A room can enforce a wave twice as long as it is

[damonrpayne]

So I'm working on a web-based room mode calculator for predicting room response and one aspect of the math gave me pause. There is a comment that "A room can enforce a wave twice as long as its dimension" for axial modes. What exactly is meant by this. The way every other tool has implemented this in the math is to make the speed of sound appear to be 1/2 its true value. Thoughts?

[Chris Robinson]

Damon,

I may be seeing it wrongly, but the two statements are simply the obverse of each other.

No difference, essentially.

Chris

[Chris Robinson]

Here's a quote from a few years ago by Artto ...

Think it's appropo ...

"Another "trick" you can use is the Half-Room Principal (Room Dimensions for Optimum Listening and the Half Room Principal, IRE Transactions on Audio, Vol AU-6, No1 Jan-Feb 1958, pp 14-15). For instance, my room is 27 wide. A 42Hz note has a wavelength of aprox. 27. So based on the longest dimension of the room, the room will accurately convey the full wavelength of a 42 Hz tone. But based on the Half Room Principal, you can expect a reasonably flat room response down to 21Hz (21Hz=54 wavelength. 54/2 (one-half of the wavelength)=27.

If you take this one step further & use the diagonal dimension (which you can do with K-horns because of their corner placement & 45 degree angle toe in) it works even better. My room has a diagonal dimension of 32 which ½is one-half of 64. 64 puts you at about 17-18Hz. My system has measured down only 9Db below 20Hz with no electronic EQ. Not bad for folded horn-loaded speaker of this size. And in fact, that puts the K-horns at about 95Db/watt below 20Hz. Much better efficiency than any of the "sub-woofers" or so-called "flat" "audiophile" speakers out there.

A dimension you want to avoid is 19 (or multiples & fractions) thereof as it is the wavelength of 60Hz (electrical hum)."

[WMcD]

I don't know about altering the speed of sound issue.

This is, though, a standing wave issue.

So call standing waves occur when there are two "sources" at either end of a transmission line where they travel toward each other.

You have to envision you room as, a bunch of paths or transmission lines.

A) The first three paths to be considered are between the side walls, the front and back walls, and the floor and ceiling. Those three are defined as where walls face each other. The path lenght is hopefully not the same. To define the length, we have to pull an imaginary tape measure.

The next is the corner pairs. Say right front bottom and left rear top. And you have the left bottom front and the right rear top. Two more transmission lines. Here if you have a normal room, these paths are of the same length.

C) Then you have to consider the other pairings of corners. Say front right bottom and front right top.

Please note these corners are not the big walls which cause reflections. They are worse in a way. in the diagongal corner pair of one corner can act as a conical horn and the other can act as an ear horn type microphone. Good transmitter feeding a good receiver.

D) These paths lead to the eigenvalues of resonances. Eigen meaning "self" in German. They are self resonating frequencies. The paths act like organ tubes with a resonant frequency. The longer the organ pipe, the lower the frequency.

D) The walls and corners can act as sources simply because they reflect sound. The original source of sound can be anywere in the room. Of course if the speaker is up against one of boundries, it tends to exite that one more.

E) It may be helpful to recall that sound waves propagate because they have two properties. One is pressure, the other is particle velocity. These trade off between each other.

If there is localized pressure, the particles move away with velocity. Then they hit other particles, bunch up, and have localized increased density. This means there is increased pressure. Then the pressure forces away particles with velocity. Etc.

Pressure highs are where velocity is low. So pressure wave and particle velocity waves are always 180 degrees out of phase; yet they exist, morphing back and forth along the path of propagation.

F) This E) is fine in free space but the sound wave hits a wall. The wall doesn't move. The particles bounce off with zero average velocity (half incoming half out going). But this also means the pressure at the wall surface is high (at least for a while). The wall is a pressure anti-node, meaning it is not a zero point. Nodes are zero points (of whatever). Walls are a velocity node. But they also flip the velocity from plus 1 (i.e. coming in) to minus 1 (i.e. leaving).

G) Standing waves are more difficult to explain. Essentially you have two wave trains strarting from either end of the track. They add and subtract along the way. Again, reflections serves as the sources in the room. You do have a sine wave resulting.

To some extent, we can look at half a sine wave as they add and subtract at every point along the path. (Remember, we have a lot of paths.)

H) Generally, you have to look at a sine wave as having the transitions from zero, to plus 1 (1/4 wavelenght) to zero (2/4 wavelenghts) to minus 1 (3/4 wavelenghts) to zero (4/4 wavelenghts). That sine can describe particle velocity. So the walls are the zero points. Note we've got TWO nodes in wavelenght. Important.

I) The lowest frequency standing wave (longest wavelenght) of the eigen frequency of the room is when the walls are spaced so they create the node at each facing wall. Note the velocity node is at the wall.

J) The above is less clear than I'd like. Diagrams would help. However, it tells a bit about how the lowest physical lenght with resonance is a half wavelenght, at least with two hard walls.

K) Also, by considering path lengths between reflectors, the room is a bunch of organ pipes. It would be nice if we could make a room where the pipes are of differing lenghts so that they even out to resonate (or have standing waves) at progressive steps in frequency or wavelength.

My pedantic rant.

Gil

F)

[Chris Robinson]

Gil, pretty durned good pedantic rant!

Into my notes that one goes ...

Chris

[damonrpayne]

Gil, some responses:

-I see from the Artto quote that the 1/2 speed of sound issue is a math trick for the half room principal

-So far I only have the math for the axial modes (the 'first 3' you mention) done. The tangential and oblique are coming.

[Chris Robinson]

Damon,

The first axial modes are the ones you can treat with sound diffusors, absorbers or reflectors. The secondary (et al.) modes are going to be much more time consuming since they deal with sound waves bouncing all over the place after the initial reflections.

Treating the first modes will get you 90% of the way there. I'd focus on those and see how it goes.

Chris

[mas]

To reinforce what Gil has mentioned:

Waves carry energy and momentum, and whenever a wave encounters an obstacle, they are reflected by the obstacle. This reflection of the object can be analyzed in terms of momentum and energy conservation. If the wall is a hard fixed boundary and the collision is 'perfectly elastic', then the wall absorbs none of the energy and all of the incident energy and momentum is reflected with an identical velocity with the reflection being 180 degrees out of phase from the incident wave.

If the wall is a non-fixed/non-rigid boundary, then the collision is 'inelastic', the restorative force is zero and the wall absorbs some of the incident energy and momentum and the waves lose some energy and velocity with the reflection being in phase with the incident waveform.

If the reflective surface is neither perfectly hard nor perfectly soft, and is somewhere in between, the restorative force is less than equity and part of the wave is reflected and part of the wave is absorbed or transmitted through the boundary surface.

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The exact behavior of reflection and transmission depends on the material properties on both sides of the boundary. The sum of this behavior is termed the acoustical impedance, which is essentially the total opposition of the wall system to sound waves comprised of resistive and reactive components.. And just like what you may be used to in electronics, the acoustical impedance also has an acoustical resistance component, which is the real component associated with the opposition and dissipation of kinetic sound energy upon striking a wall, as well as an acoustical reactance, which is a value related to the mass of the wall, along with the relative elasticity of the surface which comprises the imaginary component corresponding to the stored potential stored energy in the system.

As others have observed, the acoustical impedance of the wall system is characterized by very complex non-linear dependencies with respect to frequency. And while charts can provide some useful relative measure of a materials effectiveness regarding reflection and sound transmission characteristics, the actual effect is a complex sum of the various wall components. By far, the easiest way to determine the performance of a reflective surface is to measure it.

An easy way to visualize this phenomena is to tie a rope to a tree and 'shake it up and down' and watch the waves and the reflections that result. This phenomena is the same for electrical energy and the concept of 'termination'. A common place you will experience practical effects are in your cable or satellite distribution network, if you leave a leg 'unterminated' by a (characterisitically) 75 ohm resistor (built into a terminator cap). Reflections are the result of an imperfect impedance match - as a load equal to the source would absorb the energy rather than reflect it.

One question I do have...

Are you 'doing the math' regarding standing waves simply to build character? ;-) Is there a reason the online standing wave (eigen)mode calculators are not sufficient?

If anyone desires the equations and has lots of spare time on their hands, please say so, or PM me.

Axial Modes are the easiest to calculate as well as being the most important. Tangential modes exhibit ~ one half the intensity, while Oblique modes exhibit ~ one quarter the intensity. The concerns regarding these types of modes is when one type of mode occurs near another type of mode as the result will be effected by what is caled superposition - the summation of the waveforms, so the calculation of all of the mode types is prudent to determine where the overlap may occur, as those frequencies may be a problem.

Oh, and to comment on the diagrams that are commonly used to represent modes and the problem one experiences by mistaking a stylized description with reality! All of these modes actually hit the Entire surface of each wall. The diagrams treat them as linear 'lines' and you may get the erroneous impression that you can treat just a section of each wall corresponding to the wave-wall intersection as pictured in the representational diagrams to damp the standing wave.

Also, real rooms are not ideal, so small variations in angles are involved. The calculations provide only an idealized and overly simplified mathematical model. This, combined with the fact that the calculations provide only for the center frequency of the standing wave frequency band should reinforce why we are most concerned with modes that occur close to one another. These are not high Q phenomena.

Therefore, while room calculations and calculators are handy, it is still preferable to simply take real measurements with time based measuring tools. (see diagram of a simple standing wave)

Standing waves are addressed with traps!!

BTW: Surface treatments do not address these modes (well, none that you want in your house!) These standing waves are determined by the room geometry.

Above 300Hz, sound is influenced more by what the room is made of and the materials' characteristic surface reflectivity than by the dimensions and shape of the room.

RoomModes&HelmholtzResonatorLg.pdf

[damonrpayne]

Damon,

The first axial modes are the ones you can treat with sound diffusors, absorbers or reflectors. The secondary (et al.) modes are going to be much more time consuming since they deal with sound waves bouncing all over the place after the initial reflections.

Treating the first modes will get you 90% of the way there. I'd focus on those and see how it goes.

Chris

Chris,

This is not a room treatment project. I am creating a room-mode calculator that runs in a web application. I feel the oblique and tangential modes should be included but seperately marked on the graphs etc.

[damonrpayne]

...

One question I do have...

Are you 'doing the math' regarding standing waves simply to build character? ;-) Is there a reason the online standing wave (eigen)mode calculators are not sufficient?

If anyone desires the equations and has lots of spare time on their hands, please say so, or PM me.

...

I have the equations, etc. As I've stated I'm building a room mode calculator for my own website. This gives me the potential to tweak it to make it better. Specifically, many of the web-based tools do not create a graphical visualization but just list #s. Obviously I'd rather people used MY website than one of the other tools.

[mas]

That is fine! I sincerely applaud your goal!

But let me see if I can convince you to save some of your energy for more useful pursuits that actually result in greater utility.[]

The reason I mention this is that more precise calculations are actually spurious, as they assume a much greater degree of precision than is valid! And they do not represent real world spaces with a great degree of accuracy - even if everything else was ideal.

So my serving as the devil's advocate is only intended to prevent anyone from pretending that they are really achieving greater accuracy. As limited mathematical calulations cannot provide the desired improvement.

It is akin to calculating the area of a surface to 3 decimal place precision when the measuring instrument used to measure the surface dimensions is marked in 'whole' integer units with a tolerance of 10%!

Or, to put it another way, if all I have is a foot long stick with no markings, the precision of the instrument is to estimate to the nearest 10th of the base unit. So I can make measurements that are limited in precision to tenths of a foot. More rigid standards could be quoted to say that I am limited to the nearest whole foot! Maybe I also take measurements with a tool that can now measure dimensions to 20 decimal place precision. Now, if I then take one measurement from each series of measurements and calculate a derived value from the two measurements, say area, my precision of the derived answer is limited to the least precise measurement. Not to even mention that the calculation assumed an ideal 'perfect' form! So we have quite a few very limiting conditions already assumed. In other words, it makes no sense to pretend that you can design the latest generation CPU using a 45nm process using a meter stick precise to the nearest mm. Room modes are the same way! The up side is that it serves no valid purpose to do so.

All you need be concerned with in the calculations (due to their NOT providing a Q for the resonance) is the grouping - the clustering of the various mode center frequencies. Plus these 'ideal' calculations are good ONLY for ideal perfectly rectangular closed rooms - and they ignore coupling of adjacent spaces via doors or walkthroughs, alcoves, stairways etc., thus rendering the best calculation just a guestimation - a very general estimate - but one generally sufficient for the proverbial game of hand grenades.

Thus a tool such as ModeCalc calulates the center frequencies as well as displays the center frequencies graphically in order to show such clustering. And a rough guess is fine, especially as that is all this method is capable of providing! It's precision is more than adequate for the tools purpose.

The ONLY reasonable way to account for the real world anomalies is to measure the modes, which is easily done and easily graphically displayed via time based measurement tools.

http://www.realtraps.com/pmodecalc.htm

[colterphoto1]

Damon,

The first axial modes are the ones you can treat with sound diffusors, absorbers or reflectors. The secondary (et al.) modes are going to be much more time consuming since they deal with sound waves bouncing all over the place after the initial reflections.

Treating the first modes will get you 90% of the way there. I'd focus on those and see how it goes.

Chris

Chris,

This is not a room treatment project. I am creating a room-mode calculator that runs in a web application. I feel the oblique and tangential modes should be included but seperately marked on the graphs etc.

What is the pupose of all this math and information about the way sound waves behave in a room if not to help define what treatments are necessary to treat, or correct the room? I can see that it would be helpful for designing the room dimensions in the first place.

Is this math for math's sake?

[damonrpayne]

I feel like I'm missing some obvious point here, not enough coffee yet this morning, I'll say it again:

There are any number of spreadsheet-based calculators to do room modes that already exist. I used those to predict response and help pick my room dimensions. 20'x24'x9' The second phase of my room treatment will involve using real-world measurements and experimenting with treatments with true numbers to mess with.

The room-mode calculator I am writing currently is for other people's use and will run in the browser on KlipschCorner.com. I am doing this so people are Super Happy with KlipschCorner.com.