Tom,
Without reading the entire paper, its not possible to understand the effect of wave steepening in Compression Drivers within "listening" areas. The pic in that link is very misleading. For example it shows, significant steepening within 1 cycle. it that were true,, we cannot tolerate listening to any sounds. Further the pic shows a pure sine wave which is not an audio wave we are interested in.
The highest frequency we are interested, 20kHz, amounts to only 200 cycles before the sound reaches us at 12ft. Are we to believe there would be any detectable steepening within 200 cycles?
While the theory is right, its application of audio frequencies in listening areas is not clear.
Added:
Wiki has a good analogy.
Quote:
Shock waves can form due to steepening of ordinary waves. The best-known example of this phenomenon is ocean waves that form breakers on the shore. In shallow water, the speed of surface waves is dependent on the depth of the water. An incoming ocean wave has a slightly higher wave speed near the crest of each wave than near the troughs between waves, because the wave height is not infinitesimal compared to the depth of the water. The crests overtake the troughs until the leading edge of the wave forms a vertical face and spills over to form a turbulent shock (a breaker) that dissipates the wave's energy as sound and heat.
Similar phenomena affect strong sound waves in gas or plasma, due to the dependence of the sound speed on temperature and pressure. Strong waves heat the medium near each pressure front, due to adiabatic compression of the air itself, so that high pressure fronts outrun the corresponding pressure troughs. There is a theory that the sound pressure levels in brass instruments such as the trombone become high enough for steepening to occur, forming an essential part of the bright timbre of the instruments.[4] While shock formation by this process does not normally happen to unenclosed sound waves in Earth's atmosphere, it is thought to be one mechanism by which the solar chromosphere and corona are heated, via waves that propagate up from the solar interior.
I guess I don't understand how it effects our listening rooms.