Originally Posted by

**SAC**
Covering some ground twice, and a few areas for the first time, here are a few aspects of the overall behavior. Each has in some form or fashion been mentioned or at lest inadvertently touched upon...

This is simply an attempt to clarify a few points distinguishing some of the wave behavior confusion discussed earlier.

As mentioned above, do not become obsessed with trying to distinguish modal from specular reflections. Oh, they are distinctly different in nature and behavior. But if the appropriate tools are employed to evaluate them, the distinction becomes rather academic and simple. And you can obsess over the logical descriptions and distinctions at you leisure.

As has been stated on multiple occasions, a modal standing wave behaves differently then a focused specular reflection.

The primary distinguishing factor is their size.

Specular reflections are reflected based upon their wavelength being equal to or smaller than the dimensions of an incident surface.

Modal standing waves have wavelengths larger than the dimensions of a boundary surface.

This’ break point’ is referred to as the Schroeder ‘critical frequency’. But please do not go trying to calculate or determine this! It is neither necessary no clear cut, as you will generally have a region of overlapping modal and specular behavior as you will have various boundary dimensions resulting in some energy being reflected specularly while some energy is reflected in a modal manner. Again – don’t worry, as the measurement methods will sort all of this out very elegantly as mentioned above.

With reference to the earlier reference to Ethan’s example, the only way to remove the standing waves in a small acoustic space is to effectively remove the boundary - thus effectively requiring a 100% efficient absorber covering all of the LF frequencies! Now, as fascinating as this imagined concept is, does anyone here posit that absorbing 100% of the LF is a realistic viable option - especially considering that most would kill for a reliable LF absorber capable of decreasing the gain at an anti-node (peak) by just 6 dB SPL??

Thus, in a real world room, you will NOT remove ALL of the returned energy!

The following erroneous notion has been mentioned several times, and it seems a source of at least part the confusion.

In that statement we are trying to differentiate a standing wave from modal behavior and associate a standing wave with specular reflections. This has gotten the notions confused. If you want to associate labels, associate the standing wave with modal behavior.

Thus we are still confusing specular behavior with modal behavior. And modal behavior is not the result of two specular reflections superposing (summing). Modal behavior is the result of the same incident energy that is reflected and returned that reinforces (itself) and both the magnitude and the null of the resultant wave.

Not to get too far afield on a tangent with this element, but one that will be mentioned as it is fundamental to the behavior describes - One will also note that boundaries featuring greater acoustical impedance than the transmission medium return the reflected incident wave energy in phase, thus resulting in the constructive reinforcement of the resultant (incident + reflected) waveform. And I know of no practical effective room boundary featuring a lesser complex acoustical impedance capable of delaying or inverting the phase of the reflected energy propagation sufficiently to disrupt said reinforcement. Perhaps when we begin manufacturing walls of closed cell aerogel or of sparse matrix carbon nanotube Buckyballs…. So in a practical bounded enclosure, we are ‘stuck’ with this condition…

Jumping over to specular behavior for a moment to present a contrast, the energy content of mid and high frequency wavelengths is a fraction of that of low frequency wavelengths. There is good reason why low frequency waves, such as one might experience with thunder or ELF - extremely low frequency communications which can be perceived far away from the actual source while relatively short low energy content specular energy has already been dissipated by friction.

So, with specular reflections, we are able to control the resultant polar lobing that appears as comb filtering in a frequency response because we are more able to intercept and absorb the more limited (focused) spatial distribution of the relatively low energy content of the constituent mid-high frequency shorter wavelength energy of which specular reflections are comprised.

With low frequencies the difficulty of doing this is increased substantially.

And I know folks don’t want to hear about this, but our conceptualization of this phenomena is also confused by our wave models. We so often imagine wave behavior in the form of a transverse wave (you know, what appears to be a sine or cosine wave). But a bounded modal space the air column more effectively exhibits a behavior more consistent with a longitudinal wave featuring periodic regions of low and high pressure.

Oh, and other aspect that many forget. Sound has size. Oh, we talk of wavelengths all the time, but how often do folks actually think of the relative size of the wavelengths in the real world? Specular energy is specular precisely because the wavelengths are smaller than the incident boundaries. They are focused, meaning they do not occupy the entire room, instead being limited to smaller ray like distributions. And as a result, not only are the effects of superposition position related, but due to their relatively small size, they are able to be effective controlled in the room by the application of absorption, diffusion, or redirection/controlled reflection.

The modal standing waves, on the other hand, are not small localized waves. They are large relative to the room boundaries and to the room itself. They fill the room. Thus you have areas of relative high and low pressure distribution, but you do not in a small space have regions of modal behavior and regions lacking it. It dominates the room.

And as far as absorbing a null… how do you absorb that which is effectively 'absent', meaning the particle velocity is effectively 'zero' and the pressure is low - rarified. Technically, neither porous velocity traps nor tuned resonant absorbers are effective here! It is akin to trying to absorb a shadow. The null is a function dependent upon the relation of the dimensions of the room and the wavelength of the energy that is returned. And at the risk of creating more misconceptions rather than increased understanding (hey, can it get worse?? ;-), modal behavior is a LF behavior akin to mid-high frequency flutter echo that occurs between parallel surfaces, only modes have big honkin' wavelengths (and where small surface angle irregularities are not critical due precisely to the relative size of the wavelengths involved).

Oh, and let's jump over for a moment and consider the compounding influence of coupled spaces in the suggested room posited in the thread...At its simplest, the room functions, as you will, as a large tuned pipe With closed ends terminated in anti-nodes and open ends terminated in nodes. It is this perspective by which the myriad traditional modal calculators function. And due to ideal geometric and simplistic bounded acoustical impedance assumptions, they are estimates at best.

In the worst case, you have a series of irregularly bounded spaces that are coupled in a complex manner. And this complex topology effectively functions as multiple enclosures of the various component sizes as well as in all of the various combinations and permutations of the various component and summed space. Such calculations are complex (to say the least) in the simplest of configurations where the boundaries are assumed to be 'regular' and of constant impedance. But the difficulty scales exponentially with the complexity of the assemblage of bounded spaces - compounded still further by the real world acoustical impedances of the boundary surfaces which function as frequency and time dependent absorbers and reflectors varying with the angle of incidence. And not only are the reinforced frequencies more difficult to calculate, but the energy density distribution becomes *much* more complex.

Suffice it to say that *reliable* prediction of such complex behavior is beyond any practical desktop solution currently available. We can obtain a rough idea that tends to eliminate inadvertently creating really bad spaces, but such modeling is not capable of producing a model sufficient to replace real world proof of performance measurement and verification. (In other words, we can make them look really good for the purpose of making sales and marketing proposals! ;-)

Both resonant tuned absorbers and velocity based porous absorbers function best in regions high pressure and high velocity, respectively. And neither condition exists at the null. Thus, unlike baseball where you “hit ‘em where they ain’t”, in the treatment of modes, you “hit ‘em where they are” based upon how absorbers work.

We have a bounded space. And we have modal behavior. Our tools are relatively ineffective in the nulls. But we can mitigate the ‘peakiness’ by absorbing the peaks and minimizing the reinforced resonant energy. And if we are designing a space, we can chose dimensions that most effectively distribute the modes - spreading them out as much as possible. But as far as the nulls in an existing space, the simplest and most effective solution is to literally avoid them. Move. Assuming no other adjustments, adjust your seating arrangement forward or backward (assuming a left right symmetry) such that you are in between the null and the peak.

Then treat the room modal behavior as suggested above.

And then you can begin obsessing over the specular energy and obtain practice making and interpreting and discovering just how treatment moderates specular reflections. And that is quickly summarized above.