SECT. 4] SOUND IN THE SEA 477 



The velocity of propagation, c, depends on the way pressure changes with 

 density ; it is given by 



c2 = {dpl8p)s, (4) 



where the letter S denotes an adiabatic process. 



As absorption of sound by water is very dependent on frequency, it is con- 

 venient when studying propagation to consider waves of one frequency only, 

 afterwards, if necessary, combining a number of waves to represent the dis- 

 turbance. Indeed, one is often interested in sound of a pure note produced by 

 a harmonic generator, or in that component of a sound which is accepted by a 

 tuned detector. In all such cases equation (1) can be simplified to 



(^2 + V2),^ = 0, (5) 



where k is called the propagation constant and has been written for cojc, oj 

 being the angular frequency. 



As is always the case with wave propagation, the length A of the wave and 

 its frequency / are connected by the relation 



A/ = c, (6) 



so that k is equal to 277/A. 



B. Velocity 



The velocity of sound in sea-water has been given in several variants of the 

 form 



c = co,35,o + ^cs + Act + Acp + Acstp, (7) 



where Co,35,o is the velocity at 0°C, 35%o salinity and atmospheric pressure; 

 Act, Acp and Acs are respectively correction terms for temperature, hydrostatic 

 pressure and salinity; finally, Acstp is a^ correction term for simultaneous 

 variation of the three properties. 



A formula due to Kuwahara (1939) is given by Horton (1957); reduced to 

 metric units it is 



c- 1 399 +1.3LS + 4.592i- 0.0444^2 + 0.182/i. (8) 



More recently Del Grosso (1952), Greenspan and Tschiegg (1955) and Wilson 

 (1960) have measured the velocity of distilled water at t = 30°C,^ = 1.033 kg/cm2, 

 and Del Grosso (1952) and Wilson (1960) have measured sea-water of 35 %„ 

 sahnity under the same conditions, as tabulated below. 



Distilled Sea-water 



water (35%o) 



1546.3 

 1546.16 



