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Page 1: UNCLASSIFIED AD NUMBER - DTIC · 2018. 11. 8. · UNCLASSIFIED AD NUMBER AD 221613 NEW LIMITATION CHANGE TO Approved for public release, distribution unlimited FROM No foreign AUTHORITY

UNCLASSIFIED

AD NUMBER

AD 221613

NEW LIMITATION CHANGE

TOApproved for public release, distributionunlimited

FROMNo foreign

AUTHORITY

NRL ltr. 7103/911, 25 Aug 1999

THIS PAGE IS UNCLASSIFIED

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UWCLASS hFIED

AD?21 _i3o

AR{M FD) SVII'V ICIS fTECHNICAL INI'OItRA'IION AGEINCN(ARI.•IN(GTON IIAIl STATIONARL.INGT''()ON 12, VIRGINIA

U[ N Ct, A S) S-- " F E ED

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NOTICE: When govermLent or other drawings, speci-

fications or other data are used for any purpose

other than in connection with a definitely relatedgovernment procurement operation, the U. S.

Government thereby incurs no responsibility, nor anyobligation whatsoever; and the fact that the Govern-ment may have formulated, furnished, or in any way

supplied the said drawings, specifications, or otherdata is not to be regarded by implication or other-wise as in any manner licensing the holder or any

other person or corporation, or conveying any rightsor permission to manufacture, use or sell any

patented invention that may in any way be relatedthereto.

I

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11 Aq'il 19/.1 N.l R,' o. ;-172

NAVY 7,". Z!!r

Report on

.LT) The Velocity of sound in Sen. "T/tpr

NAVAL P O I'RCtl LAO. TCRYANACOSTIA STPTIO!l.7AT•-•r?'G'IOU, D. C. f

Number of Pages: Text - 6 Tables - 2 Pl:te'; - 18

Authorization: Problem U5-2C BuShips Ltr. C-NC/s68(4-15-R4-6/24) of 4-27-39.

Reported by:E. B. Stephenson, Senior Physicist

F. J. Joodsmaai, Assistant "lectrical Enrgineer

Revievied by:

H. C. Hayes, Principal PhvsicistSuperintendent, Sound Division

Approved by:11. G. BT.Ven, Rear Ad".irel, U9i. Director

Distribution: ,

coo (Fleet Training (40)BuShips (10)File (50) .

I !p ,/f k...

ect , ./

I;e

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AASTRACT

The purpose of this report is to presentthe latest available data on the velocity of sound insea water as modified by changes in temperature, salinity,and depth. These are given in both metric and Englishunits in a series of tables, curves, and equations fordepths to 1300 feet.

The basic data have been compiled from thepublished reports of competent authorities who calculatedthe velocities from fundamental physical equatloas whoseconstants have been experimentally determined with precision.They have been checked with numerous direct measurements,and agree ;ii.hin an experimental error estimated to be lessthan 0 2p. The soundness of the theoretical basis for thecalcula'ionig and the consistency of the results indicate thatthe cairvlated values are accurate to within less than 0.05%at temperatures below 700 F.

A bibliography of source materials is included.

I

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TA I E: OF COC!?-,'. ,'3

Intrnduc t i nnDefriqition of Salinity ..........................Calculation of the Velocity of Sound in .".tcr 1Calculoted Velocity DataV•locity Tablos .

Velecitv Curves ...............................Velocity FquatLiora .......................... 3Exanples in the Use of the Graphs and Eou;ation. 5Additi onal Data .................................. 6Biblto~ raphYv ................................... 7

Appendix: Velocity of Sound in Vario,,.-; i:edia

Tables

Comperison of Swm-aI Sources of Velocity Data ........ 1Velocity of Sound in Sea Water, in Metric Units

(From Kuwahara) ................................. 2

Plates

Velocity of Soundi in Sea Water, in Metric Units.(Four 3h.'etzS) ...................... ............ I

Rate of Change of Velocity with Respect t/ Temperature,in Metric Units............................... 2

Rate of Change of Velocity with Respect to Salinity,in Yetric Units............................... 3

Summary of Sea Water Data, in Metric Units ............ 4Velocity of Sound in Lake Water, in Ifetric Units ...... 5Velocity of Sound in lea Water, in Mnglish Units.

(Six Seets) 6.............................. .. . 6Rate of Cblnge of Velocity Yd th Respect to Temperature,

in Ewplish Units. . ........... ....... 7Rate ot Change of Velocity with Respect to Salinity, in

Zng2lish Units. 8..........3)umrmary of Sea Water Data, in Ehrlish Units.........9Velocity @f Sound in Lake Water, in English Units 10

I

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Thu Velocity of Sound in Sea Water

INTRODUCTION

1. Experimental determination of the velocity ofsound in sea water over wide ranges of temperature and sallinitiespresents many difficulties. Consequently several comnuted tableshave been published based on fundamental physioal theory and data.These tables are more accurate and comprehensive than directexperimental determination s.

2. The purpose of this report is to present some ofthe latest available data in a form convenient for use.

D•FINITION OF SALINITY

3. The salinity is a measure of the salt contont ofthe water in parts per thousand by weight and is written S = ppt.or 0/00.

4. The salinity of the open sea water may range from

30 to 40 ppt. "Standard" salinity is conventionally chosen as

35 ppt.

CALCULATION OF THE VMO•CITY OF SOUND IN WATTR

5. The velocity is given by the expression

I dpS(I)

where p is the pressure and e is the density. For convenience incalc-ulation from vell established physical data the formula used is

V cc (2)

where y is the ratio of the specific heats at constant volume andconstant pressure and C is the comrressibility. The numerical valuesof these quantities depend on the temperature, salinity, and depthor pressure. The detailed formulae and the necessary correctionsare explained fully in the references to the original data.

CALCUJLTE VELOCITY DATA

6. The firnt com~rehensive tablfes were puluiishd byHeck and Service in 1024. They checked their tpbi'e• by wiresoundings, and concluded that the calculated values were probably

more accurate than the exp)orient:, dotermiriatiors. In 1Q27, theBritish Admirply published an c-collont set of tables for- hoth pur-and sea water that w-ere the rio.t ,•xt,.sivc and accurate at tVia, tim,-.

In 1939, Kuwahara hrourht ot n new ;c.t of volority tables 'i.;h

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A!.i!9 1",~fm' t I - V A -l typi hl I nhe'I t ov-i -;,(-1:i d m' f 1.:ile:; wh ~ch ai1'r-, .'(ryoln -ully -ailit Kiiwns.:ra ' 1. "Text booe of `Thund"(13

,vs w.~ -I ;1-a'. i~~ ~I V'r-ocit~y LIn s'a" water at "z7 cr0"ldep ib..

I Talble I 'ow'a apii e.of V1't.p;iind'pr

8. ',A.nce the t~ahles of Kuiwha.i -,Ire hplol 1vO( to bethe nesc-t arouvrte availrhle at this time, they have hoee. used inthpe nre-pai ation (If' "he son voiti ~r urvP5s and enuat ors a'1VoCj

ata S ert1 iW onq th1.q r ersr t Vn'r f're-h Wntr~ a rdr 1 ~r~1" s~Is

water, the va_-.- used are those of the Bri ti 3h Admiral ty tnbl efn of

VELOCITLY TPRLES

9. Because the velocity tables of Kuwahara nip~y isotreadily be available, a part of his data is dven ,is Tab) e 2. Fordepths less than 400 meters, a pressure norrection of 0.0181 meterper second per me~ter of depth should be added. For greater' depths,the pressure correction is not so simple, and reference should be

made to the original source.I VELOCITY CURVES10. Since the effect of pressure is riot great, and a

correction may' easily be made for depths not exceedling about 400meters or 1300 feet, the velocity rurves in this report have beendrawn for zero depth.

lie Plate 1 fives the vel~ocity in nmeterv3 per seecnnd inordinary sea water for Centigrade temperatures. These curves areass precise as the dnta frtir which they wer~i firsA'n - that is-, to thenearest 0.1 meter pcar it,-ozid .

12, Plateo 2 shows in metric unlt.i the temperaturecoefficient of velocity - that i:-, the change in velocity in metersper second for A chornge in tho, te-mperature of one degree Centigrade,It ig to be noted that this coefficienrt is by no meens constant,decreasing from~ about 4~.7 to About 2.0, so Uhat It cannot be usedto caloj7~te accliratE-il~y the 're~ocity at one temperature from aknowledge of the velocity Of Another temperature, unless the twotemperatures 6re quite close together. Although this curve wasdrawn for 3 - 35 ppt., l ittle error will be introduced by using itfor any salin~ity between 30 ppt. and 40 ppt. In case greateraccuracy is required, tht equations Oiven in Paragraphs 17 to 22inclusive, may be used,

13, Plate 3 -,hc~r i py-oxiznately tbe salinity coefficientof velo-ity that i-, thf- ohangie in velocity in meters per secondfor a chang-e Jrn the ,;r,1ni~y of' one ppt. Thifs coefficient i!; nearlyindependent, of t~he sal-inity, -)o that for a fixed teaerature, thevelo'iity at one salinity mV~ be calculated frc~n a knowledge of the

2.-

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velocity at some other value of salinity. For greater accuracy,the equations riven in Paragraphs 17 to 22 inclus-ive may be used.

14. Plate 4 gives a summary on one sheet of the dataof the preceding plates with some loss of ,'recision due to thesm.aller scale.

15. Plate 5 shows the velocity of sound in pure andnevrly pure water, in metric units, with n precision of about 0.5meter per !ýecond.

16. Plates 6 to 10 give the same data a3 plates I to 5,expre-sed in Dnglish units of feet an! Fahrenheit degrees.

VF1OCITY EQUATION S

17. T'ro empirical equations haive been set up and theconstants calculated to fit the data 5,iven in the tables and curveswith the pr-cision speclfie-. In or(ier to preserve the accuracyof the eouations, the varinableo: should not fall outside the ranresindicated. The following: slymol.s w'ill be employed.

Vm . velocity of sound in sea water, in meters persecond

Vf = velocity of sound in sea water, in feet persecond

S = salinity ir ppt., between 30 and 40 ppt.YM a depth in meters belovi sea surf:ice; between

0 and 400 metersyf - depth in feet below 't a surface; bet.'en 0

rMd 1300 ft.

tc . water temperature in °C; between 0 and 32 0C.

tf = water temperature in OF; between 32 and 00 1F.

18. For a fir-t approxiration, n nurdratic function of thu.temperature war assrse', . T,-ngthe '-et,,,nd of 'east 'T res,e-xpression for the velocity in 'reters pur n.C-;d an a function of t!,,Centirrade temner.ture w;as obftained for zf.re ,enth nrtd ,tand•ardsalinity of 35 -!t. Then tf.ij, exnrrin v:xrc.-'ied to renr(':r'ntthe vrlocity in fcet per s-(co-d for F:ahronheit t,-,xr, ture:. Theequations 'ire-

vm - 1 .... i.... ., . _ (3]

a 2d

n nd

,. - , , * . .. tf -- V,' (.1)

Vaiu,:- of v..c.-it~v ",-:., ,, •. . ..*'* , ') :.s*. .-' ,:t .h, ".- ,.

-iiven by v ' .r "" L. .- '. 'u ,i . ... /s:" , -ar nv' r "- rrzr -1.1 'v r,

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difference in v(.1ocity per d(Iorre tp-peraturt, -ii f, r, r- -r,with the aid of ,-uM.jio: (3) -w; be in error 1w 11 to 10'. IW:t.(4) is of the z;:re -. rcentA,4e preci-icr ai:: ,-ati inn (3).

19. ýIre-it,r cnecordance :rith tho dtPta narv be obtai ni dfrom a- cubic eauation. Using the Method of Loa t Squares, anequation for the velocity in -tYn'e po,. ::u,:crd -:t a function of !i.Centigrade termerature ima,. obtained for z7ro depth and ctandnrdsalinity of 35 ppt. Then this enuation vf.,e 'odified to repre-entthe velocity in feet per second for Fahrenheit ter.poratu'res. The.;eequation 5 are :

V 1445.4-4 + 4.6684 tc - 0.056,527 to2 +0.0003151 tc3 (

,and gf = 4742.2 + 8.509 (tf - 32) - 0,054,239 (tf - 32)2

+ 0.000i7 7 (tf - 32)3 (6)

Values of velocity computed with the aid of equation (5) agree :ith thevalues given by KPaahara to writhin a maximum error of 0.1 m/sec, orO.00"7%, and an ave;. re error of 0.04 m/seo, or 0,003%. Moreover,it is believed that the values for the difference in velocity perdegree difference in temperature, as calculated from enuation (5), areprecise to 0.01 m/sec, or 0.5% or better. Fauation (6) is of thesame percentage [recision as eauttion (5).

20. Having obtained the above cubic expressions for thevelocity in terms of the temperature at standnrd salinity and zerodepth, other terms for the salinity and pressure effects -ere added,yielding

Vrmj - 1445.44 + 4.6684 tc - 0 056527 t 2 + 030003151 tc3

+ (1.304 - 0.0106 tc + 5.7 x 10 t c4 [(S-35) + 5.2 x

10-5 tc (S-%35)2] + 0.0181 Ym (7)

and

Vf 4742.2 + 8.50P (tf - 32) - 0057,239 (t.f32) 2 . 0.0001773

(tf .32)3 + [4.278 -0.0193(tf-32) + 1.78 x 10- 8 (tf-32)h

((-35) + 2.9 x 10-5 (tf-32) (3-35)2]. 0.0181 yf (8)

21. The precision of equations (7) and (8) is not as greatas thie precision of equations (5) and (6). However, pn about 100well-distributed trials over a temnrsture ranre of 0 to 30 0 C, over asalinlty range of 30 to 40 ppt. and over a depth rnnfe of 0 to 400meterw, the velocities computed from equation (7) agreed vith thevelocities given by Kuwanhraus tables to 0.1 meter per second or better.The larger discrepancies were found at the cxtremes of temnervture,salinity and nepth. The percentege preel3ion of Pecuation (8) is thesame ac that cf equation (7).

22. To obtain the rate of chance of' velocity with respect to

-. 4-

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temperature, salinity, or depth, equations (7) and (8) may bedifferentiated, obtaining:

dVM 2St- 4.6684 - 0.113,054 to & 0.0009453 t+1-0.0106 + 0.23 x 10-6 tc 3 ] (S-35)

46.8 x 10-5 - 0.110 x 10- 5 tc + 1.5 x 10-11 to 4 ] (S-35)2

(oonstant salinity and depth) (9)

ds - [1.304 - 0.0106 tc + 5.7 x 1o-8 tc [I + 1.04 x 10-4 tc(S-35)]

(constant temperature and depth) (10)

d-m . 0.0181 (11)

dym (constant temperature and salinity)

dVf 2- 8.509 - 0.114,478(tf - 32) + 0.0005318) (tf - 32)

"* [-0.0193 + 7.1 x 10-8 (tf-32)3) (S-35)

"* [12.4x0"5 - 0.112 X 1- 5 (tf-32)+25.8 X 10- 13 (tf-32) 4 ](S-35)2 (12)

(constant salinity and depth)

dV•- [4.278-0-0193 (tf-32) + 1.78 x 10- (tf-32)8 [1

+5.8 x 10-5ftF - 32) (S-35) ] (13)(constant temperature and depth)

dVf- 0.018- (14)

(constant tmyperature and salinity)

EXAMfPLES IN THE USE OF TIH GRAPHS AND SZUATIONS

Exanple 1

23. To firr] the aprcximate velocity in 'niters pnrsecond for a temperature of 10 .50 C, a salinity of 34.2 ppt. and adenth of zero.

24. At 16.5 0 C., tMY ',,Tves on Platrt I -.show V 1¶ýn.2 for"-33, an•i V w 1508.6 for ;=35. -;irce onu-atic( (7) " ;.' t thet thsal inity -orrection v:iri f ap-1r'x .i t, p.'t xin'...rv !t.th II , i .r, ;w,have thpt the velocity for 34.2 is

V 3 f" ( ( ý'; '6 1 {)':.'

] 0 ? . ' , " ". ,• , ,

I

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q "'1 "curwvi , on P1.to 4:., ,lo rrj'inv t~hf,voloc!I.v in !,er-;,re,--, Ir the z;am data n; in .; xarpe C.

26. rt 1!;.5C, curve 1 ot' FlPte 4 shews n veloci t v of102.5 .for -35.0. ,-t 16.50C, Curve 3 ohows a salinity coefficientof 1 .132. He(nce, *)h deýJr,,; velocitv is

V - 1508.5 - (35.0 - 34..2) x 1.137 - iB07.6 •,etercicr nqecon d •

_saMple

27. For the -- r-e temperature and salinity data as inExample 1, hut for a depth of 275 meters, find the velocity.

28. Since the velocity correction is 0.0181. m/sec permeter of depth (nee equation 7), the desired velocity is

V - 1507.6 + 0.0181 x 175 - 1510.8 meters per second.

&Kample 4

29. At a temperp ture of 8.8 C, and a salinity of 35 ppt.,determine the temperzture rate of variation of velocity.

30. From Plate 2, the answer is found to be 3.741 meter¶iper defree Centigrnde. From emiation (9) the calculated value is

3.747 meters per second per degree Centi;nrade.

ADDITIOIrAL DATA

31. The Naval Research Laboratory i: collecting data inthis field and would appreciate contributions from any nource,theoretical or experimental, or surFestions as to convenient forms ofpr e sen t-ti on.

() -

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BIBLIOGRAPHY

1. Velocity of Sound in Sea Water, by N. H. Heck andJ. H. Service, USC and GS Special Publication No. 108, 1924.

2. Tables of the Velocity of Sound in Pure 1.1ater and SeaIlater for Use in Echo-Sounding and Sound Ranging, byD. J. Mathews, British Admiralty Publication H.D. 282,first edition 1927 snd second edition 1939.

3. Velocity of Sound in Sea Water and Calculation of theVelocity for Use in Sonic Sounding, by S. Kuwahara, theHydrographic Review, vol. XVI, No. 2, Nov. 1939, pp. 123 - 140.

4. A Textbook of Sound, by A. B. Wood, 0. Bell and Sons, London,1932, pp 245 - 250.

5. Velocity of Sound in Sea Water, by E. 13. Stephenson,Physical Review, vol. 21, pp. 181-185, Febrivry, 1923.

6. Recert Acoustic !%crk of the U. S. Coast and GeodeticSurvey, by P. A. Smith, Field Engineers Bulletin No. 8,December, 1934, pp. 60- 75.

7. Velocity amd Rm' Paths of Sound Waves in Sea Water, by 0. W.Swainson, Field Dg4ineers Bulletin No. 10, December, 1936.

-7-

-- 7 -

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A 'endix

The following. tai',) ivr-4 v p:- r V" iu, • "sound in seve~ral :i.?dia. These valu, ý:; v .. n t rk n -lished in handbooks :ind -xtbooks, ani -i, I ii v, I i ,in 1% to 54.

Tormp.-rature 200 . 68o IF., un!,;.' -. u .'

I.Material rp'-r r,_ _ _ _ _ Cnd Ac rrnd

Aluminum 5100 1 6,(7w0Brass 3500 11,500Copper 3560 I1, 70CIron, cast 4700 15,41{)Lead 1230 4 ,O00Nickel 4970 16,300Silver 1 2610 fP,560Steel 5000 1A,400Tin 2500 P,200Zinc 3700 1 2,100

Brick 3650 12,000I Cork 430-530 14.00-1740

Glass ,5000-6000 ,i',/,00-19,700lce, 00 C 3200 1 10,520.Paraffin, 151 C. 1300 ' 4,260Quartz I 5500 ' 18,000Rubb:r ' 30-70 ' 98-230

Wood '100-4700 ',200-1 5•",C

Alcohol, 12.5' C. ' 1240 1 4,070Castor oil '1555 5,100Benzol, 170 C. 1170 3,840ffercury 1410 4,625

Air (dry, 760 rm.) ' 344 1,12PCarbon dioxide, 00 258 840Hydrogen, 00 C. I 1270 4 4,17(,",'ethaiep, 00 C. 432 I'J7

Oxygen, 00 C. ' 317 1,040Steam, 1000 C ' 405 !,Air, O°C. (dry, C%• free, 760 mm) ' 331.4 ' l,')?.3

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TABLE 1

VELOCITY OF SOUID IN SEA "ATER

(From various tables and formulas)

Meters per .5econdDepth I --- -

in Temp. Sal. Heck & Br.Adm. Br.Adrn.Meters 0C. ppt. Service Wood 1927 1939 Kuwahara

0 0 31 1445 1445 1440.3 1440.2 1440.3

"10 " 1482 1484 1481.9 1481.9 1482.0

20 " 1508 1515 1514.3 1514.3 1514.3" 30 " - 1538 1539.0 1538.9 1539.1

0 0 35 1450 1450 1445.3 1445.4 1445.5" 10 " 3489 1488 1486.6 1486.7 1486.8" 20 1 1514 1519 1518.6 1518.7 1518.7"I 30 " - 1543 1543.0 1543.1 1543.2

400 0 35 1.454 - 1452.6 1452.7 1452.8

"10 It 14012 - 1493.8 1493.9 1494.1

"20 " 1518 - 1525.8 1525.9 1525.9

" 30 - -- 1550.3 1550.4 1550.6

3000 0 31 1190 -- 1494.7 1494.6 1494.4

" " 35 14 9 8 1499.7 11499.8 1499.8

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'" I,

"-' '] pvt- '**l p it I : '•' ppt :'"37 ;pt S;-3';' ppt

0 1440.3 I 4;. ( 144' J - I/44P. 1 1450.71 1 .• , 4.4 50.0 '2.6 55.22 -9.4 51.9 54.5 57.1 59.63 p 58.9 61.4 64.04 1 60.6 63. 1 65.6 68.1

5 16-2.3 1464.8 1467.3 1469.8 1472.36 66.5 r) r.9 71.4 73.9 76.3

7 70.5 73.0 75.4 77.9 80.38 7/.5 76.9 79.3 81.7 84.29 70.3 "80.7 83.1 85.5 87.9

10 L482. 0 1484.4 1486.8 1489.:P 1491.6ii f5.7 88.0 90.4 92.8 95.112 89.2 91.6 93.9 96.3 98.613 92.7 95.0 97.3 99.6 1502.014 96.0 98.3 1500.6 1502.9 05.2

15 1499.3 1501.6 1503.9 1506.2 1508.516 1502.5 04.7 07.0 09.3 11.517 05.6 07.9 10.1 12.3 14.618 08.6 10.8 13.0 15.2 17.519 11.5 13.7 15M9 18.1 20.3

20 1514.3 1516.5 1518.7 1520.9 1523.121 17.2 19.3 21.5 23.7 25.922 19.8 22.0 24.1 26.3 28.423 22.4 24.6 26.7 28.8 31.024 25.0 27.1 29.2 31.3 33.5

25 1527.5 1529.6 1531.7 1533.8 1535.926 29.9 32.0 34.1 36.2 38.327 32.3 34.3 36.4 38.5 40.628 34.6 36.6 38.7 40.8 42.929 36.9 39.0 41.0 43.1 45.1

30 1539.1 1-541.2 1543.2 1545.3 1547.3

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UNITED STATES GOVERNMENT

memorandum7103/911

DATE: 25 August 1999

FROM: Burton G. Hurdle (Code 7103)

SUBJECT: REVIEW OF REFS. (a) THROUGH (c) FOR REMOVAL OF RESTRICTIONS

TO: Code 1221.1 • 7"2Y/t1

VIA: Code 7100

RF (a) NRL Report S-1204, 16 Oct 1935, E.B. Stephenson /y -

(b) NRL Report S-1670, 3 Dec 1940, E.B. Stephenson ,9 • - / -(c) NRL Report S-1722, 11 April 1941, E.B. Stephenson and F.J. Woodsmall

eu P;'/6/1. References (a) through (c) are a series of reports and documents in underwateracoustics. Refs. (a-c) have been declassified earlier, but restrictions still exist.

2. The science, technology, equipment and operational utility of these reports havelong been superseded. The current value of these reports is historical.

3. Based on the above, it is recommended that references (a) through (c) beavailable with no restrictions.

Acoustics DivisionCONCUR:

EDWARD R. FRANCHI DateSuperintendentAcoustics Division

OPTIONAL FORM NO. 19(REV). 1-80)GSA FPMR(41 CFR) 101-11.65010-114