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

44 3. Sound Wave Propagation and Characteristicsthe basic laws of refraction, the most useful of which issin θic 1=sin θrc 2(3.13)whereθ i = angle of incidenceθ r = angle of refractionc 1 , c 2 = speeds of sound in medium 1 and medium 2, respectively.Equation (3.13) should be recognized as the analog to the Snell law for lightrefraction. While the analysis of refraction does not figure prominently in noisecontrol, we cannot overlook the fact that zones of severe temperature differencesdo occur in the atmosphere and oceans. When sound travels from zone to zone,often across regions of severe temperature gradients, the direction of propagationchanges measurably to an extent that cannot be ignored.For example, the surface of the Earth heats up more rapidly on a sunny day thanthe atmosphere. Due chiefly to conduction, the temperature of the air close to theground rises correspondingly. Because the speed of sound is higher in the warmerlower layer, sound waves traveling horizontally are refracted upward. Similarly ona clear night the Earth’s crust cools more quickly, and a layer of cooler air formsand bends the sound waves downward toward the surface. Thus the noise from anindustrial plant would be refracted downward at night and would seem louder to ahomeowner residing near the plant than during the day (when upward refractionoccurs), which is often the situation.Nonuniform sound speed also constitutes a very important factor in underwateracoustics owing to the persistent presence of temperature and salinity and pressuregradients in the ocean. It is not unusual to find a minimum in c at some depth,usually in the order of 1 km, with higher values above and below that stratum.Interesting possibilities can occur, one of which is communication through soundchannels in which trapped signals traveling horizontally retain their strength moreeffectively than if they had been able to spread in all directions. Another is theexistence of shadow zones, where sound waves from a particular source neverarrive, so they provide good places for submarines to hide.3.9 DiffractionIn Figure 3.10, sound waves impinge upon a barrier. Some of the sound is reflectedback, some continues onward unimpeded, and some of the sound bends or diffractsover the top. The barrier does not provide a sharply delineated acoustical shadow.Another example of diffraction is bending of sound around a building corner. Weusually can hear voices on the other side of a wall that is approximately 3 mhigh.