The Master Handbook of Acoustics, Fourth Edition

About the turn of this century Lord Rayleigh was puzzled because some very powerful sound sources, such as cannon fire, could be heard only short distances some times and very great distances at other times. He set up a powerful siren that required 600 hp to maintain it. He calculated that if all this power were converted into energy as sound waves and spread uniformly over a hemisphere, how far could it be heard? Knowing the minimum audible intensity (10 ?16 watts per sq cm), his calculations indicated that the sound should be audible to a distance of 166,000 miles, more than 6 times the circumference of the earth!
It is indeed fortunate that such sound propagation is never experienced and that a range of a few miles is considered tops. There are numerous reasons why sound is not heard over greater distances. For one thing, the efficiency of sound radiators is usually quite low; not much of that 600 hp was actually radiated as sound. Energy is also lost as wavefronts drag across the rough surface of the earth. Another loss is dissipation in the atmosphere, but this is known to be very small. The result of such calculations and early experiments that fell far short of expectations served only to accelerate research on the effects of temperature and wind gradients on the transmission of sound.
Refraction changes the direction of travel of the sound by differences in the velocity of propagation. Diffraction is...