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Re: Ethan and MahlerFreak

Posted by MahlerFreak (A) on March 11, 2007 at 11:46:14

In Reply to: Re: Ethan and MahlerFreak posted by David Aiken on March 10, 2007 at 22:17:51:

If anyone reading this doubts the dangers and inefficiencies created by scientific and mathematical illiteracy, this discussion should go a long way toward convincing you. Although, to be fair, inefficiencies almost always create perverse opportunities as well, without which such lucrative industries as high end speaker cable manufacturing and magical room treatment devices would greatly suffer.

There are so many flaws in David's post that it's difficult to know where to begin, but I'll simply point out that:

1. The "inference" made from the calculations I performed in my previous post is that the devices in question would have to violate conservation of energy - dramatically - in order to create the measured differences. Since David has already agreed that conservation of energy is a reasonable assumption to make, it is his argument that that draws logically invalid inferences - namely, that there is some principle of operation other than "absorption" which would allow the devices to violate conservation of energy. To be fair, it is possible that David does not recognize that inference, due to the more serious logical flaw of arguing from incomprehension of the subject at hand. Unless you can refute my very simple calculations and modeling assumptions, there is no room for "reasonable doubt" about the validity of these measurements - they are not the result of the devices as described being used as described in a realistic listening room (and note with care the contingencies in that statement, lest David come back and insist that you might create these measurements by using the devices as earmuffs, or attaching them directly to the woofers of your loudspeakers, or stuffing your head into a box constructed of these devices, or some similar bit of face-saving nonsense).

2. I never used the word "bogus" to describe the measurements. I will leave it to the reader to speculate as to the origins of these measurements, as there are many possible explanations which do not violate the laws of physics, almost all of them having to do with, umm, human factors.

Beyond this, I am bothered that my previous post describes the issue of room non-linearity in a somewhat awkward and potentially misleading way, and manages to miss an important point at that. The point becomes clearer, hopefully, by concrete example.

For simplicity, assume we have a listening room 10 feet long, constructed with very rigid walls. For the sake of this example, the other dimensions can be ignored. This 10 foot long room will have "room modes" related to the 10 foot length, room modes being patterns of cancellation and reinforcement in sound frequencies related to the 10 foot length. In this case, we will have room modes at multiples of the frequency 56.5 hertz. For instance, there will be a room mode at 113 Hertz. If we have our speakers play a 113 hertz tone at an average sound level of 100 DB, and begin measuring the sound level at various points in the room, we will discover some interesting things. For instance, at the front and back walls, the sound will actually measure louder than 100 DB. Aha! Here is proof that all of that conservation of energy stuff is BS! How can the sound be louder?! Well, because at other points in the room, it is quieter. For instance, if we measure the sound at a listening location 2.5 feet from the back wall, we will discover that the sound level is way below 100 DB. In fact, if we measure the sound at frequencies in the neighborhood of 113 hertz at that listening location, we will find that there is a sharp dip in the frequency response graph, centered at 113 hertz. This sharp dip occurs because sound reflecting from the back wall is canceled by sound of opposite polarity reflecting from the front wall, at that location, at that frequency.

Now let's introduce some sound treatment devices on our front and back walls. If these are passive devices, with no power source of their own, conservation of energy says that these devices can't create or destroy the sound energy, only transform it in some way. Part of that transformation might be from sound energy to heat, part of that transformation may be reflection of sound, some of it may be conversion into dynamic magnetic fields which interfere with the skin effect in your $12,000 speaker cables (don't worry, that last is mostly a joke, until it appears in someone's marketing brochure).

Let's assume for the sake of this example that the sound treatment devices in question are well designed passive absorbers covering much of the back and front walls, capable of absorbing most of the sound energy impinging on their front surfaces at 113 hz. Now we do some measurements again. We find that, intuitively enough, the sound level at 113 hz is significantly reduced near the back wall. Not so intuitively, as we measure the frequency response in the neighborhood of 113 hz at the listening position, we find that the dip in the frequency response graph is not as deep or sharp as before.

Why? Because our sound treatment devices have now negated much of the sound waves that reflect from the back and front wall and interfere with each other at the listening position, partially removing the non-linearity caused by the cancellation of those two waves. Although our devices absorb energy at non-modal frequencies as well, they do not absorb as much, because the sound at the boundaries is not as loud at non-modal frequencies. The serendipitous result is that a non-linearity at the front and back walls is aiding us in canceling an opposite non-linearity at the listening position, exactly what we want if more uniform frequency response is the goal.

This leads to an even more non-intuitive conclusion, easily verified with active sound cancellation devices. In order for our sound treatment devices to lower the relative 113 hz level at the listening position, they would have have to amplify the 113 hz level at the front and back walls! Passive, non-powered devices can't amplify, of course. They could be designed and physically constructed to be ineffective absorbing frequencies in a narrow band around 113 hz, thus "amplifying" 113 hz in a relative sense - but that would obviously require a priori knowledge of the room into which they were placed, and of course would be counterproductive if removing room effects is the desired goal.

What can we learn from all of this? First, every room will have non-linearities due to reflections from the room boundaries, regardless of the dimensions or shape of the room. Second, placement of devices so as to take advantage of room non-linearities is crucial - fortunately, almost all two and three wall corners work well in practice. Third, any boundary reflection energy not absorbed, or canceled by energy from powered, active devices, will continue to create some non-linearities. And finally, to the point of my previous post, it is not possible to introduce generic, passive devices into a room and achieve uniform reduction in sound energy across the frequency spectrum - not that this is desirable for accurate sound reproduction in any case.

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