Gearslutz.com - View Single Post - Above the Schroeder Frequency. Diffraction.

SAC · 29th January 2010

Maybe I can help clear up a bit of the confusion regarding a few things

Don't get hung up on Schroeder versus Davis. they are essentially the same!

Manfred Schroeder (an incredible mathematician) did a comprehensive study of what makes the best large concert halls so good. In the process he determined just how large a hall must be to support a reverberant sound field.

But it’s a little more than that, as you see, the lower the frequencies you want to produce, the larger the space must be. Common reference points for this are 80 Hz for speech and 30 Hz for music. Thus, if the halls should be primarily for speech, then its volume should be ~35,000 ft^3 or larger, and if it for music, then it should be ~250,000 ft^3 or larger.

But don't worry about this! The only thing you need to know is that you are NOT dealing with a Large Acoustical Apace! And the significance of this is that the acoustical behavior in the room is DIFFERENT from Large room acoustical behavior.

You are dealing with a Small Acoustical Space. And as such a space does not support statistically reverberant sound fields, the room is dominated by modal standing waves in the low frequencies, and by focused specular reflections in the mid and high frequencies.

And Don Davis, along with Dick Heyser and Dr. Eugene Patronis and a notable group of fellow researchers (including Dr. Schroeder) did substantial research into the behavior of sound with the advent of Dick Heyser’s revolutionary TEF analyzer. And out of this can such acoustical room models as the LEDE and RFZ concepts.

OK...

To deal with the gray area that seems to confuse... Don't let it!
That just means that, depending upon the room dimensions, that each dimension supports different modes based upon their length. And as the sound wavelengths reach the point where they are shorter than the room dimension, they cease to act as a pressure wave and begin to be reflected as a specular reflection.

Remember, wavelengths longer than an object is large, flow around the object like water does a boulder in a stream. Wavelengths smaller than an object are reflected and blocked. Hence why some support standing pressure waves, and others support specular reflections.

So, for instance, the height of say 8 foot will only support standing waves for frequencies with wavelengths of 8 ft or more (~141 Hz and below). A room with a length of, say, 20 feet, will only support standing wave modes of frequencies with wavelengths longer than 20 feet (56 Hz and below).

You see, as the dimensions support differing modal ranges, and as the wavelengths become shorter, modes are supported less and less by different surfaces, until the wavelengths are smaller than all of the room surfaces and you then have a region above which all behavior is specular in nature.

So you have a transition region where one dimension will support modes, but the others will support specular reflections. It is not necessarily one fixed frequency at which a magic change occurs.

The important thing is to understand that this occurs. And that you will have a LF region where you deal with room modes.
And these are most easily identified with the frequency response and the cumulative spectral decay or waterfall plot. (they are not exactly the same, hence listing both, but for all practical purposes, they will look the same to you and you interpret them the same!)

In a Small Acoustical Space (SAS) which small rooms are, you have a finite amount of acoustical energy that drives the room. And it decays quickly.

And where you have thought of decay times and reverb, you will have ALL of that info in the CSD/waterfall in terms of each frequency’s persistence. These are resonances that persist in time. And they will coincide with the reinforced modal frequencies. So, essentially by identifying and treating the modes, you deal with the decay issues.

So, for the most part on the forum, we have the modal frequencies and frequency responses and waterfalls down.

But above that point, all that has been 'known' is that the frequency response displays comb filtering. And comb filtering is the nature response to the combination of signals (think direct signals and reflected signals) that are from spaced sources. And spaced sources vary in time and distance. And this last statement is important!

As time and distance are simply two ways to describe the same event! For instance, if a signal traveling at a fixed velocity travels for 5 seconds more than another signal; we know that the later arriving signal travels a distance of 5 seconds X the rate of travel.

So, if sound travels at 1130 feet per second, it travels at 1.13 feet per ms.
And if a signal arrives, say, 5 ms after the arrival of the direct signal, we can accurately say that the signal traveled (5ms X 1.13 feet per second) or 5.65 feet further than the direct signal used as a reference.

So....all we need now is a way to determine with precision, the arrival times of each reflection, and to determine the exact path the focused (specular) reflection has traversed.

And the tool that provides us with exactly the arrival time and the ability to determine this for each reflection, is the Envelope (Energy) Time Curve first introduced by Dick Heyser and his TEF/TDS measurement system.

Once we have that info, depending upon the sophistication of the measurement system you are using, we can rather quickly determine the exact path of the reflection.

This can be done in a variety of ways, ranging from very basic to quite elegant.

Let me start with a few basics...

(NOTE! I am dealing here with only the mechanics of the process. I am NOT addressing the available acoustical room models by which you might want to tune the room response. This is important, as in practice you need to know where you are going! You need to know what and why you are treating reflections in a certain manner, as you are wasting your time if you simply start 'treating ' reflections without a defined goal! But that is another important discussion as it gets into the psycho-acoustics of how we hear and how we want to adjust the room response to make maximal use of that understanding!)

If we know the location of the speaker used to generate the source signal, and we know the location of the mic capsule that received the signals, we know the distance and time of the direct signal simply by looking at the ETC. It is the first spike in the ETC {generally! But I won't bore you here with the occurrence of acasual or 'signals arriving before they left'. And yes, you can occasionally encounter this due to say a speaker sitting on something and being tightly coupled where the rat e of signal transmission is faster through that medium than it is through air! So the signal arrival via the alternative medium arrives before the direct signal through air!! ;-))

But weirdness such as that aside, - oh, and the ETC and Heyser spiral can indeed tell you about those too! - but let’s move on.

In some systems you must calculate the propagation delay of the equipment and correct for that by subtracting it from the signal arrival times. After all, the real travel time is simply from when the signal leaves the speaker and when it arrives at the mic. Some gear lets you simply correct for this by moving the reference point in the display to correspond to the direct signal arrival time. We will assume this. (If it does not, you simply have an additional correction to make for each signal time.)

So, assuming that we have the arrival times for each reflection relative to the direct signal, we know how much further the reflection traveled to reach the mic.

Now, how to determine the path…
The most basic method….

Say we have a string, and we mark the string with the distance that corresponds to the time of travel of the reflection.

We know the start and ending points of the travel, right? The speaker acoustic center and the mic capsule. So....if we fix the ends of the string at those points, we will have some amount of loose string left. Now, if we extend the loose string by holding it loosely at one point and see where the loop might touch any boundary surface, where it touched with the string being taut, IS the reflection point of incidence. This will be the spot many refer to when they use the mirror trick. But it will be much more precise, as we will not simply be guessing and saying that some reflections will go that way or that way; instead we have identified the specific path that THIS particular reflection has gone. And we can do this for essentially all of the reflections - including those that may touch on multiple surfaces. (Oh, and if we encounter a symmetrical instance where two reflective paths have the have the same length and coincide with the arrival times...no problem, we can easily identify both in the same manner and we will know this as their gain will reflect this (sorry for the pun) accordingly!)

A more practical method is, after identifying a reflection of interest, to repeat the measurement manually or to let the platform automatically repeat it at intervals, and to use a small piece of absorption to block a path to the side of the microphone. And as you move the blocking piece around the mic, you will eventually identify a position where that particular reflection is 'gone' - or blocked. And here you know that you have intercepted it in 'flight'. From this, you can extrapolate the path from the mic capsule through the blocking location to identify the general location of the reflection incident point on a boundary. Further iterations of this process can further refine the location.

After doing this a 'few' times, pattern recognition will quickly set in, and as you will know the relative distances of the various boundaries in a room (walls, ceiling, floor, etc., and you will be able to quickly identify the source of the first, second and third, etc. reflections. And this will help you to more quickly focus in on the particular spot of reflection incidence.

'Larger' measurement and analysis platforms enable one to more quickly do this. One even is able to generate a 3D ETC that when you move the cursor to the particular point of the reflection, will generate the X,Y, and Z coordinates such that you can replace the mic with a laser pointer mounted in a mount similar to a surveyor's transit and to simply dial in the X,Y, and Z coordinate and the laser will point to the exact spot on the boundary surface!

What makes this even more significant is that some reflections will be of much higher strength (gain) then others. And if they arrive too hot, or at the 'wrong' time to cause problems in the imaging or intelligibility of the signal, we can identify them and correct for the particular issue specifically. And that is the key difference that a 'professionally' tuned room offers differently from a 'non-professional' room. The reflection energy is used to literally tune the room. It is not simply seen as an enemy to be eliminated! In fact, a key component in many designs is to take exactly that excess focused energy and to both reduce it to a desired level (not eliminate it!) and to spread it out in time (temporal dispersion) and to disperse it in space (spatial dispersion) such that we create a more well-behaved semi-diffuse sound field.

OK, I'll stop here for now...

A sample ETC so that you have something to look at....

29th January 2010	#21
SAC Registered User Join Date: Dec 2009 Posts: 2,622	Maybe I can help clear up a bit of the confusion regarding a few things Don't get hung up on Schroeder versus Davis. they are essentially the same! Manfred Schroeder (an incredible mathematician) did a comprehensive study of what makes the best large concert halls so good. In the process he determined just how large a hall must be to support a reverberant sound field. But it’s a little more than that, as you see, the lower the frequencies you want to produce, the larger the space must be. Common reference points for this are 80 Hz for speech and 30 Hz for music. Thus, if the halls should be primarily for speech, then its volume should be ~35,000 ft^3 or larger, and if it for music, then it should be ~250,000 ft^3 or larger. But don't worry about this! The only thing you need to know is that you are NOT dealing with a Large Acoustical Apace! And the significance of this is that the acoustical behavior in the room is DIFFERENT from Large room acoustical behavior. You are dealing with a Small Acoustical Space. And as such a space does not support statistically reverberant sound fields, the room is dominated by modal standing waves in the low frequencies, and by focused specular reflections in the mid and high frequencies. And Don Davis, along with Dick Heyser and Dr. Eugene Patronis and a notable group of fellow researchers (including Dr. Schroeder) did substantial research into the behavior of sound with the advent of Dick Heyser’s revolutionary TEF analyzer. And out of this can such acoustical room models as the LEDE and RFZ concepts. OK... To deal with the gray area that seems to confuse... Don't let it! That just means that, depending upon the room dimensions, that each dimension supports different modes based upon their length. And as the sound wavelengths reach the point where they are shorter than the room dimension, they cease to act as a pressure wave and begin to be reflected as a specular reflection. Remember, wavelengths longer than an object is large, flow around the object like water does a boulder in a stream. Wavelengths smaller than an object are reflected and blocked. Hence why some support standing pressure waves, and others support specular reflections. So, for instance, the height of say 8 foot will only support standing waves for frequencies with wavelengths of 8 ft or more (~141 Hz and below). A room with a length of, say, 20 feet, will only support standing wave modes of frequencies with wavelengths longer than 20 feet (56 Hz and below). You see, as the dimensions support differing modal ranges, and as the wavelengths become shorter, modes are supported less and less by different surfaces, until the wavelengths are smaller than all of the room surfaces and you then have a region above which all behavior is specular in nature. So you have a transition region where one dimension will support modes, but the others will support specular reflections. It is not necessarily one fixed frequency at which a magic change occurs. The important thing is to understand that this occurs. And that you will have a LF region where you deal with room modes. And these are most easily identified with the frequency response and the cumulative spectral decay or waterfall plot. (they are not exactly the same, hence listing both, but for all practical purposes, they will look the same to you and you interpret them the same!) In a Small Acoustical Space (SAS) which small rooms are, you have a finite amount of acoustical energy that drives the room. And it decays quickly. And where you have thought of decay times and reverb, you will have ALL of that info in the CSD/waterfall in terms of each frequency’s persistence. These are resonances that persist in time. And they will coincide with the reinforced modal frequencies. So, essentially by identifying and treating the modes, you deal with the decay issues. So, for the most part on the forum, we have the modal frequencies and frequency responses and waterfalls down. But above that point, all that has been 'known' is that the frequency response displays comb filtering. And comb filtering is the nature response to the combination of signals (think direct signals and reflected signals) that are from spaced sources. And spaced sources vary in time and distance. And this last statement is important! As time and distance are simply two ways to describe the same event! For instance, if a signal traveling at a fixed velocity travels for 5 seconds more than another signal; we know that the later arriving signal travels a distance of 5 seconds X the rate of travel. So, if sound travels at 1130 feet per second, it travels at 1.13 feet per ms. And if a signal arrives, say, 5 ms after the arrival of the direct signal, we can accurately say that the signal traveled (5ms X 1.13 feet per second) or 5.65 feet further than the direct signal used as a reference. So....all we need now is a way to determine with precision, the arrival times of each reflection, and to determine the exact path the focused (specular) reflection has traversed. And the tool that provides us with exactly the arrival time and the ability to determine this for each reflection, is the Envelope (Energy) Time Curve first introduced by Dick Heyser and his TEF/TDS measurement system. Once we have that info, depending upon the sophistication of the measurement system you are using, we can rather quickly determine the exact path of the reflection. This can be done in a variety of ways, ranging from very basic to quite elegant. Let me start with a few basics... (NOTE! I am dealing here with only the mechanics of the process. I am NOT addressing the available acoustical room models by which you might want to tune the room response. This is important, as in practice you need to know where you are going! You need to know what and why you are treating reflections in a certain manner, as you are wasting your time if you simply start 'treating ' reflections without a defined goal! But that is another important discussion as it gets into the psycho-acoustics of how we hear and how we want to adjust the room response to make maximal use of that understanding!) If we know the location of the speaker used to generate the source signal, and we know the location of the mic capsule that received the signals, we know the distance and time of the direct signal simply by looking at the ETC. It is the first spike in the ETC {generally! But I won't bore you here with the occurrence of acasual or 'signals arriving before they left'. And yes, you can occasionally encounter this due to say a speaker sitting on something and being tightly coupled where the rat e of signal transmission is faster through that medium than it is through air! So the signal arrival via the alternative medium arrives before the direct signal through air!! ;-)) But weirdness such as that aside, - oh, and the ETC and Heyser spiral can indeed tell you about those too! - but let’s move on. In some systems you must calculate the propagation delay of the equipment and correct for that by subtracting it from the signal arrival times. After all, the real travel time is simply from when the signal leaves the speaker and when it arrives at the mic. Some gear lets you simply correct for this by moving the reference point in the display to correspond to the direct signal arrival time. We will assume this. (If it does not, you simply have an additional correction to make for each signal time.) So, assuming that we have the arrival times for each reflection relative to the direct signal, we know how much further the reflection traveled to reach the mic. Now, how to determine the path… The most basic method…. Say we have a string, and we mark the string with the distance that corresponds to the time of travel of the reflection. We know the start and ending points of the travel, right? The speaker acoustic center and the mic capsule. So....if we fix the ends of the string at those points, we will have some amount of loose string left. Now, if we extend the loose string by holding it loosely at one point and see where the loop might touch any boundary surface, where it touched with the string being taut, IS the reflection point of incidence. This will be the spot many refer to when they use the mirror trick. But it will be much more precise, as we will not simply be guessing and saying that some reflections will go that way or that way; instead we have identified the specific path that THIS particular reflection has gone. And we can do this for essentially all of the reflections - including those that may touch on multiple surfaces. (Oh, and if we encounter a symmetrical instance where two reflective paths have the have the same length and coincide with the arrival times...no problem, we can easily identify both in the same manner and we will know this as their gain will reflect this (sorry for the pun) accordingly!) A more practical method is, after identifying a reflection of interest, to repeat the measurement manually or to let the platform automatically repeat it at intervals, and to use a small piece of absorption to block a path to the side of the microphone. And as you move the blocking piece around the mic, you will eventually identify a position where that particular reflection is 'gone' - or blocked. And here you know that you have intercepted it in 'flight'. From this, you can extrapolate the path from the mic capsule through the blocking location to identify the general location of the reflection incident point on a boundary. Further iterations of this process can further refine the location. After doing this a 'few' times, pattern recognition will quickly set in, and as you will know the relative distances of the various boundaries in a room (walls, ceiling, floor, etc., and you will be able to quickly identify the source of the first, second and third, etc. reflections. And this will help you to more quickly focus in on the particular spot of reflection incidence. 'Larger' measurement and analysis platforms enable one to more quickly do this. One even is able to generate a 3D ETC that when you move the cursor to the particular point of the reflection, will generate the X,Y, and Z coordinates such that you can replace the mic with a laser pointer mounted in a mount similar to a surveyor's transit and to simply dial in the X,Y, and Z coordinate and the laser will point to the exact spot on the boundary surface! What makes this even more significant is that some reflections will be of much higher strength (gain) then others. And if they arrive too hot, or at the 'wrong' time to cause problems in the imaging or intelligibility of the signal, we can identify them and correct for the particular issue specifically. And that is the key difference that a 'professionally' tuned room offers differently from a 'non-professional' room. The reflection energy is used to literally tune the room. It is not simply seen as an enemy to be eliminated! In fact, a key component in many designs is to take exactly that excess focused energy and to both reduce it to a desired level (not eliminate it!) and to spread it out in time (temporal dispersion) and to disperse it in space (spatial dispersion) such that we create a more well-behaved semi-diffuse sound field. OK, I'll stop here for now... A sample ETC so that you have something to look at....