International Journal of Computer Applications (0975 8887)

Volume 9 No.12, November 2010

Modeling of Acoustic Wave Absorption in Ocean

T. B. Mohite-Patil. A.K.Saran S. R. Sawant R. H.Chile T. T. Mohite-Patil

Lecturer (Sel.Gr.) Scientist Professor and Head Professor Vice-Principal
D.Y.Patil Engineering NIO, Goa, Shivaji University, Guru Govind Sanjeevan Engg
College, India. Kolhapur, India. College of Engg. College,
Kolhapur, India Nanded, India. Kolhapur, India.

Fisher and Simmons [1] have proposed the equation for the
ABSTRACT sound absorption in sea water as follows.
Effective under-water communication systems require
A1P1 f1 f 2 2
detailed study of acoustic wave propagation in ocean. The
preamplifier parameter tuning techniques for the under- f12 f 2
Af2 P22f2f f2 A3 P3 f 2
2
water communication systems have been greatly affected
by the recent information available on the respective area. (1)
Many investigators have studied the absorption of acoustic
waves in ocean water and formulated empirical equations, Where alpha () is coefficient of absorption in sea
however no one has made an attempt to offer the simulation water.The first term in above equation represents the sound
model for the under-water acoustic propagation. This absorption due to the Boric Acid. The second term gives
paper reports the comparative study of acoustic wave the sound absorption due to magnesium sulfate. The third
absorption carried out by means of modeling in MATLAB.
term indicates the absorption due to pure water. The
The results of simulation have been compared with the
practically measured values in the Arabian Sea near Goa contribution of sound absorption due to other chemical
and Atlantic Ocean. The model has been used to determine ingredients has been found to be negligible. The third term
sound absorption for given values of depth (D), salinity (S), provides sound absorption because of pure water. Constants
temperature (T), pH, and acoustic wave transmitter P1, P2 and P3 indicate effect of pressure. Frequency
frequency (f). From the results a correction factor for dependence is shown by frequencies f1 and f2. These are
faithful reception has been evaluated. Using the correction
relaxation frequencies of Boric Acid and Magnesium
factor, magnitude of the received signal has been corrected.
sulfate, f is the frequency of sound. Values of A1, A2 and A3
depend on water properties such as temperature, salinity
Keywords
Sound absorption simulation model; Salinity; and pH of water.
Temperature; Pressure; Sound Speed; Depth; Frequency;
Mathematical formulae. 1.2 Review of sound absorption
investigations
1. INTRODUCTION Research work on the absorption of sound in sea water
The absorption of sound waves in sea water has been forms topic of interest for many researchers. The outcome
studied by many investigators [1 - 4 ]. Some researchers have of their efforts is the formulation of different empirical
carried out these studies using the measurements made by relations for calculating the sound absorption in sea water
mixing the various ingredients present in sea water while as a function of different sound frequency ranges, different
others have used the measurements actually taken in the sea sound speed ranges and other ingredients of the sea water.
water. The results so far reported through former studies Pinkerton[2] using radar pulses of 7-66MHz frequencies
suffer from errors. This may be because the mixing of has measured the absorption of sound in pure water.
different ingredients is not taking place in the required Leonard[3] at el have measured the absorption sound in pure
proportions. Empirical formulae have been developed by water at frequencies of 15- 480KHz using resonance
these investigators however no one has made an attempt to method. Leonard et al.[4,6] have established that the
design the simulation model for the underwater acoustic presence of MgSO4 in sea water is the cause of increase in
propagation.In the present communication we report sound absorption. Marsh and Schulkin [5] have also
simulation model developed for the acoustic wave developed the equations for sound absorption. Del Grosso
absorption. The results of the simulation model have been [7]
has published the absorption tables to summarize the
compared with the actual results. The agreement is found to results of Kurtze and Tamm. Murphy et al., [8] have studied
be satisfactory. the absorption of sound in natural sea water at frequencies
of 60,142 272,and 467KHz and observed that their values
1.1 Sound absorption are lower than the values determined by Del Grosso. Fisher

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 International Journal of Computer Applications (0975 8887)
Volume 9 No.12, November 2010

[9]
has established the dependence of pressure on the sound sound speed (SS) from outside world with the Simin
absorption using the laboratory measurements. Shulkin and subsystem. Already measured data has been read with this
Marsh [5] adjusting the constants in the sound absorption subsystem. The prerecorded data imported in MATLAB
equation based on Wilson- Leonards data [6], have devised workspace from excel file has been read by simin
the equations which are functions of Salinity, Temperature subsystem. The coefficient of sound absorption has been
and Pressure.Fisher and Simmons[1] have published sound determined by using this data with the simulation model
absorption equation based on the measurements carried out shown in fig.2.
by Lyman and Fleming[10] in artificial sea water. R.E.
Francois and G. R. Garrison [11] have formulated the
equation for the sound absorption in the frequency range
400Hz to 1MHz which includes the contribution of Boric
Acid, Magnesium Sulfate and Pure water. The results given
by this equation are very close to the practical results. We
have used this equation to develop the model of sound
absorption.

2. SIMULATION MODEL
The main simulation model of sound absorption and
correction is shown in fig.1.

Fig.2 Simulation model for sound absorption

Fig.1. Main Simulation model for sound absorption and

correction in sea water
Fig.3. Reading external data for the Simulation model
It consists of five sub models namely
Absorption coefficient due to Boric Acid
Simin subsystem
A1P1 f1 f 2
Sea water parameter reading subsystem attn1
f12 f 2
Observed sound absorption coefficient 8.86 (0.78 pH - 5)
subsystem A1 = 10 , dB Km-1KHz-1
c
P1 =1,
Sound absorption coefficient
35 4 - 1245 ,
0.5
calculating subsystem f1 =2.8 S 10 KHz
Sound absorption coefficient correcting Where c is the sound speed (m/s), given by
subsystem c=1412+3.21T+1.19 S+0.0167 D,
Acoustic Wave attenuating subsystem
T is the temperature( 0 C),
Attenuated acoustic signal correcting subsystem
The simulation model reads the data concerned with sea =273+T,
water parameters such as temperature(T), pressure(P), S is the salinity( 0 00), and D is the depth (m).
salinity(S),depth(D), pH of sea water(pH),frequency(f),

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 International Journal of Computer Applications (0975 8887)
Volume 9 No.12, November 2010

Absorption coefficient due to MgSO 4 shown in figure 4. It consists of variety of mathematical

operation blocks like multipliers, adders, dividers, power
A2 P2 f 2 f 2 blocks and constant blocks. With these basic mathematical
attn2
f22 f 2 blocks the value of sound absorption due to boric acid is
S
A 2 =21.44 1+0.025T dB Km -1 KHz -1 estimated for the formulae given by Fisher and Simmons.
c
The sound speed is estimated by using the formula given by
P2 =1-1.37 10-4 D+6.2 10-9 D 2
R.E. Francois and G. R. Garrison. This calculated sound
8.17 10
8 - 1990

f2 = KHz speed is used to calculate the coefficient of absorption. The
1+0.0018 S-35 other terms like A1, P1, f1 and (degree kelvin) are also
Absorption coefficient due to Pure Water estimated with this model. The resultant coefficient of
absorption due to boric acid is outputted on output port1
attn3 A3 P3 f 2 named as attn1.

For T 200C,
A3 =4.937 10-4 -2.59 10-5 T+9.1110-7 T 2 - 1.50 10 8 T 3 dB Km-1 KHz -2

For T 200C,
A3 =3.964 10-4 -1.146 10-5T+1.45 10-7 T 2 - 6.5 10-10 T 3 dB Km-1KHz -2
P3 =1 - 3.83 105 D + 4.9 1010 D 2

The operation of this model is based on the R.E.Francois

and G.R. Garrison empirical formula for calculating the
coefficient of sound absorption. From equation 1 it is seen
that three factors contribute for the absorption of sound
waves in sea water namely Boric Acid, Magnesium sulfate
and pure water. The absorption coefficient has been
determined with the simulation model as shown in fig 2
taking into account these three factors. The input data files
have been read from workspace of MATLAB with simin
submodel as shown in fig 3 In detail design of Boric Acid
contribution based simulation model is as in figure 4. The Fig.4. Simulation model of sound absorption due to Boric
functioning of this model is based on the contribution of Acid in sea water.
Boric Acid to absorption of the acoustic wave. Similarly
absorptions due to the Magnesium Sulfate (MgSO4) and The sound absorption due to magnesium sulphate in sea
pure water have been determined by the simulation models water is estimated with the model shown in fig. 5. This
shown in fig (5) and fig (6). These models are based on the model is designed by using different blocks like input port
formulae as follows.The sound absorption model shown in block (through which the data concerned with the different
figure.2 is main model which calculates the coefficient of parameters of sea water like salinity, temperature and
absorption of sound. The basic data like salinity, depth), adder, multiplier, and divider, exponential and
temperature, ph, depth and frequency to calculate the sound constant block. With these basic blocks the basic terms A2,
absorption is read from the input ports shown by numbers P2, and f2 are used to calculate the coefficient of absorption
ranging from 1 to 6. The coefficient of absorption due to due to magnesium sulphate and it is output on output port1
Boric acid, due to magnesium sulpate and pure water are named attn2.The model shown in fig.6 is designed using
estimated by three subsystems and resultant is obtained by basic blocks like input port, adder, multiplier, exponential
adding those three coefficients with a sim block adder.Error output port and constant block. This model estimates the
in calculated sound absorption coefficient and observed terms A3, P3 and calculates the coefficient of absorption
sound absorption coefficient has been determined with the due to pure water. This value is output on output port1
simulation model as shown in fig 9. The required data to named as attn3.
calculate the coefficient for absorption of sound in sea
water is read from the excel files with the help of the simin
blocks as shown in fig. 3. This data is output to the
subsystems which do actual calculations for the coefficient
of absorption. The schematic of simulation model designed
to calculate the sound absorption due to boric acid is as

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 International Journal of Computer Applications (0975 8887)
Volume 9 No.12, November 2010

ACO 1
1
SIGNAL
ATTN
MULT
2 ALPHA WATER

Fig.7. Simulation model of sound correction

1
ATTN 1
SIGNAL CORRECTED O/P
2
COEFF. Divide
ABSORPTION

Fig.8. Simulation model of sound wave absorption (attenuation)

factor correction model.

The model in fig.8 is named as correction model which consists

of input port block, divide and output port. Through input port
block 1 the attenuated signal is read. The resultant coefficient of
absorption estimated by the different models explained earlier is
Fig.5. Simulation model of sound absorption due to
read through input port 2. With divide block the attenuated
Magnesium Sulfate in sea water.
acoustic signal is corrected to input propagated signal and put
on output port 1 named as corrected output.

1
ALPHA
CALCULAT ED

2 1

ALPHA ALPHA ERROR

OBSERVED ALPHA ERROR

Fig.9. Sound absorption error detecting simulation model

Error in calculated sound absorption coefficient and observed

sound absorption coefficient has been determined with the
simulation model as shown in fig 9. with two input ports named
as alpha calculated and alpha observed the data concerned with
calculated coefficient of absorption and the observed coefficient
of absorption is read and an error in alpha is calculated with
subtract block.

Fig.6. Simulation model of sound absorption (attenuation) 2. RESULTS

due to Pure Water. -3
Coefficient of Absorption V/S Depth(m)
x 10
7.8

The model shown in fig.7 generates the attenuated acoustic 7.7

signal artificially using blocks like input port, multiplier

Coefficient of Absorption

and output port. The attenuation provided to the acoustic 7.6

wave propagating through sea water is totally governed by

7.5
the resultant coefficient of absorption of the sea water. The
multiplier block multiplies the transmitted acoustic signal 7.4

with the resultant coefficient of absorption and gives

artificially attenuated acoustic signal to the output port1 7.3
0 10 20 30
Depth(m)
40 50 60

named as ATTN water.

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 International Journal of Computer Applications (0975 8887)
Volume 9 No.12, November 2010

Fig.10. coefficient of absorption V/S Depth Fig.14. Coefficient of absorption due different parameters

COEFF. OF ABSORPTIONS AT MEDITERIAN SEA

0.7
INPUT AND ATTND SOUND SIGNAL CALCULATED COEFF. OF ABS.
10 0.6 OBS. COEFF. OF ABS.
ERROR IN COEFF.OF ABS.
0.5

COEFF. ABSORPTION
5 INPUT SOUND SIGNAL
0.4
AMPLITUDE(V)

ATTND SOUND SIGNAL

0.3
0
0.2

-5 0.1

0
-10
0 10 20 30 40 50 60 -0.1
0 5 10 15 20 25 30 35 40
TIME
FREQUENCY(KHz)

Fig.11. The transmitted acoustic signal and attenuated Fig.15. Simulation result for data at Mediterian Sea
signal
COEFF.OF ABS AT MEDITARIAN SEA
INPUT AND CORRECTED SOUND SIGNAL 0.7
COEFF OF ABS DUE TO DIFFBORIC ACID
10 INPUT SIGNAL 0.6
COEFF OF ABS DUE TO MgSO4
COEFF OF ABS DUE TO H20
CORRECTED OUTPUT SIGNAL
AMPLITUDE(V)

TOTAL COEFF. OF ABS.

0.5
Fig.12.5 Corrected output acoustic signal 0.4

COEFF.ABS
0.3
0
0.2

-5 0.1

0
-10
0 10 20 30 40 50 60 -0.1
0 5 10 15 20 25 30 35 40
DEPTH(D) FREQUENCY(KHz)

Fig.16. Coefficient of absorption due to different

parameters

Fig.12. Corrected output acoustic signal

3.1 Comments on graph
Figure.10. represents variation of total absorption of sound
COEFF.OF ABS.V/S FREQUENCY AT ATLANTIC OCEAN
0.2
CALCULAT ED ALPHA(COEFF.OF ABS)
waves as a function of depth of sea for the practical data
COEFF. OF ABSORPTION

0.15
OBSERVED ALPHA (COEFF.OF ABS) collected at Goa. It is seen that the total absorption is
ERROR IN ALPHA (COEFF. OF ABS)

0.1
maximum (7.8x 10-3dB.Km-1) at about 220m distance from
the sea surface. The transmitted acoustic signal and the
0.05
attenuated acoustic signal are shown in fig.11 and fig.12.
0 The simulation results are shown in fig.13 and fig.15
-0.05 where in the calculated alpha and simulated alphas have
0 5 10 15 20 25
FREQUENCY(KHz) been compared and the error has been calculated. The error
observed is negligibly small. Also individual contribution
Fig.13. Simulation result for data at Atlantic Ocean of sea parameters is also shown in fig.14 and fig.16.

4. CONCLUSION
With the present simulation model coefficient of
absorption has been calculated by inputting the sea water
parameters. Using these absorption coefficients the
COMPARATIVE STUDY OF COEFF.ABS DUE TO DIFFERENT SEA INGRADIENTS
0.2
simulation model corrects the received acoustic signal. In
COEFF OF ABS DUE T O BORIC ACID
COEFF OF ABS DUE T O MgSO4
this manner the simulation model proposed helps provide
0.15
COEFF OF ABS DUE T O H2O
faithful reception in the underwater communication
COEFF.ABS

T OT AL COEFF OF ABS SEA WAT ER

0.1
irrespective of the sea and water quality.
0.05

0
5. ACKNOWLEDGEMENTS
-0.05
0 5 10 15 20 25 30 The authors are thankful to the National Institute
FREQUENCY(KHz)
of Oceanography (NIO) Goa, India for providing the
practical data of whole year of Arabian Sea water.

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 International Journal of Computer Applications (0975 8887)
Volume 9 No.12, November 2010

6. REFERENCES [7] V.A. Del Grosso, Dependence of sound absorption

on concentration, frequency, and temperature in
MgSO4 solutions equivalent to sea water Naval Res.
[1] F.H.Fisher and V.P.Simmons, Sound absorption in
Lab., Washington, DC (January 1954).
sea water, J. Acoustic. Soc. Am.62, 558564(1977).
[8] S. R. Murphy, G. R. Garrison and D. S. Potter,Sound
[2] J.M.M .Pinkerton, A pulse method for the
absorption at 50 to 500 kc from transmission
measurement of ultrasonic absorption in liquids:
measurements in the sea, J.Acoust. Soc. Am.30,
results for water, Nature 160,128(1947).
871875(1958).
[3] R. W. Leonard, The attenuation of ultrasonic waves
[9] F. H. Fisher, Effect of high pressure on sound
in water, J.A coust. Soc. Am. 20, 224(1948).
absorption and chemical
[4] R.W. Leonard, P.C. Combs, and L.R. Skidmore, The equilibrium,J.Acoust.Soc.Am.30,442448(1958).
attenuation of sound in synthetic sea water,
[10] J. Lyman, R. H. Fleming, Composition of sea
J.Acoustic. Soc. Am.21, 63(1949).
water,J.Mar.Res.3,134-146(1940).
[5] H. W. Marsh and M. Schulkin, Report on the status
[11] R.E.Francois and G.R. Garrison,Sound absorption
of Project AMOS Tch. Memo. No.1110-023-52,
based on ocean measurements.PartII:Boric acid
U.S.Navy Underwater Sound Lab., New London, CT
contribution and equation for total absorption, J.
(1952).
Acoustic. Soc. Am.72(6),18791890(1982).
[6] O. B. Wilson, Jr., R. W. Leonard, Measurement of
sound absorption in aqueous salt solutions by a
resonator method,J. Acoustic. Soc. Am. 26, 223-
226(1954).

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