THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

416 15. Underwater Acoustics15.5 Underwater Transmission LossTransmission loss TL quantitatively refers to the weakening of sound between apoint 1 yard from the source and a point someplace in the sea. 2 Let I 0 indicate theintensity at the reference point 1 yard from the “center” of the acoustic source (thus10 log I 0 denotes the source level) and I 1 is the intensity at the point of interest.The transmission loss TL between the source and the point of interest isTL = 10 log I 0dBI 1Time averaging is implied in the above definition. For short pulses, a TL equivalentto that for continuous waves is given by the ratio of the energy flux density at 1 yardfrom the source E 0 to the energy flux density E 1 at the point 1 of interest, i.e.TL = 10 log E 0dBE 1If the metric units of distance are used so that the reference distance is 1 m, TLwill be 0.78 dB less than that for the TL based on the reference distance of 1 yard.Transmission loss can be subdivided into two types of losses: part of the losses isdue to spreading, a geometric effect, and the remainder is attributable to absorptionlosses that represent conversion of acoustic energy into heat.If a small source of sound is located in a homogeneous, infinite, lossless medium,the power generated by the source radiates outward uniformly in all directions.The total power radiating outward remains the same, as its wave front expands asa spherical surface with an increasing radius (the radius increases at the rate ofc × time t). Since power P is equal to intensity times the area, i.e.,P = 4πr 2 1 = 4πr 2 2 =···=constantand setting r 1 = 1 yard, the transmission loss TL to surface r 2 isTL = 10 log I 1I 2= 10 log r 2 2r 2 1= 20 log r 2which can be readily recognized as the inverse-square law of spreading, also knownas spherical spreading.When the medium is bound by upper and lower parallel planes, the spreading isno longer spherical because the sound cannot cross the boundary plates. Beyond acertain range and as shown in Figure 15.4, the power radiated by the source spreadsoutward as a wavefront that constitutes a cylindrical surface represented by anradius expanding at the rate of c × time t. The power P crossing the cylindrical2 The U.S. Navy still employs an odd melange of dimensional units in defining, say, source strengthin terms of decibels (based on the metric reference of 1 μPa for sound pressure level or 1 pW forsound power level) and the distance from the source of 1 yard rather than the 1 meter used elsewhere.Conversion to the entirely metric system requires the subtraction of 0.78 dB from the U.S. value.