SECT. 4] SOUND IN THE SEA 479 



G. Impedance 



The product, pc, of the density and the velocity of propagation gives for plane 

 waves the quotient of the acoustic pressure and the particle velocity. It is 

 called characteristic impedance and is the measure of an important property 

 of the medium in that it controls, among other things, the passage of sound 

 normally across the common boundary of two media. 



For plane sinusoidal waves the intensity, i.e. the power through unit area 

 perpendicular to the direction of propagation, is given by 



P = Ipcvo'^ = Po^l2pc, (9) 



if po and vq denote not the instantaneous values but the maxima of acoustic 

 pressure and of particle velocity. 



D. Attenuation 



a. Geometric spread 



Conservation of energy requires that, if the sound energy radiated from a 

 point inside an unbounded homogeneous medium is not dissipated, the energy 

 flowing through unit area perpendicular to the direction of propagation shall be 

 inversely proportional to the square of the distance from the source of sound. 

 This spherical spread results in a rapid decrease in intensity. In terms of 

 acoustic pressure it is expressed by the formula 



por = C, (10) 



where r is the distance from the source of sound and C is constant for any given 

 source. In very deep water this law is, for moderate ranges, a good approxima- 

 tion of what actually happens. 



If, on the other hand, propagation took place from a point between the two 

 parallel plane boundaries of an otherwise unbounded medium, the intensity 

 would be inversely proportional to the range, and there would be cylindrical 

 spread given by 



pory^ = C. (11) 



This law would apply to propagation in shallow seas of uniform depth if 

 reflection from the surface and the bottom were perfect. 



b. Absorption 



Another cause of decrease of intensity is the gradual conversion into heat of 

 the energy of the wave. Viscosity, thermal conductivity and inframolecular 

 processes all play their part in producing this attenuation, which is, in general, 

 much larger than the value predicted on the assumption that viscosity is the 

 sole cause. In liquids other than mercury, thermal conduction has a negligible 

 effect, so for the sea there are only viscosity and inframolecular processes to 

 consider. They both produce an exponential decrease of intensity which it is 



