Dipole woofer nonlinear distortion

[markus76]

This spot in the middle with no pressure is not a null?

In the idealized case of a room with no absorption and no doors or windows, yes.

I.e. yes, it's not a null. But humble audiophools like me would consider a spot with no pressure a "null", because nothing can be heard.

 

[gedlee]

In that idealized case, it IS a null. But arguing semantics and idealized situations like this are rather pointless don't you think?

I was basically responding to your comment
"But there are not only room modes below 100 Hz. In a typical small room there are about 10 modes. Between them there are frequencies the subs IMO dominate the room."

Which is a "real" world situation correct? These idealized "standing waves" and "axial modes" don't address the issue. When looking at a "real" room response, for a room that is well damped (maybe more than typical -as an audiophile might do), the space between the modes is likely to be a lull that will be a combination of the "nodes" and modal summation depending on the modal density - basically the frequency. For the first few modes this "lull" (most often not a full "null") is more likely to be a nodal surface, but very quickly there will be enough modal interaction that these "lulls: and "nulls" are more likely to be the result of modal summation cancellations.

It is often disturbing to people to find out that once there are enough modes, peaks in the response are no longer "likely" to be modes, and nulls are almost certainly NOT nodal surfaces. This is just the nature of the LF sound field in a small room.

The complexity of the situation is why it is so room dependent and why it makes no sense to me to talk about specific cases and examples. We can talk about what "likely" to happen, but then someone always points out the "idealized" example where this isn't the case and then pushes this as proof that the "typical" case is wrong, which is not true at all. When one talks about "typical" situations or statistical results we have to realize that there will always be excepts to the rule, but that doesn't change the statistics one bit.

Acoustics, because it is the interaction of a number of seperat proceses, is often a purely random situaton. You just have to get used to this. There are only a few situations where the sound field need not be thought of as random (the two that come to mind are the first two or three modes and the direct field) - the rest are basically random.

 

[Pano]

Slightly OT, but fun with low tones.

Last night I had filled a CD with a low A note (27.5Hz sine) for woofer breakin. Just to test that the CD was right, I listerned to it over headphones. Must have been very loud, because I could hear it just fine.

But wow, did it ever modulate the trumpet that was coming from my computer speakers in the same room. A real steady "vibrato." Completely garbled. I had to turn it on and off a few times to be sure what I was hearing. Funny!

There was no electrical connection, just acoustic.

So it makes me wonder what the loud bass distortion harmonics might be doing to the rest of the music.

 

[gedlee]

When you think that the sound from the computer speakers has to be coming thorugh the headphones - either the driver or through the seals - its not hard to imagine this modulation effect. In a room however the sound that gets to your ears is not normally going through a modulated system (although this can happen, like in coaxes) so nothing akin to this would happen.

 

[markus76]

Earl,

just wanted to make sure you don't get misquoted about "modes" and "nulls".

As to the soundfield being random or not, I think one has to consider how a room was built. In Europe there are a lot of rooms with masonry walls. The modal behavior is less random. In the US rooms are built using drywalls. Even if a masonry wall exists, a drywall is mounted in front of it. This helps a lot in taming modes and makes the LF behavior more random.

Best, Markus

 

[gedlee]

As to the soundfield being random or not, I think one has to consider how a room was built. In Europe there are a lot of rooms with masonry walls. The modal behavior is less random. In the US rooms are built using drywalls.
Best, Markus

Markus

I don't think that this influences my comments very much. The hard walls will lower the LF absorption and this will tend to make the very first few modes more discrete, but this only pushes my comments up a few modes (and a few Hertz) to maybe five or six modes instead of two or three. After that what I said still applies.

The European rooms tend to also be smaller which raises the issues up a few more Hertz. I imagine getting good bass in these kinds of rooms is a real problem - use more subs I guess!

 

[markus76]

I guess in this discussion I have to play the part of the bad guy: had bigger rooms in Germany than in the States.

 

[goskers]

I will just take a random guess at this one but I would say that unless the rooms in Germany on the order of twice or three times larger than those common in the US that the same rules apply.

 

[markus76]

It's not about room size but about the way walls are built, what makes the biggest difference when comparing the US to Europe. You can have big or small rooms everywhere. That's just a monetary question. But I would agree to the assumption that the typical room sizes within urban areas are smaller than that outside.

 

[gedlee]

The construction can be a big thing. For the HF I would prefer the more solid construction but for the lows the flimsyer one is prefered. So Europeans get good highs but poor bass. Maybe thats why their speakers have no bass - it just sounds bad, so why do it?

Multiple subs would be a big help, but nothing is going to cure a room with a very low damped discrete very low frequency mode - its going to boom no matter what. This is where an active absorber would work wonders. Its not going to do anything to a well damped room, but it can easily take out a few discrete modes. Interesting problem.

By the way, there is a lecture by Jens Blauert on "Sound Quality" from the last AES convention in SF that is avaialable to hear on www.aes.org. Its very good. (Under "Tutorials", but you have to be a member - you should be anyways!)

 

[markus76]

Thanks for the tip! http://www.aes.org./tutorials/

 

[john k...]

Two points John

First, the equation that you show is that for a 2nd order bandpass (you forgot about the "k" out in front which is in the numerator), not a Highpass.

Second, in general, this equation is complex with complex eigenvalues and the eigenmodes. Only in the idealized case where the eigenvalues are purely real (no absorption) and hence the eigenmodes purely real will the product of the two eigenmodes in the numerator have zeros (real cosines). In an actual case where the room has damping the eigenmodes and eigen frequencies are complex and the product in the numerator will not be zero for a single mode (the modes are similar to complex cosines which don't have zeros). The summation over many modes CAN be zero or near zero when the modes intereact. But this is nit picking. My point was that the zeros that we see in the frequency responses for "real" rooms are more likely the result of modal interaction when there is a decent modal density than a spatial nodal line, although this later aspect cannot be rulled out at the very lowest frequencies. It is highly unlikely when there is a decent modal density.

Hi Earl,

1) What you are saying is technically correct from a casual examination of the equation. However, it warrants interpretation. The leading term (outside the summation) represents the source. The summation is the transfer function between source location and observation point, i.e. the room, source to listener, transfer function. To understand the roll of the room modes we need to keep the room transfer function separate from the behavior of the source. For example, if the source were to radiate flat SPL in free space then the source strength, Sw, would go as 1/k. For a typical sealed box woofer system Sw would have a band pass response. The point being that to understand the modal behavior only the terms in the summation are to be considered. The modal contribution is that of the 2nd order LP filter as I indicated (not HP).

2) I agree that with damping the eigen functions as well as Kn are complex. Thus no true zeros will occur for a single mode when damping is present. However, as the damping rises from zero to some finite values the roll of the damping is to reduce the depth of the nulls (and height resonance peaks) which would occur with zero damping. That is, while there are no true nulls there will still be minimums (instead of true zeros) throughout the room which will still be well below what the SPL would be in the absence of room modes.

{edit} I want to correct this because the absence or presence of a null in a specific mode does not imply that the SPL at the modal frequency will be zero. There will still be contributions to the SPL at that frequency by the other modes. Even in the case of zero damping where zeros do exist in the modal transfer functions a zero in a mode only implies that the contribution of the mode to the SPL is zero, not that the SPL is zero.

So, in summary, while damping means there are no identical zeros in individual modes, there can still be minimums which implies that the contribution of that mode to the in room SPL is small. That does not mean the SPL will be correspondingly small because there are contributions to the SPL at the frequency of the (close to) zeros in a given mode by other modes. Clear as mud, right?

 

[gedlee]

John

I mostly agree with 2), but I not sure that I agree with 1). The pressure response from a constant volume velocity source has to be a bandpass. If you agree with this then we are all set, and its just a matter of where one puts the "k" (frequency dependence), inside the summation or outside, but if you don't then there is a problem somewhere.

As to 2) you state

"which will still be well below what the SPL would be in the absence of room modes"

I'm not sure that this is true. I certainly don't see that its obvious or how you can conclude this. I would have to look at the equations more closely as I'm not actually sure - its never come up before. But I also don't see what significance it would have.

 

[john k...]

Hi Earl,


Please read my edit. As I say, There are two different questions. A) whether or not there are zeros in the modal transfer functions, and B) what that means in regard to the SPL at that modal frequency. The answer to A is yes if there is no damping, but it does not follow that this results in a "null" SPL.

As for you comment to part 1, a constant volume velocity source radiates a sound pressure proportional to frequency time the volume velocity. That is, a constant volume velocity source radiated a sound pressure that decreases by 6dB/octave in free space. For constant sound pressure the volume velocity must behave as 1/f.

 

[gedlee]

First paragraph - yea "clear as mud"

Second paragraph, ah, did you think that I didn't know this? (Although I think that you said it wrong. "That is, a constant volume velocity source radiated a sound pressure that decreases by 6dB/octave in free space." You mean increases right?) We were talking about room modes, not free space. Am I missing something?

 

[john k...]

First paragraph - yea "clear as mud"

"That is, a constant volume velocity source radiated a sound pressure that decreases by 6dB/octave in free space." You mean increases right?) We were talking about room modes, not free space. Am I missing something?

Yes, I meant increases. Are you missing something? I think so.

In any case (free space, in a room, ....), as you know, the sound pressure radiated by a simple source at any point in that space can be expresses as

P((r|ro) = -iZkSw G(r|ro)

Here Sw is the volume velocity of the source and G(r|ro) is the Greens' function for that space, including the terms required to satisfy the boundary conditions of the space. Sw can be whatever you like. If the source were meant to model a sealed box woofer, for example, Sw would have a band pass response about the box fc with Sw behaving a 1/f (decreasing with increasing frequency) at frequencies above fc and as f (decreasing with decreasing frequency) below fc. The volume velocity of the source has nothing to do with the room modes. It is a property of the source.

G(r|ro) is then the transfer function between source, located at ro, and observation point at r. In my expression posted previously, G(r|ro) has been expressed in a series expansion of the room modes. The summation represents the room transfer function between the source at ro and the observation point, r, both located in the room. Each modal contribution to G(r|ro) has the form of a 2nd order LP filter. G(r|r0) can be computed independently of the form of Sw. The theoretical sound pressure for a source with arbitrary volume velocity, at any point in a room can then be computed form knowledge of G(r|r0) and the volume velocity of the source. The volume velocity of the source is not a function of the space which the source is in, it is just a property of the source, just as room modes are not a function of the type of source in the room.

There is a difference between looking at the form of the room modes and how they contribute to the in room SPL, and what the resulting SPL at some point in that room is for a source with given volume velocity.


Anyway, I believe we are now in agreement that nulls in the in room SPL are not a consequence of nulls, or zeros, or minimums of a singel mode. SPL nulls are a consequence of the interaction between modes. Placing a source at a position where a single mode has a zero or minimum simply means that at that point that mode does not contribute to the in room SPL. But all the other modes which do not have zeros or minimums at that point will. Looking again at my initial expression the SPL at any frequency is dependent on the sum over all modes. So if a single mode is zero at r or ro, it just drops out of the sum. But the sum does not go to zero at that frequency. Nulls in the in room SPL require the sum to go to zero (or very small).

 

[gedlee]

But John what you are say IS what I was saying. I think of the modal response of a room AS the Greens function and as you admit yourself,

"G(r|r0) can be computed independently of the form of Sw. "

actually "can" is the wrong word because the Green's function is "always" independent of the source, but otherwise I agree with this statement.

But you stated initially that you summation contained the source terms out in front, which means that this was NOT the Green's function form. If you look at Morse (Vibration and Sound) pg. 424 you will find the equation for the room pressure from a "simple source" (meaning constant volume velocity) which DOES show bandpass forms for the modes NOT LP. To take this omega value outside of the summation and lump it into the source makes the source NOT a simple source, but then the modes become LP.

This is all semantics and simply a matter of where one chooses to put the frequency dependence, but I will state that my view of the modes being bandpass is the more standard in the field even though one CAN choose to define things, as you have, such that the modes look to be LP. One COULD define the source term in such a way that the modes looked to be HP for that matter, but for a "simple source" with no frequency dependence to its volume velocity, the modes are bandpass.

One last and not very important point, the source in a room at LFs is not actually independent of the room, it couples to the room. This is a major complication in analysis with fairly small effect, which is why its ignored. To first order it can be ignored.

 

[john k...]

One last and not very important point, the source in a room at LFs is not actually independent of the room, it couples to the room. This is a major complication in analysis with fairly small effect, which is why its ignored. To first order it can be ignored.

Yes agreed, but it doesn't alter the room modes. It primarily alters the mass loading on the source which alters the volume velocity from what it would be in free space, ot other rooms. This has most impact on low mass systems (electrostatic panels for example) and on the output of a ported system. I guess it also has some affect on the radiation impedance.

As for the other, I though I made it clear that the leading term with, k Sw, was that of the source (with Sw unspecified) and the sumation represented the room modes, which remain of 2nd order LP type.

As you say, perhaps a little internet confussion. Anyway, no big deal.

 

[gedlee]

I though I made it clear that the leading term with, k Sw, was that of the source (with Sw unspecified) and the sumation represented the room modes, which remain of 2nd order LP type.

With that non-standard deffinition, yes.

To be precise, the room modes do couple to the driver and the modes shapes, i.e. the eigenmodes, will change, but this is more like a third order effect. However, if you do a calculation of a room, via FEA for example (including absorption such that the modes are complex and the energy flow is available) and do not include the source in this calculation but add it afterwords as a forcing function via the Green's function approach, you will find that there is no energy being emitted by the source. This is because the sources effect on the near field - via the complex modifications to the eigenmodes - is not represented. The energy just appears out of space some distance from the source. I did a paper on this effect in FEA about 25 years ago.