frequency with humidity, The standard is in error any-
where from 3S to 75 percent. Secondly, the standard does not account for
the change in slope. However, a tenfold increase in humidity produces only
a slightly greater than tenfold increase in relaxation frequency, so that
the error due to the two-slope effect is not very serious. finally, a 40° C
increase in temperature increases the relaxation frequency by a factor of
8.5 according to the standard but by a factor of 13 according to measurement.
For frequencies below 2000 }it, where Sound
 absorption in nitrogen becomes
the dominant process in the Lartl ► t s atmosphere, the new ANSI Standard, whale
more accurate than anything available previously, could still lead to a
substantial measurement error,
REFERENCES
1. A.J. ""uckerwar and W.A. Griffin, J. Acoust. Soc, Am. 65, S48 (A) (1979).
L.B. Evans, J. Acoust. Soc, Am. Sl, 409-411 (133').
3. D. Chang, F.D. Shields, and H.E. Bass, J. Acoust. Soc. Am. 63, 577-58
(1973).
4. M.C. Henderson et al., J. Acoust. Soc. Ain. 45, 109-114 (1969).
S. P.W. Huber and A. kantrowitz, J. Chem. Whys, 15, 375 -2S1 (1947).
8
M.._._,	 ._. __^
._.4
25
f
Y
20
riZ IS
F
10
3
SOUND ABSOPTION IN Nq•N oA AMURES
0
3.16	 31,6	 316
FREQUENCY/ PRESSURE (Hz /atm)
Slide 1
9
> >	 ^*
x
1000
100
E
v
N
r.
a
wV
10
VIBRATIONAL.. RELAXATION IN NITROGEN
tf/P),,i VS. HUMIDIFY
7-
0.01	 0.1	 !	 10
HUMIDITY ( mole %)
Slide
10
zc
z
A I
X
C ifs U n AnnrAn+1*Att,5n resuits — Da3t and pre3ent
	 10.6
H.0 CONCENTRATION (MOLE 9/6)
Slide 3
11
Reaction Rates
(kl,o, koi)
(k20, k02)
(k 3 a, kQ3)
(k40, ko4)
(iso, kos)
+ N2 =N2 + N2
lq*Z .+ H20 =N2 + H20
N* + H^O ^ N2 + H20*
H20* + H20 -H20 + H20
H20* + N2 ==H20 + N2
Slide 4
12
Slope According To Tuesday w Boudart
	
[ it (f/P)max
	
ki o l
ksokso + kso(k4o ° keo)h
k2o • kio + Ro3 * kso
" + (' K'4o~: R30 Kga
ksakso
SOO + S i - kzo _ k10 +	 boa + ; Q 	 (h small)
ks o (k4 0 - 'ks o)
S(h) 
-r Sj x k2o	 kxo +	 —	 k	 (h large)
k40 - kso - oa
Slide S
13
.. tn52.3
2.0
cO
U
avw
1.5
C
1.0
Nz
a^
^ 6	 4	 -5	 .4	 -3	 -2	 -1	 0
LOG HUMIDITY (mole fraction)
Slide 6
14
SLOPE VS, HUMIDITY
2	 1^5
^	 I
0
v-
u
E	 0
`0	
2
N
VI
l^
rN
N
t
^ 0
^	 2
a0
G)
0 l	 .	 1	 1	 1	 1	 1
.6	 -S	 -4	 -3	 -2	 -1	 0
IM HUMIDITY (mole fraction)
Slade 3
x
e
l5
S
TEMPERATURE (°K)
10
	 0 600	 500	 400	 300
^- x X05
v
v
17
9
8
7
6
47
0
E
0 3
z0U 2
^a
LANDAU - TELLER PLOT
H2* + H2O	 N2 * H20•
0 ZUCKERWAR & MEREDITH (HIGH N)
ZUCKERWAR g MEREDITH (LOW H)
n CHANG, SHIELDS, & BASS
a EVANS
0 HENDERSON ET, AL,
v	 v HUBEcR s KANTROWITZ
vv
v
v ° v
v
v
0.11	 0.12	 Q13	 0.14	 G15
	 Q16
(TEMPERATUR6v3 (°K f1/3
Slide s
Ica
RELAXATION FREQUENCY OF NITROGEN IN AIR AT 1 ATM
R.N. m 10% R.N. - 1OOZ
T-273°K Z&M 8,55 Hz 87,18 Hz
ANSI 21,11 211.05
T-313°K ZW 108.17 U54.44
•ANSI 179.19 1701,90
Slide J
1'^'


Propagation of sound through the Earth's atmosphere. 1: Measurement of sound absorption in the air. 2: Measurement of ground impedance

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