1/4 wavelength confusion

[Vaughan Odendaa]

Ethan, I think I understand. Thank you. Although when I do find the statements, I will post them so you can scrutinize for me.

Savant, thank you as well for your explanations. I appreciate it. BTW, I have just read through my book and I think for it to all settle in nicely I'm going to have to read it another 2 to three times.

What books would you recommend to purchase that would go more in depth in theory compared to Alton Everast's book ? Like, for example, when talking about room modes, Everast doesn't really go into detail as to the "how", or "why", corners excite all room modes, or what exactly happens in corners.

I would like more indepth explanations as to why this is. As to the how and why. Ethan, in your opinion, what books would you recommend as an upgrade over Everast ?

Thanks a lot. Not only have I learned something in this thread, but you guys are learning from this thread too. Great stuff !

--Sincerely,

 

[Savant]

Vaughn: Depending on how deep you want to get into it, I would reiterate my earlier suggestion of Kuttruff's book. Beranek's Acoustics is also a basic must-own in my world and covers room resonance in detail. Last, but by no means least, Newell's Recording Studio Design is a great reference and is less theoretical than the former two. (Of course, I realize it's a bit out of place here in HT-world! ) Any/all should give you much more detail and explanation on room resonances and boundary interference. If you like, I can also give you some references to numerous papers, but most are not available for free anywhere online. Let me know.

Ethan: As I mentioned, I find no fault with your experiment. It's a pretty decent theoretical study. I also believe blanket application of this sort of theory to practical situations should be avoided in public forums like this. It can sometimes cause confusion for folks just trying to understand enough to help their room sound better. The "bringing up" of the null as you described can occur to a degree in real-world applications, but not "exactly" as you described. Let me try to walk (or crawl) through what I'm getting at:

For example, if a material absorbs only 0.25 at a given frequency, that reduces the strength of the reflection by 3 dB.

Now, for starters, an absorption coefficient of 0.25 would imply a reduction of a little more than 1 dB in accordance with the science you are assuming, not 3 dB. That minor issue aside, it is extremely important to point out that the science involved:

(a) Cannot be applied using published absorption coefficients for most, if not all, acoustical materials and

(b) Is only relevant if the absorption coefficient is measured at the frequency of interest.

Regarding (a): Normal incidence absorption coefficients are rarely, if ever, measured and published for a material. The absorption coefficients that are published are for random incidence - the "chamber" method. They are most often published in octave bands, but sometimes in 1/3-octave bands. The usage of 0.25 as you've implied in the above quote would only be applicable for a normal incidence absorption coefficient.

Regarding (b): Even if the normal incidence absorption coefficients were readily available, they would most likely have been measured using (only) the center frequency of the 1/1- or 1/3-octave test band. If there were a boundary problem in a room at, say, 117 Hz, there would be no easy way to know how well the absorber in question would "bring up the null," if at all! The 4" absorber you mentioned might very well perform fine at 50 Hz, relatively speaking. But at 55 Hz, the performance could be nil. I have done quite a bit of FR "before and after" testing by analyzing a single reflection from a wall, similar to the "parking lot" method you describe above. I have seen this radically cyclic performance of good/bad/good/bad/great/horrible over a very small range of frequencies. And in the low and high bands.

I hope this helps clear up my thinking. I hope I didn't confuse things too much...

 

[Ethan Winer]

Vaughan,

> Ethan, in your opinion, what books would you recommend as an upgrade over Everast ? <

I don't have any of the "math heavy" books Jeff mentioned because I'm not much of a math guy. I prefer to understand things in practical, empirical terms. But if you have the math skills to follow detailed theoretical explanations, I'm sure the first two books Jeff mentioned will deliver. I do have Newell's Recording Studio Design and I agree with Jeff that it's a great reference for people like me who'd rather avoid the math.

> what exactly happens in corners <

You don't need math to understand this. A corner focuses sound much like when you cup your hand over your ear. Or the way a satellite dish antenna focuses radio waves to the antenna element in the center.

Another reason bass collects in the corners is because low frequency sound waves tend to travel along walls as well as bounce off them. Jeff can probably explain this better than I can, and he can probably give you the math that describes how and why this happens, and at what frequencies waves transit from simply bouncing off a surface to travelling along the surface.

--Ethan

 

[Ethan Winer]

Jeff,

> I also believe blanket application of this sort of theory to practical situations should be avoided in public forums like this. It can sometimes cause confusion for folks just trying to understand enough to help their room sound better. <

In this case Vaughan asked a specific technical question, so I see no need to dumb down the explanation.

> an absorption coefficient of 0.25 would imply a reduction of a little more than 1 dB in accordance with the science you are assuming, not 3 dB. <

How so? If a material absorbs 0.50, half the wave will be absorbed and the other half will pass through and be reflected by the rigid boundary behind. So if half the wave pressure comes back off the boundary, that's a loss of 6 dB. So for 0.25 instead of 0.50 that would be a 3 dB reduction. At least that's how I see it. If this is wrong, please explain.

> Cannot be applied using published absorption coefficients for most, if not all, acoustical materials <

Agreed. I said "if a material absorbs only 0.25 at a given frequency" with no reference to how that absorption was determined.

> Is only relevant if the absorption coefficient is measured at the frequency of interest. <

See above.

> The 4" absorber you mentioned might very well perform fine at 50 Hz, relatively speaking. But at 55 Hz, the performance could be nil. <

I see no basis in science for that.

Seriously, if you measure a disparity like that it will be due entirely to room placement issues, not that the absorption of rigid fiberglass ever varies dramatically (from "fine" to "nil") over a 5 Hz range!

> I hope I didn't confuse things too much... <

Well, now that you mention it...



--Ethan

 

[Glenn Kuras]

I love to watch these sword fights between Ethan and Jeff.. It is better then the movie Braveheart..

Glenn

 

[Savant]

Jeff,

> I also believe blanket application of this sort of theory to practical situations should be avoided in public forums like this. It can sometimes cause confusion for folks just trying to understand enough to help their room sound better. <

In this case Vaughan asked a specific technical question, so I see no need to dumb down the explanation.

I wasn't talking about dumbing it down.

> an absorption coefficient of 0.25 would imply a reduction of a little more than 1 dB in accordance with the science you are assuming, not 3 dB. <

How so? If a material absorbs 0.50, half the wave will be absorbed and the other half will pass through and be reflected by the rigid boundary behind. So if half the wave pressure comes back off the boundary, that's a loss of 6 dB. So for 0.25 instead of 0.50 that would be a 3 dB reduction. At least that's how I see it. If this is wrong, please explain.

10*log(1-0.25) = 10*log(0.75) = -1.25
10*log(1-0.5) = 10*log(0.5) = -3.01

Halving or doubling pressure is a 3 dB decrease or increase, respectively.

> The 4" absorber you mentioned might very well perform fine at 50 Hz, relatively speaking. But at 55 Hz, the performance could be nil. <

I see no basis in science for that.

Seriously, if you measure a disparity like that it will be due entirely to room placement issues, not that the absorption of rigid fiberglass ever varies dramatically (from "fine" to "nil") over a 5 Hz range!

If normal incidence absorption is still the topic, these sorts of swings would not be out of the ordinary. I agree that if the measurement of the normal incidence absorption were conducted in a room setting, then placement could absolutely be a factor. A host of other things could affect the results as well - type and size of absorber, mounting, etc. As hard as I tried when performing these types of measurements, I doubt my conditions could have been considered "ideal." It could be that measuring the normal incidence absorption in a large impedence tube could reveal more stability. But I believe some significant variation over a relatively large* frequency range would still be measured.

*The difference between G1 and A1 - a whole step, which I think you would agree is a significant musical interval - is "only" 6 Hz. To put it another way - though I dislike stating it in these terms - a 5 Hz jump from 50 Hz is a 10% increase in frequency. Again, I would think you'd agree that that's significant.

 

[Ethan Winer]

Glenn,

> I love to watch these sword fights between Ethan and Jeff.. It is better then the movie Braveheart.. <

I enjoy it too because it keeps me sharp and makes me think through all the issues carefully. What amazes me is that Jeff and I basically agree on all of this stuff. At least I think we agree. So the real question is why does Jeff feel he must object to everything I post?

--Ethan

 

[Ethan Winer]

Jeff,

> Halving or doubling pressure is a 3 dB decrease or increase, respectively. <

I'm pretty sure that's not the case. Halving or doubling either voltage or current gives a 6 dB change in power. It seems to me that acoustic pressure is equivalent to voltage, so a doubling or halving should give a change of 6 dB. However, I do stand corrected on absorption of 0.25 (versus 0.50) which is 2.5 dB, not 3 dB as I stated. But 0.50 absorption reduces a reflection by 6 dB, assuming SPL is what's being reduced by 0.50.

A quick test using THIS acoustic calculator confirms the relationship. I entered an SPL of 100 dB and it reported the Sound Pressure as 2 Pa. When I added 6 dB to make the SPL 106 dB, Pa doubled to 3.99052463. (At least I'm pretty sure this confirms what I'm saying.)

As for calculating the drop in reflection strength when absorption is 0.50 or 0.25 or whatever, it depends on whether the amount absorbed is considered as power or pressure. I'm pretty sure it's considered as pressure, because ASTM C423 describes the reverb room test as measuring the change in SPL when the room is empty versus with the absorbing material present.

> I believe some significant variation over a relatively large* frequency range would still be measured. <

Earlier you said:

The 4" absorber you mentioned might very well perform fine at 50 Hz, relatively speaking. But at 55 Hz, the performance could be nil.

To me "nil" means nothing, but rather than argue about the meaning of the word "is" let's say by nil you mean 1/4 what it had been at 50 Hz. Even this much variation seems far-fetched over only a ten percent change in frequency, from 50 Hz to 55 Hz. Also, your example is backwards because we were considering porous absorbers 4 inches thick. With this type of material absorption falls off as you go lower, not higher. But I'd rather avoid nitpicking details like this, lest I start becoming more like you.

Are we there yet?

--Ethan

 

[Savant]

Jeff,

> Halving or doubling pressure is a 3 dB decrease or increase, respectively. <

I'm pretty sure that's not the case. Halving or doubling either voltage or current gives a 6 dB change in power. It seems to me that acoustic pressure is equivalent to voltage, so a doubling or halving should give a change of 6 dB. However, I do stand corrected on absorption of 0.25 (versus 0.50) which is 2.5 dB, not 3 dB as I stated. But 0.50 absorption reduces a reflection by 6 dB, assuming SPL is what's being reduced by 0.50.

I apologize. The above statement was an error. The halving or doubling of pressure does indeed decrease or increase the level by 6 dB. Even after years in this business I still get these concepts confused. When I typed that sentence, I had the sum of two sources in mind, e.g., two sources at 100 dB combine to produce 103 dB.

However, this is not, in fact, the concept involved with reflection reduction. In that case, the reduction in level is found as shown in the equations I posted above. Generally, for normal incidence:

10*log(1-a)

where a is the normal incidence absorption coefficient. That's what I was trying to point out and - again - my sincere apologies for my embarrassing error.

As for calculating the drop in reflection strength when absorption is 0.50 or 0.25 or whatever, it depends on whether the amount absorbed is considered as power or pressure. I'm pretty sure it's considered as pressure, because ASTM C423 describes the reverb room test as measuring the change in SPL when the room is empty versus with the absorbing material present.

We're not talking about ASTM C423. Besides, it calls for measuring changes in decay, not SPL.

To me "nil" means nothing, but rather than argue about the meaning of the word "is" let's say by nil you mean 1/4 what it had been at 50 Hz. Even this much variation seems far-fetched over only a ten percent change in frequency, from 50 Hz to 55 Hz. Also, your example is backwards because we were considering porous absorbers 4 inches thick. With this type of material absorption falls off as you go lower, not higher. But I'd rather avoid nitpicking details like this, lest I start becoming more like you.

I have a feeling the difference in our thinking lies in the differences between normal and random incidence absorption. I'm discussing the former, exclusively.

But I'm fine with letting it drop!

 

[Ethan Winer]

Jeff,

> I apologize. <

Not at all. A lot of people miss that, especially since it's clearer when viewed from an electrical perspective. The reason doubling voltage increases power four-fold rather than only two-fold is because when the voltage is doubled, the current drawn also doubles. Since Power = Amps times Volts, with both doubled the power is quadrupled. And if SPL is equivalent to voltage, the same rule will apply.

So does this mean I get to borrow your title of "Audioholics Resident Acoustics Expert" for a week or two?



Jeff, you know I love you man and I'm only kidding. You've always been a true expert as far as I'm concerned.

> this is not, in fact, the concept involved with reflection reduction. <

That's what I'm hoping we can clarify because I'm not 100 percent clear on this myself.

> We're not talking about ASTM C423. Besides, it calls for measuring changes in decay, not SPL. <

I mentioned that only because the ASTM spec says the decay rate is determined by measuring the change in SPL. And also because when I talk about a 4-inch panel absorbing 0.25, I mean as such a panel would be measured. Not the part about random versus straight incidence! Just the basic concept of how absorption is measured as a function of SPL change over time.

Maybe this is getting too theoretical for anyone!

So all of that said, now how do we equate a given amount of absorption with the dB reduction in a straight-incidence reflection outdoors with no competing reflections?

--Ethan

 

[Savant]

Not at all. A lot of people miss that,...

Oh, I didn't miss it. Simply got confused. Not surprising considering the time I was posting (see above).

> this is not, in fact, the concept involved with reflection reduction. <

That's what I'm hoping we can clarify because I'm not 100 percent clear on this myself.

> We're not talking about ASTM C423. Besides, it calls for measuring changes in decay, not SPL. <

I mentioned that only because the ASTM spec says the decay rate is determined by measuring the change in SPL...

...over time. Rate of decay is what is physically measured (dB/s)....

And also because when I talk about a 4-inch panel absorbing 0.25, I mean as such a panel would be measured. Not the part about random versus straight incidence! Just the basic concept of how absorption is measured as a function of SPL change over time.

I added the emphasis to the last two words.

Maybe this is getting too theoretical for anyone!

So all of that said, now how do we equate a given amount of absorption with the dB reduction in a straight-incidence reflection outdoors with no competing reflections?

It is probably getting a little heavy, but it is important - crucial, IMHO. Which is why I've spent much time studying it. Normal and random incidence absorption are simply not the same quantity. Normal incidence absorption coefficients are calculated using measured intensity differences before and after a sample, as we've been discussing. The relationship is quite simple:

a = (Ii-Ir)/Ii

where a is (as above) the normal incidence absorption coefficient, Ii is the incident intensity, and Ir is the reflected intensity.

Random incidence absorption coefficients are calculated using the room volume, change in decay rate, and the area of the sample. There is a theoretical relationship between these two coefficients, but there are simply too many assumptions and variables in the random method to say it is equivalent to (or even "close enough to") the normal method. Beranek explains, clarifies, and emphasizes this very clearly in Noise and Vibration Control, Section 9.1 (1988 ed.).

I believe this is where the fundamental disconnect here is coming from. And a forum like this is not exactly my favorite medium for trying to explain it. I have repeatedly - in at least three different forums - attempted to explain this concept. Understanding it is also crucial to understanding the "absorption coefficients > 1.0" thing. I am probably doing a piss poor job of explaining it thus far, though, since I often feel I receive the e-equivalent of hundreds of blank stares...if there are even hundreds of people still following along at this point.

Anyway, I hope this helps. Further discussion is probably best left for another place and time, though...

 

[Vaughan Odendaa]

Like Ethan, I'm not a big math guy. I'm more into practical and empirical explanations.

So, in that respect, Savant, could you recommend some books that would be an upgrade over Alton Everasts in terms of practical or empirical explanations, but more indepth ?

I know that math is important but I find indepth (theory) explanations make far better sense to me. Thank you.

--Sincerely,

 

[Savant]

Vaughn,

Well, acoustics is a subset of physics. Physics is a lot of math. I hope you can appreciate the quandary. If math ain't your thing, then books like Beranek's are probably going to be a little bit challenging. The best two books I can think of that keep the math manageable, but cover theory well are Music, Physics and Engineering by Harry Olson and Sound System Engineering by Don and Carolyn Davis. Olson is a great author for clear explanations of things. The Davis book (often referred to as "the yellow book") is a lot more in-depth and covers many aspects of acoustics and audio. You might hold out on buying a copy, though - the 3rd edition (by Davis and Petronis) should be coming out in the next few months. Of course, you might be able to find a used copy of the 2nd ed., which is very good.

Not to steal any Audioholics thunder, but there are also a lot of good referrals in this JLS thread.

Happy reading!!!

 

[Ethan Winer]

Jeff,

> ASTM C423 ... calls for measuring changes in decay, not SPL. <

I just caught this. Sorry, my bad. Of course I meant to say "change in SPL over time."

So do we now agree on everything related to 1/4 wavelengths peaks, nulls, and how much absorption is needed to bring up a null by a given amount?

So what's next, poly versus QRD diffusors?

--Ethan

 

[Savant]

So do we now agree on everything related to 1/4 wavelengths peaks, nulls, and how much absorption is needed to bring up a null by a given amount?

Everything? I should hope not. But I also don't think it matters whether we agree on anything.

So what's next, poly versus QRD diffusors?

If you like...