NOLTR UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK,, MARYLAND 1

Transcription

1 ACOUSTIC IMPEDANCE OF SEAWATER AS A FUNCTION OF TEMPERATURE, PRESSURE AND SALINITY 3d 19 JULY 1966 UNITED STATES NAVAL ORDNANCE LABORATORY, WHITE OAK,, MARYLAND 1 CLEARINGHOUSE FOR FEDEPAL SCIIINTIFIC AND TECHNICAL 1NFO1IMATION Har' p- M ic- rorich - - Distribution of this document is unlimited.

2 ACOUSTIC IMPEDANCE OF SEA WATER AS A FUNCTION OF TEMPERATURE, PRESSURE AND SALINITY by David L. Bradley and Wayne D. Wilson Approved by T. F. Johnston Acoustics Division ABSTRACT: The acoustic impedance (pc) of sea water is presented as a function of temperature, pressure and salinity. This acoustic impedance has been calculated from empirical equations developed at the Naval Ordnance Laboratory to represent the velocity of sound and density of sea water as functions of the parameters temperature, pressure, and salinity. Tables of the calculated data and graphs are given. Physics Research Department U. S. Nz Uial Ordnance Laboratory White Oz., Silver Spring, Maryland

3 19 July 1966 Information on the acoustic properties of sea water is of continuing interest to the U. S. Navy. In anticipation of the future needs of the Fleet, information has been obtained on the extremes of temperature, pressure and salinity and various related acoustic properties likely to be needed in naval applications. The present work was funded under FR-27, "Structure of Liquids". This information will be useful to anyone computing the transmission properties of acouatic waves in sea water. "CM W J. DARE S MUtE m IFb1,,OU II II.', Cap-tadin, USN C mmander A Z. I. SLATISKY Y.... By direction 10.t AVAL mdiwo MMU* ii Ll

4 TABLE OF CON~TENTS Page INTRODUCTION 1 THE ORY 1 EQUATIONS 2 RESULTS 3-3 v -5

5 LIST OF ILLUSTRATIONS Tables I - V - Computed Values of Acoustic Impedance of Sel Water Figure 1 - Acoustic Impedance of Sea Water at 0 C. Figure 2 - Acoustic Impedance of Sea Water at 10 0 C. Figure 3 - Acoustic Impedance of Sea Water at 20 0 C. Figure 4 - Acoustic Impedance of Sea Water at 30 0 C. iv

6 INTRODUCTION T characteristic impedance of a medium for acoustic wavesli) is analogous to the index of refraction (n) of a tjsparent medium for light waves and to the wave impedance V Lof a dielectric medium for electromagnetic waves. The product of the velocity of sound (c) and the density () provides a measurement of this characteristic impedance and is useful in the investigation of transmission phenomena of acouitic plane waves. The results presented in this report were obtained from two empirlr equations based on precision data taken at NOL. The first represents sound velocity in sea water as a function of the three parameters: temperature, pressure and salinity. The second equation( 3 ) represents the specific volume of sea water as a function of the same parameters. Both equations were developed to represent experimental data obtained from laboratory measurements. The product of the two, (c x 1/v), provides the acoustic impedance. The impedance data was calculated for the following parameter ranges: Temperature: OOC < T < 300c, pressure: I bar < P < 1000 bars, salinity: 09bo < S < 379bo. The bar as used in this report means 106 dyne/an 2. ThEORY To avoid confusior,, a brief summary of the various impedance terms is given. There are three kinds of acoustic impedances in common usage. First, the ratio of pressure to volume velocity, 2 which is useful in discussing acoustic radiation from vibrating surfaces, and the transmission of this radiation through lumped acoustic elements at low frequencies. Second, the radiation impedance 2r, the ratio of force to velocity, is useful in calculating the coupling between acoustic waves and a driving source or driven load. It is part of the mechanical impedance of a vibrating system associated with the radiation of sound. Last, the specific acoustic impedance, is a characteristic property of the medium and of the type of waves that are being propagated through it. By definition, the complex ratio of acoustic pressure (') in a medium to the associated particle velocity (U') is the srecific acoustic impedance. In general Z P-r+ jx, u

7 where Z = is a complex quantity. The term r is called the specific acoustic resistance and x the specific acoustic reactance of the medium for the particular wave motion being considered. EQUATIONS The equations representing the sound velocity and specific volume in sea water are empirical equations which were fitted to the laboratory experimental data. The coefficients of the equations were obtained by making a least squares fit to the experimental data on an IBV computer. Equation (1) can be used to calculate the sound velocity and Equation (2) the specific volume. C = T x 10-2 T x 10-4 T x 10-6 T x 10-1F x 10-5F x 10-9F x i (S-35.0) x 10-3 (S-35.0) 2 + (s-35.0) ( x 10-2 T x 10-7 T x 10-5p x I0-7P2 (1) x 10-8 PT x 10-9PT 2 ) F ( x 10-4T x 10-6T x 10-ST p 2 ( x 10-7T x 10- T 2 ) P3 ( x 10-10T) v = ,001055T-0., T 2( T)S P T T S The units of the various parameters are: Specific volume (cm 3 /gm), sound velocity (m/sec), temperature (OC), pressure (bars) and salinity (/bo). The standard ceviations were computed from the expression N2 r (x e - xc n=1 c Cr = N - (3) (2) N-kW... p2

8 where xe and x c are experimental and calculated data points respectively, N is the total number of data points and k the number of coefficients in the representative equation. For Ecp1ation (1) a a 0.30 m/sec and for Equation (2) a = cm /gm. These standard deviations show how well the empirical equations fit the experimental data. The equations are very convenient for machine conputations since they provide analytic expressions for the data. R~ESUJLTS The results from the computations are shown in Tables I to V and also are presented graphically in Figs. 1 to 4. 3

9 REFERENCES 1. Kinsler and Frey, "Fundamentals of Acoustics", Wiley and Sons, New York (1950). 2. W. Wilson, J. Acoust. Soc. Am., 32, 1357 (1960). 3. W. Wilson and D. Bradley, NOLTR , 1-41 (1966). h

10 TABLE I Salinity a 00/oo 2 Acoustic Impedance (gm/cm2 sec) T p 0 C 10 0 C 20 C 30 C 1 bar 1.402x x x x " " " " " " " g

11 CABLE II Salinity - 100/00 2 Acoustic Impedance (gm/cm2 -sec) P T o 0 C 100C 20 C 300C 1 bar 1.427x x10 5 A. 502x x " " " " " " " " " "

12 TABLE III Salinity - 200/00 2 Acoustic Impedance (9m/c1n2 sec) P T 0 0 C 10 0 C 2 0 C 3 0 C 1 bar 1.452x x xi x " " " " " " '

13 TABLE IV T Salinity = 30 /oo 2 Acoustic Impedance (gm/cm2 sec) P 0 0 C 10 C 20 C 30 0 C 1 bar 1.477x x xi xi o " g "b i " " " "

14 TABLE V Salinity a 350/00 Acoustic Impedance (gm/cm. sec) T p 0 0 C 10 C 20 C 30 C 1 bar 1.490x x x x " ' " " " " " "

15 I.880X10 5 NOLTR (3) ()S %

16 NOLIR 66-;, X Laj C.) X _.6-2, K SALINITY Moo.) FIG. 2

17 1.88 X105NOR K C.)) I0[ / SA LINI T Y ( FIG 3

18 NOLIR X S OO SPk 00 CL 00 p T 30 *C SALINITY (0) FIGA.

19 UNCLASSI FIED Security Classification DOCUMENT CONTROL DATA -R&D (SecuTty clificat gin of title body of abstract end indexing alnotation must be entera when the verall report is cla1alfld) ORIGINATING ACTIVIlY (Corporate author) 124 RCPORT SECURITY C LASSIFiCATION U. S. Naval Ordnance Laboratory 2b GRO Unclassified 3 REPORT TITLE Acoustic Impedance of Sea Water as a Function of Temperature, Pressure and Salinity 4 DESCRIPTIVE NOvES (Type of report And inclusive datee) S AUTHOR(S) (Leet name first name. initial) Bradley, David L. 6 REPORT DATE 178 TOTAL NO O PAGES j 7b NO Or REPS CONTRACT OR GRANT NO 9* ORIGINATOR'S REPORT NUMBER(S) PROJECTNO MAT 03L 000/F NOLTR c 9b OTHER REPORT NO(S) (Any other numbers that -,ey be ess:gred this report) d 10 A V A IL ABILITY/LIMITATION NOTICES Distribution of this Document is Unlimited. It SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY 13 ABSTRACT The acoustic impedance (oc) of sea water is presented as a function of temperature, pressure and salinity. This acoustic impedance has been calculated from empirical equations developed at the Naval Ordnance Laboratory to represent the velocity of sound and density of sea water as functions of the parameters temperature, pressure, and salinity. Tables of the calculated data and graphs are given. DD JAN6" Security Classification 7_-

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