566 



INDEX 



pressure effects, 19-20 



ray equations, 46-49 



refraction effects, 197-200 



shallow-water transmission, 138 



summary, 242 



supersonic transmission, 142-150 



target depth correction, 49-51 



wake theory, 478-479, 480-483 



wave equations, 15-17 

 Velocity-depth variation in ray acous- 

 tics, 54-59 



beams in linear gradients, 54-58 



layer effect, 56-57 



transmission anomalies, 58-59 

 Vertical temperature gradients in the 

 ocean 



see Temperature gradients in the 

 ocean 

 Vertical transmission of underwater 



sound, 79, 507-509 

 Viscosity (fluid) effects on sound in- 

 tensity, 27-28 

 Volume reverberation of sound 



average intensity, 255-256 



definition, 253-254 



depth, 282-284 



frequency, 284-288 



index, 259 



intensity, 256-258 



level, 258, 335-337 



range, 281 



scattering coefficient, 243, 286, 336- 

 337 



Wake geometry in sound transmission 

 aerial photographs, 494-495 

 submarines, 501-502 



summary, 541-542 



surface vessels, 497-501 



target strength, 513-514 



widening measurements, 495-497 

 Wake-laying vessel, acoustic measure- 

 ments, 491 

 Wakes, acoustic 



absorption, 541-543 



decay rate, 520-521, 539-540 



definition, 441 



echo ranging, 484, 543-546 



evaluation of research, 443-448 



fathometer records, 486-488, 497-501 



frequency, 523 



geometry, 494^95, 513-514, 541 



index, 513, 519-520, 543 



listening gear, 484 



long pulses, 515-516 



measurements, 490-492 



oceanographic effects, 492-493 



oscillograms, 488-490 



physical properties, 514-515 



propellers, 530-532 



pulse length, 522-523 



scattered sound, 480-483 



short pulses, 516-519 



sound range recorder, 484 



submarine, 501-502, 523-526, 538- 

 539 



surface vessel, 526-530, 537-538 



target strength, 512-513 



temperature structure, 479^80 



theory, 541-546 



thickness, 498-501 



training errors, 491-492 



transducer directivity, 522 



velocity structure, 478-479 



widening rate, 495-497 



Water wave, sound transmission, 233- 



235 

 Wave acoustics 



boundary conditions, 13-14, 28-34 



equation, 10-13, 43-45, 242 



equation of continuity, 8-10 



equations of motions, 10 



fluid viscosity effects, 27-28 



general waves, 36-37 



harmonic waves, 17-18, 22-23 



intensity, 20-22, 37-38 



mathematics, 39-40 



normal mode theory, 34-38 



plane waves, 14-17, 34-36 



pressure versus velocity, 19-20 



reciprocity principle, 38-39 



sources, 23-27 



spherical waves, 18-19 

 Wave equation for shadow boundary, 



ray acoustics, 66-67 

 Wave fronts, ray acoustics 



eikonal equation versus general equa- 

 tion, 64-65 



equations, differential, 43—46 



general waves, 42-43 



spherical waves, 41-42 

 Wave length effects on target strength 



measurements, 386-387 

 Wavelets for reflected sound pressure, 



356 

 Wide-band pings, frequency analysis of 



reverberation, 332-333 

 Widening rate of acoustic wakes, 495- 



497 

 Wind effects in sound transmission 



force, 337 



speed, 295-299 



supersonic, 150 



* U.S. GOVERNMENT PRINTING OFFICE : 1969 O— 3S7-418 



