Hi Guys,
Ryan, maybe it would be more correct to day that unless the sources are about 1 / 4 wl apart, they do not combine in a way that is uniform in all directions or fully “feel” the radiation pressure of the other unit.
For example, two sources a half wavelength apart radiate in a figure 8 pattern with nulls in line with the sources and forward / rear lobe. No gain in efficiency is attained but there is some forward gain from directivity.
The greater the spacing, the larger the number of lobes and nulls, conversely, once the distance is ¼ wl or less, the radiation pattern is a circle and fully mutually additive.
So, yes the 3.12 feet is how close you need the sources at 90 Hz for them to fully add in all directions.
Tamas, well so far as I’m aware, the phenomena that causes excess absorption is only present at “high” sound levels. It was called “shocking up” by my old boss Roy Whymark, an old time English acoustician.
Here is what happens (same thing as throat distortion also), sound travels at, well the speed of sound.
The speed of sound is temperature dependant also.
When one has a really loud sound, say 155dB or more, one finds the pressure side of the wave is actually a little bit warmer than the vacuum side. The result is, the pressure side, travels a little bit faster than the vacuum side. If you apply this to a sine wave, over a number of wavelengths, the top of the sine creeps forward until a saw tooth wave is created.
Here is why the reference to Shock. A shock wave is created by a pressure which is high enough to heat the air via pressure. The shock wave travels outward at a new speed governed by how hot it is.
At the tail side, one finds the rarified recovery part of the wave which makes those cool visible expanding clouds of condensed moisture. Loud Sound can be dangerous.
Anyway, the same thing which cause the shock wave to be a saw tooth cause an intense sine wave to become one. If you can get a 155dB sine wave and a reflector, one can levitate Styrofoam balls up to about 1 /4 wl in diameter. Get to 165dB and you can levitate iron, glass, live cockroaches (in out 21KHz acoustic levitation back at Intersonics). At 173 dB, one can light a cigarette with acoustic friction.
One can put your finger in a sound this loud (at 21KHz) but any gap between your fingers will be burned immediately. For reggae or dance floors, there might be a happy medium, perhaps some non-lethal sound level that would also cause clothing to rapidly fatigue, fail and fall off without the unpleasantness of catching on fire haha.
Kids, I’m just kidding
Best,
Tom