I hope nobody minds, but I figured it's best to start a new topic for this rather than tack it onto the end of the existing cue balls thread.
Last night I spent the evening with my genius friend and lifetime mentor Bill Eppler. Not only is Bill an expert on all matters audio, he can also explain advanced concepts in a way even I can understand. Where else could one get a college-level education for the cost of three beers and a dinner?
Bill and I discussed some very interesting stuff, and by the end of the night I had learned a lot and walked away with even more to think about and share / ask / discuss here.
In the Cue Balls thread I believe we all ended up agreeing that at higher frequencies sound does in fact travel like a cue ball, but at lower frequencies - below the Schroeder frequency for the room - the "ray tracing" model breaks down and sound waves instead propagate as pressure patterns in the room. This brings up two new questions:
1. How can some low frequency room modes involve four or six surfaces when nothing is actually bouncing off those surfaces at an angle like a ray?
2. If non-axial modes do travel so they touch four or six surfaces, as shown in all of the text books, why is the first non-axial mode's frequency higher than the first axial mode which has a shorter path length?
In my Acoustics FAQ is this drawing of a 2 by 4 foot absorbing panel that's 4 inches thick:
In the accompanying text I explain that with a panel this thick, having four inches of edge surface all the way around increases the 8 square feet of front surface area by 50 percent. Therefore, this is what accounts for absorption coefficients greater than 1.0, because the edge surface is not included in the calculations that convert Sabins to an absorption coefficient. While this panel is considered by the conversion formula to have 8 square feet of surface, it's really 12 square feet when you include the edges that are also exposed to the room during testing.
It has been suggested that this explanation is wrong, and the true cause of coefficients greater than 1.0 is diffraction of sound waves at the edges of the front surface. When a sound wave travels along a surface and reaches the end, the surface impedance changes suddenly and the wave then wraps around that edge. Sort of like water that's travelling in a pipe and is contained by the pipe. When the water reaches the end of the pipe it is no longer constrained to the size of the inside diameter, and so is free to expand and spread out. And since there had been outward pressure against the pipe walls, when the impedance changes suddenly at the end of the pipe the water does in fact start to spread outward.
But this does not change the fact that the higher absorption is still caused by having more surface area! Whether a wave that travels along the surface wraps around the corner and is then absorbed by the edge, or it's just that the edge is present in the room in the first place, either way it's still the edge that's absorbing. Moreover, I'm not convinced that diffraction is a big contributor at the frequencies the panel is absorbing. Frequencies that are in the range the panel can absorb will enter the panel, rather than skate along the surface. Perhaps at extreme angles of incidence, and with very dense material, a midrange frequency will skate rather than sink in. But it seems to me in that case much of it will skate again anyway when it wraps around the edge.
In the Cue Balls thread I was asked how a sound wave could travel like a cue ball, and I said:
Now, I was considering only the high frequency content of that wave. However, what some folks may not realize is that a single impulse - no matter how brief - has significant energy at frequencies lower than the pulse length might imply. As proof, consider a 1 millisecond impulse that repeats every 10 milliseconds. Clearly you will have energy at 100 Hz. And if it repeats once per second you can see there is energy at 1 Hz. So by extension even if it never repeats there is still energy down to as low a frequency as you care to measure.Suppose you make a very short click sound in a wave editor program, let's say with fast rise and fall times and 1 millisecond duration. Now play that click through a loudspeaker in a room. The speaker cone lurches forward for a moment sending a sound wave "bouncing around the room" until it runs out of energy.