# Bill Eppler on cue balls, modes, diffraction, and impulses

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### Bill Eppler on cue balls, modes, diffraction, and impulses

Folks,

I hope nobody minds, but I figured it's best to start a new topic for this rather than tack it onto the end of the existing cue balls thread.

Last night I spent the evening with my genius friend and lifetime mentor Bill Eppler. Not only is Bill an expert on all matters audio, he can also explain advanced concepts in a way even I can understand. Where else could one get a college-level education for the cost of three beers and a dinner?

Bill and I discussed some very interesting stuff, and by the end of the night I had learned a lot and walked away with even more to think about and share / ask / discuss here.

Cue balls:

In the Cue Balls thread I believe we all ended up agreeing that at higher frequencies sound does in fact travel like a cue ball, but at lower frequencies - below the Schroeder frequency for the room - the "ray tracing" model breaks down and sound waves instead propagate as pressure patterns in the room. This brings up two new questions:

1. How can some low frequency room modes involve four or six surfaces when nothing is actually bouncing off those surfaces at an angle like a ray?

2. If non-axial modes do travel so they touch four or six surfaces, as shown in all of the text books, why is the first non-axial mode's frequency higher than the first axial mode which has a shorter path length?

Diffraction:

In my Acoustics FAQ is this drawing of a 2 by 4 foot absorbing panel that's 4 inches thick:

In the accompanying text I explain that with a panel this thick, having four inches of edge surface all the way around increases the 8 square feet of front surface area by 50 percent. Therefore, this is what accounts for absorption coefficients greater than 1.0, because the edge surface is not included in the calculations that convert Sabins to an absorption coefficient. While this panel is considered by the conversion formula to have 8 square feet of surface, it's really 12 square feet when you include the edges that are also exposed to the room during testing.

It has been suggested that this explanation is wrong, and the true cause of coefficients greater than 1.0 is diffraction of sound waves at the edges of the front surface. When a sound wave travels along a surface and reaches the end, the surface impedance changes suddenly and the wave then wraps around that edge. Sort of like water that's travelling in a pipe and is contained by the pipe. When the water reaches the end of the pipe it is no longer constrained to the size of the inside diameter, and so is free to expand and spread out. And since there had been outward pressure against the pipe walls, when the impedance changes suddenly at the end of the pipe the water does in fact start to spread outward.

But this does not change the fact that the higher absorption is still caused by having more surface area! Whether a wave that travels along the surface wraps around the corner and is then absorbed by the edge, or it's just that the edge is present in the room in the first place, either way it's still the edge that's absorbing. Moreover, I'm not convinced that diffraction is a big contributor at the frequencies the panel is absorbing. Frequencies that are in the range the panel can absorb will enter the panel, rather than skate along the surface. Perhaps at extreme angles of incidence, and with very dense material, a midrange frequency will skate rather than sink in. But it seems to me in that case much of it will skate again anyway when it wraps around the edge.

Impulses:

In the Cue Balls thread I was asked how a sound wave could travel like a cue ball, and I said:

Suppose you make a very short click sound in a wave editor program, let's say with fast rise and fall times and 1 millisecond duration. Now play that click through a loudspeaker in a room. The speaker cone lurches forward for a moment sending a sound wave "bouncing around the room" until it runs out of energy.
Now, I was considering only the high frequency content of that wave. However, what some folks may not realize is that a single impulse - no matter how brief - has significant energy at frequencies lower than the pulse length might imply. As proof, consider a 1 millisecond impulse that repeats every 10 milliseconds. Clearly you will have energy at 100 Hz. And if it repeats once per second you can see there is energy at 1 Hz. So by extension even if it never repeats there is still energy down to as low a frequency as you care to measure.

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ethan:
It has been suggested that this explanation is wrong, and the true cause of coefficients greater than 1.0 is diffraction of sound waves at the edges of the front surface. When a sound wave travels along a surface and reaches the end, the surface impedance changes suddenly and the wave then wraps around that edge. Sort of like water that's travelling in a pipe and is contained by the pipe. When the water reaches the end of the pipe it is no longer constrained to the size of the inside diameter, and so is free to expand and spread out. And since there had been outward pressure against the pipe walls, when the impedance changes suddenly at the end of the pipe the water does in fact start to spread outward.

The fire brigade won't like this. They want the water coming out of the hose to be directed, wouldn't they?
So do sound engineers designing horns and line arrays.

Ethan:
Now, I was considering only the high frequency content of that wave. However, what some folks may not realize is that a single impulse - no matter how brief - has significant energy at frequencies lower than the pulse length might imply. As proof, consider a 1 millisecond impulse that repeats every 10 milliseconds. Clearly you will have energy at 100 Hz. And if it repeats once per second you can see there is energy at 1 Hz. So by extension even if it never repeats there is still energy down to as low a frequency as you care to measure.

Highest regards,

Bert
bert stoltenborg
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

I hope those beers were Belgian?
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Congratulations Ethan:

Perhaps at extreme angles of incidence, and with very dense material, a midrange frequency will skate rather than sink in

Andre
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ethan,

Before Hugh thinks that me is starting another war on you (you know that we had some very interesting discussions here and there without going at each others throats ):

When you have an impulse in your time window of ETF or whatever, and you window it, cut it of, at 1 msec, that is something completely different than a dirac pulse, and that is what your buddy is suggesting, IMO.

When you window your impulse at 1 msec and you apply a FFT, you will see that the thing is really limited in freq bandwidth. Try it, and you'll see.

Regards (no sarcasme, really),

Bert
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

A dirac pulse is a theoretical concept that has all freqs in it.
But as infinite high freq's have infinite small time information, you'll get an infinite high impulse because you try to store all this information in a infinite small amount of time.
So it has a very high spike in the start of the impuls. The lower freqs need time to develope, as states the uncertainty theory of Werner Heisenberg, so a real dirac pulse also has infinite long time resolution. You are not allowed to limit it to just 1 msec.

Bert
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ive always dreamed about turning this into a forum about quantum mechanics
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Then we should definitely discuss Bell's Theorem!

Cheers,

Jim
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert,

> When you have an impulse in your time window of ETF or whatever, and you window it, cut it of, at 1 msec <

That's not what I'm talking about.

> a dirac pulse <

Nor is that. I'd never heard of that, but this first link Google returned says it's a myth because its infinitely short and thus impossible to realize. So while this type of pulse may have some academic interest, it's clearly irrelevant to what I described.

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

> a dirac pulse <

In the real world would that be pink noise?

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert,

> The fire brigade won't like this. They want the water coming out of the hose to be directed, wouldn't they? <

Sure, and this amplifies my point even better about how small the effect of diffraction really is. And of course fire hoses (like garden hoses) use nozzles to direct the flow. But my basic premise remains - what really increases absorption is the presence of all that edge surface, regardless of anything else going on.

Right?

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ethan Winer wrote:Bert,

> The fire brigade won't like this. They want the water coming out of the hose to be directed, wouldn't they? <

Sure, and this amplifies my point even better about how small the effect of diffraction really is. And of course fire hoses (like garden hoses) use nozzles to direct the flow. But my basic premise remains - what really increases absorption is the presence of all that edge surface, regardless of anything else going on.

Right?

--Ethan

hmmm?

Ethan, have a look at the picture in my studio diary of the huge makeshift absorber I was testing in my room. The absorber itself made a great difference for the better as I've already said.

However take a look at the MDF tops I put on the rockwool. I tested with and without those MDF tops, and they actually made NO Difference worth even worrying about. I was pleased by this of course, as I wanted some more worktop space in the studio. But I was quite prepared to leave that top edge ( of quite apreciable area ) absorbent if it HAD have made a difference.

And if the diffraction effect was that small how comes many pro studios soffit mount their monitors to cure the diffraction around the speaker cabinet. Even though soffit mounting excites mroe mdoes than free standing speakers, and thus requires a lot more rear wall absorption.

My Genelecs Soffit mounted sound so much better than freestanding, and it ain't just because I've got a better room now. The previous room was pretty good in fact acoustics wise. Just not as good as the new one, and had NO soudnproofng

I'm not directly disagreeing with you, as I don't know enough to do that, I'm just throwing some questions into the discussion.

Paul
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Paul,

> I tested with and without those MDF tops, and they actually made NO Difference worth even worrying about. <

Sure, at low frequencies. But I bet blocking all that surface would make a very large difference at higher frequencies like those measured when testing absorber panels. And to better test that directly you'd want to measure reverb time rather than frequency response.

> And if the diffraction effect was that small how comes many pro studios soffit mount their monitors to cure the diffraction around the speaker cabinet. <

My understanding is the main benefit of soffit mounting is to avoid SBIR, where sound leaving the rear of the speaker causes comb filtering off the front wall (the wall behind the speakers). And I'm not saying that diffraction does not occur or is insignificant! I'm saying that regardless of whether diffraction causes wrapping or not, it's still the presence of the additional edge that increases the absorption. At least that seems like the most plausible explanation.

How else would the act of diffraction alone increase a panel's absorption?

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ethan Winer wrote:
> a dirac pulse <

Nor is that. I'd never heard of that, but this first link Google returned says it's a myth because its infinitely short and thus impossible to realize. So while this type of pulse may have some academic interest, it's clearly irrelevant to what I described.

Well, just for linguistic clarity, it doesn't say it's a myth, but rather a mathematical fiction (which is very different than a myth, especially where said mathematical fiction serves as a predictive tool). Impossible to realize in the context of seismic activity (per said link), but in other descriptions of the use of Dirac pulses (e.g., medical use), they say that it can be realised only approximately, and that the Dirac function serves as a predictive tool.

Perhaps you guys are indeed talking about different things but, after reading a few of the links in the google search Ethan linked to, I feel I'm none the wiser as to how this may or may not be relevant in this context (perhaps because of lack of some fundamental understanding).

Any good links on Dirac pulses that might give some more entry level info on what they are and how they would be used in this context, Bert? I guess I'm seeing conflicting information as to whether a Dirac impulse is extremely short or infinitely long.

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Hey Scott,

When you try to store all waves to the infine small freqs you wil have waves that are so short that they will store all energy in an infinite amount of time. So you get an infiniteamount of energy in an infinite slice of time.
That sounds like it must go wrong, doesn't it?

But that's a dirac pulse. In reality we try to get close to this ideal, like in ETF of Mlssa or whatever.

But of course the low energy is smeared over time (longer waves) and doesn't appear as this spike of the highs.

When you FFT such a spike it analyzes all waves in it (amplitudes ad eventually phase) and gets you to the freq domain.

But you understand: a spike like this, because it is always describes as an infinite puls, seems a very short pulse.

But to get to he low freqa, you have to examine the proper amount of time, the tine a wave needs to develope.

So a dirac is infintite in time as well as in freq.

When you take a 1 msec pulse as ethan says, he might consider it as a gunshot (also much highs in the impulse) but it has only time resolution to 34 cm = 1000 Hz.

Ethan sas I don't understand his impulses that yield low freqs at 1 msec, so: go for it, my man.

Goddammit, this took an hour, I'm just back from a gig, drunk and stoned
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

When you try to store all waves to the infine small freqs you wil have waves that are so short that they will store all energy in an infinite amount of time. So you get an infiniteamount of energy in an infinite slice of time.
That sounds like it must go wrong, doesn't it?

Infinite SMALL amount of time, of course
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert,

> go for it, my man <

If the 1 millisecond pulse repeats at a slower rate than 1 KHz - or if it never repeats! - there is still low frequency energy. Or maybe FFT algorithms can see into the future and can tell if a repeat of the pulse is going to happen soon?

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Scott,

> it doesn't say it's a myth, but rather a mathematical fiction <

You're right, my bad for lumping the two together. The main point is that infinitely narrow pulses are a theoretical exercise, where what I'm talking about is reality that can be easily measured.

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

If the 1 millisecond pulse repeats at a slower rate than 1 KHz - or if it never repeats! - there is still low frequency energy.

I really don't get it, Ethan. Could you please explain?
A 1 millisecond pulse is a pulse lasting 1 millisecond, and thus has a bandwidth of 1 millisecond which in the frequency domain is 34 cm = 1000 Hz?
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert,

> I really don't get it <

Okay, let's say you use an audio editor program to make a pulse that's 1 millisecond long with fast rise and fall times. Now insert 9 milliseconds of silence, then paste the pulse at the end of the silence. Now you have a 1 ms pulse, 9 ms of silence, and the pulse again. Repeat this sequence a couple of hundred times so you have essentially created a 100 Hz square wave with a 10 percent duty cycle.

Now analyze the file. What frequencies do you have?

Then do it again but with 10 seconds between each pulse, and analyze again. What frequencies do you have now?

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Now you have a pulse train with a time length of much more that 1 msec.
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert,

> Now you have a pulse train with a time length of much more that 1 msec. <

Okay, so analyze just one pulse's worth of the train. This is why I joked about an FFT algorithm being able to see into the future. The LF content is there, even before other pulses arrive later. Even though it may not be intuitively obvious, I'm telling you there is content below 1 KHz!

Do you have a spectrum analyzer program to try a test yourself?

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

I'm aware of the validity of your remarks, but your 1 msec pulse statement doesn't make sense. You are using a delta function (pistol shot) in a pulse train like MLS does, and your 1 kHz remark is confusing
You do nothing with a 1 kHz filter or someting, you're just exiting a speaker or whatever with a delta function (dirac pulse), an approximation of a perfect pulse.
IMO this makes your statement about the pulse bouncing through the room, in the cue ball thingie, less valid.
You in fact use a wideband signal

Bert

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert,

> I'm aware of the validity of your remarks ... You in fact use a wideband signal <

Yes, a narrow pulse is wide band!

Here's another way to look at it: Flip the polarity so instead of thinking of the pulse as narrow up, it's narrow down. Now you should be able to see that there's lots of energy for a long time, yes?

If you still don't get it let me know and I'll ask Bill for a math-based explanation. I'm not a math guy, so Bill knows to explain things to me without any math. But I'm pretty sure there's a formula that will prove the point.

Also, nobody has any comments on edge surface and diffraction? Or an explanation for why non-axial modes that hit all four surfaces start at a higher frequency even though it would seem the path length is longer?

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ethan Winer wrote:.....Or an explanation for why non-axial modes that hit all four surfaces start at a higher frequency even though it would seem the path length is longer?

--Ethan

I'm not saying this is correct, it is only a theory of mine, and part of why I don't think the cue ball notion is correct.....

If you look at the rectangle described by a tangential mode off 4 surfaces in a rectagular room, I can certainly see why this can be considered a 'path'

But I look at it as more of Boundaries containing a space, rather then paths.

Now, any rectangle 'inside another rectangle' ( at an angle ) HAS to have smaller area than the outer ( room ) rectangle.

I kind of visualise a 'container' for resonance to occour in. Even with an axial mode of only two surfaces, the 'container' they make for trhe resonance is bigger than the 'container' for the tangential moe, hence the axial mode has a lower freqeuncy.

That's the way I currently see it, and although I appreciate it could be way off the mark, it does conform to the tangential freq being lower than the axial.

Paul
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Bert wrote:
Ive always dreamed about turning this into a forum about quantum mechanics

http://www.glafreniere.com/sa_plane.htm
(at least this page relates to sound, however, there are many more pages.)
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Paul,

> I kind of visualise a 'container' for resonance to occour in. <

One problem with the non-axial animations that Jeff linked is they don't show how a wave oscillates between the surfaces. That is shown for the axials, and an equivalent image for non-axials would help clear this up.

--Ethan

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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

Ethan Winer wrote:Paul,

> I kind of visualise a 'container' for resonance to occour in. <

One problem with the non-axial animations that Jeff linked is they don't show how a wave oscillates between the surfaces. That is shown for the axials, and an equivalent image for non-axials would help clear this up.

--Ethan

It certainly would. This is the very bit Im having trouble getting my head around.

Perhaps I need a 4 dimentional head

Paul
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

One problem with the non-axial animations that Jeff linked is they don't show how a wave oscillates between the surfaces. That is shown for the axials, and an equivalent image for non-axials would help clear this up.

Hey Ethan, I just came across this, but I've never seen this concept before. Maybe this is SIMILAR to what you are refering to.
web page

fitZ
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### Re: Bill Eppler on cue balls, modes, diffraction, and impulses

bert stoltenborg wrote:A 1 millisecond pulse is a pulse lasting 1 millisecond, and thus has a bandwidth of 1 millisecond which in the frequency domain is 34 cm = 1000 Hz?

huh? I've not really been following the detail of this thread, but I don't understand this statement, bert.

Bandwidth isn't measured in time. And the frequency domain has nothing to do with wavelengths or the speed of sound.

Perhaps I should have been paying more attention to your debate with Ethan, but this seems seriously confused and confusing!

hugh

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