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Re: Ethan and MahlerFreak

Posted by MahlerFreak (A) on March 9, 2007 at 16:00:33

In Reply to: Ethan and MahlerFreak posted by David Aiken on March 8, 2007 at 19:15:06:

This discussion is now well past the point of ridiculous, and I will not post again after this in hopes of getting the last word on a philosophy major :)

However, for anyone still following this thread it is worth looking at two reasons why the devices in question cannot produce the given measurements, because they illuminate some important issues in room acoustic treatments.

First, the devices in question, used as described, cannot produce anywhere close to the level of attenuation of bass seen in the graphs in any kind of real-world listening room. Second, it is impossible create a constant reduction in bass level across the frequency range in a real world room using passive devices placed as described.

To point 1: David is correct that I did not account for the two sides of the devices in question when considering the conservation of energy question. This does not double the potential effectiveness of the device, however, because if one side of the device is 100 percent effective in attenuating the sound signal, it will partially "corrupt" - attenuate - the signal reaching the opposite surface, in a way quite dependent on the frequency of the signal and the placement of the device. Nonetheless, let us make the assumption that the inventors have magically prevented this effect, and built a device capable of 100% attenuation of the signal on both front and back surfaces. Let us also make the assumption that the measurements were taken in a room fully treated as recommended - two panels in each upper room corner.

The measurements in question show a 15DB attenuation in bass frequency sound, plus or minus a fraction. Decibels are a measure of sound energy, but they are not linear measures like Miles Per Hour or similar - decibels are measured on a logarithmic scale. Thus, a 3db change in decibel measurement corresponds to a doubling or halving of sound energy. A 10 decibel reduction corresponds to a 90% reduction in sound energy, and a 15 DB reduction corresponds to approximately a 97% reduction in sound energy. In other words, for the panels to have produced the attenuation shown in the graphs, at least 97% of the bass energy in the room must impinge upon the two surfaces of the panels (assuming, again, perfect attenuation). The panels have approximately 2.5 square feet of surface area apiece, 20 square feet total. Let's generously assume that the room is very small, 12 x 10 x 8, or 592 square feet of surface area. We've agreed that a passive device cannot attenuate more energy that impinges upon its surfaces. It should be readily apparent that, even with the corner amplifying room modes, we are way short of having sufficient surface area to attenuate 97% of the sound energy in the room. An order of magnitude or more short, in fact. We could go on to calculate exactly the number of Sabins of attenuation, and therefore surface area, necessary to create a 15db reduction in overall sound pressure level in a given room, but I'm too lazy right now, and in any case the calculation is relevant only for the average sound level, due to the non-linear effects mentioned below.

This type of analysis holds true for any passive sound treatment device, and explains why you shouldn't expect large changes in bass response from small passive devices, ever.

Point 2: the graph shows a perfectly constant, within fractions of a DB, reduction in sound pressure across the measured frequency range. This is not theoretically possible to achieve using passive devices covering part of the surface of the room. The reason is that the frequency response of the speaker/room system is different at every point in the room. From a systems analysis standpoint, we would say that the speaker/room/listener system has a different, non-linear transfer function for every listener position (and speaker position, and room treatment panel position) in the room. This non-linear response occurs primarily as the result of sound waves "interfering" with each other - reinforcing each other at some points, canceling each other at others. These cancellation effects can be roughly categorized into room modes and boundary interferences, room modes occurring as the result of cancellations between waves reflected from opposing pairs of walls or corners, boundary interferences occurring as the result of reflected sound from boundaries canceling or reinforcing the direct sound from the speakers. Combined, these two categories of interferences account for most of the "shape" of the room frequency response curve, and the waterfall plots as well.

Of course, the patterns of interference, and the corresponding frequency response anomalies, will be different at every different location in the room. The passive sound cancellation device in the corner of the room "hears" a different frequency response from that "heard" at the listening position. If the panel perfectly cancels the sound it hears, it will cancel more sound at some frequencies, and less at other frequencies - and the shape of that cancellation curve will not match the shape of the non-treated frequency response curve at the listening position, and the result will be that the shape of the curve at the listening position will change. The passive treatment panel has no way to "know" what the transfer function (frequency response) at the listening position actually is, and therefore no way to create a uniform attenuation in sound level at that position.

In theory, one could approximate uniform attenuation using active devices controlled by powerful DSP engines programmed with actual room measurements at different positions. This wouldn't be particularly useful, though, because the result would be identical to applying a conventional parametric digital or analog filter over the desired frequency range - including phase shift anomalies.

The irony of all of this is that these panels, if they have any attenuating effect at all, should produce small but measurable changes in the room's frequency response curve - certainly greater changes than could be measured by switching between amplifiers or cables of similar electrical characteristics. It's just that the data currently presented doesn't allow for honest assessment of the panels' actual performance, which I am left to assume is because that performance is not particularly noteworthy.

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