Yup, acoustics, a science of it’s own. Let’s stop using the definition as it’s pretty useless in combination with our usual ray theory approach 🙂 since our normal approach to radiation impedance of real loudspeakers fails when we’re taking all kinds of boundaries and enclosed spaces with leaky components into account. Just measure the results and correct accordingly.
That is kind of what I was getting at in a round about way. Just looking at the response graph and noting where it starts to roll of it can look kind of pathetic but when you consider these other factors it may be just what is needed.
I probably should have explained my context a bit better as the universe of approaches differ depending on the situation. In this case I am thinking in terms of normal (not sub) woofer in a high efficiency multi-way speaker appropriate for SET or modest class A triode PP so the modern method of EQ the snot out of it and driving it with an arc welder is a no go. For a subwoofer that would be another matter. I still wouldn't be inclined to beat it into submission but high power SS and maybe a touch of EQ would be fine for sub use. I might also consider a transmission line for sub use but for mains it can get a little unwieldy size wise if high efficiency is desired.
If you use a high enough Q driver on a reasonable baffle you don't need to EQ down to fs and EQ below fs is usually pointless unless you use a boatload of high excursion drivers as you will just run out of excursion.
I don't think that group delay is what makes OB bass so sweet. I think it has more to do with box resonances and interior reflections that are missing in the OB. Of course the figure 8 radiating patter probably comes into play as well.
It seems that the overall effect of series resistance is to reduce output at the higher frequencies which of course flattens the curve. Another interesting approach that doesn't reduce efficiency as much is a series capacitor. The resulting response can appear a little bit like porting but without unloading the woofer at low frequencies.
Another intriguing approach is to use a class A pentode amplifier with current sense feedback. This raises Zout without necessarily throwing away power.
Radiating pattern for sure - but note that any box resonances will be at much higher frequencies than the bass we're talking about (may possibly affect harmonics and harmonic distortion products though).
Here is an example. The Beyma 15WR400 The fs is 36Hz and the Qts is a very low 0.3 but though the rolloff starts well above 100Hz it is only down 11dB at 32Hz (Low C 16 foot rank). And the slope is only about 6dB/8va between 32Hz and 64Hz so even if room gain is only 6dB/8va you would be essentially flat once you hit that first room mode. If you wanted to tweak it a little to make the slope a little more linear and lifted up a little below 41Hz a 1200uF cap could do the trick. As a bonus the cap would provide a little bit of protection if someone hooked it to a big momma solid state amp and cranked it. Any way you slice it you will need a sub for the last 8va below 32Hz. Seems like an acceptable compromise. If you did have a big room and a more powerful amp you still have some room for EQ.
Using my current KT-88 SEUL of about 8W/Ch you could get max 103dB at 32Hz without any room gain assuming the OPT is up to it.
Using my current KT-88 SEUL of about 8W/Ch you could get max 103dB at 32Hz without any room gain assuming the OPT is up to it.
Yes and no. The 4 subs at the front wall are positioned within about 5-10 mm as ideal for a DBA versus width and height. The 4 sub at the back wall are positioned ideal versus width but about 5 cm off versus height, due to practical reasons. Subs at front wall are 18”, at the back wall less efficient / lower pump volume 15”. But the diagrams does not show a ”real DBA”, -as there is no EQ applied like 20 ms time delayed back wall subs, nor any correction for the efficiency differences between front and back. If that had been applied, the 40 Hz bump / dip would have evened out and also some less wiggles at other bass frequencies.
What can be taken from comparison between simulated and the in room response curves, is that room gain plays a role and that pressure gain (for me) starts to kick in a few Hz below 20 Hz and for pressure gain it doesn’t matter if subs are playing in phase or not.
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Take a pair of identical 15" drivers with low Q, 15mm max excursion and decent power handling.
Put (A) into a 50 litre sealed box, so that final Q = 0.7
Put (B) into a larger sealed box, so that final Q = 0.5
(Assume perfect boxes with no backwave / cabinet noise)
Feed brown noise to both drivers, and raise the volume until you get 10mm of cone movement. Box (A) will require more electrical power to reach this level of movement.
In both cases, at 10mm of excursion, the cone will be displacing 850ml of air. Therefore both boxes will be generating exactly the same amout of acoustic energy.
The response curves will have a different shape, but the total amount of bass energy (the area under the curve) is going to be identical.
Here are the best measurements I have seen for room gain.
https://data-bass.com/#/articles/5cb5fb285389a80004c7e58a?_k=yat1ns
For a 1-second summary, just scroll down to "Average Gain Profile".
A sealed 15" that (measured outdoors) was -6dB at 40Hz, would be more-or-less flat to 40Hz, in this room.
OK, but I am not sure of the relevance. Acoustic energy over a range is not really of interest in music reproduction as I see it. To my way of thinking the issues are perceived frequency balance in room with reasonably low distortion and maximum SPLs at specific frequencies of interest. For me overall the frequencies of interest go down to 16Hz. For mains I am quite satisfied with usable output down to 32Hz and would accept 40Hz for a general system.
Depending on the room the perfect slope would vary. My suspicion is that the normal Qts =0.7 is not quite ideal for most rooms assuming the f3 is reasonably low. I am beginning to suspect that a much lower Qts can be fine as long as f10 (anechoic) is low enough.
As you suspected: I am quite certain my room would have been a bass boomy nightmare if I had chosen the ”typical” Qtc of 0,707 when I built my subs. All 6 surfaces are thick concrete, half below ground level, with small windows and solid wood and steel doors. Also as my room is well sealed, it should have an even stronger augmentation than what is shown in the Fig 12 for a typical listening room in America. (Results in the link in post #2.)
A paper by John Krevskosvsky very well worth reading: http://www.geocities.ws/kreskovs/Box-Q.html . The paper was one of the reasons why I chose to build subs with such a low Qtc as 0,36, F3 around 118 Hz and with Fb around 48 Hz, well above the lowest room mode. (Theoretically 21,8 Hz, versus length 7,86 m)
Some excerpt from it:
”However, if a sealed box woofer system is placed in a relatively small, closed room, with room gain as depicted in Figure 12, the response below the fundamental room resonance will be augmented by room gain. If the room was perfectly sealed and the walls were perfectly rigid, the room gain would results in a 12dB/octave increase in SPL with decreasing frequency below the room’s fundamental resonance. Coupled with a speaker of correct resonance and Q the resulting response would extend flat well below the speaker’s and room’s resonant frequency. However, if the speaker’s resonance is below that of the rooms, then room gain effects can result in a blotted, boomy bass response. A low Q woofer system will help reduce this effect because of the greater roll off of the bass response from the woofer above it’s resonance. There is clearly a need to consider the room size, woofer resonance and woofer Q when trying to achieve the smoothest, most extended bass response in a given room rather than building/buying a woofer simply because it has the lowest fs. If fs is well below the room resonance the room will be overloaded and the bass will almost certainly boom.”
Plus: ”In summary, when you hear a speaker that sounds boomy but is otherwise well designed it is more likely not so much due to the overhang in the step response of the system. Rather it is because the particular woofer alignment (fs and Q) does not interact well with the local environment.”
Other papers from Krevskovsky which might e interesting: http://musicanddesign.speakerdesign.net/tech.html
A paper by John Krevskosvsky very well worth reading: http://www.geocities.ws/kreskovs/Box-Q.html . The paper was one of the reasons why I chose to build subs with such a low Qtc as 0,36, F3 around 118 Hz and with Fb around 48 Hz, well above the lowest room mode. (Theoretically 21,8 Hz, versus length 7,86 m)
Some excerpt from it:
”However, if a sealed box woofer system is placed in a relatively small, closed room, with room gain as depicted in Figure 12, the response below the fundamental room resonance will be augmented by room gain. If the room was perfectly sealed and the walls were perfectly rigid, the room gain would results in a 12dB/octave increase in SPL with decreasing frequency below the room’s fundamental resonance. Coupled with a speaker of correct resonance and Q the resulting response would extend flat well below the speaker’s and room’s resonant frequency. However, if the speaker’s resonance is below that of the rooms, then room gain effects can result in a blotted, boomy bass response. A low Q woofer system will help reduce this effect because of the greater roll off of the bass response from the woofer above it’s resonance. There is clearly a need to consider the room size, woofer resonance and woofer Q when trying to achieve the smoothest, most extended bass response in a given room rather than building/buying a woofer simply because it has the lowest fs. If fs is well below the room resonance the room will be overloaded and the bass will almost certainly boom.”
Plus: ”In summary, when you hear a speaker that sounds boomy but is otherwise well designed it is more likely not so much due to the overhang in the step response of the system. Rather it is because the particular woofer alignment (fs and Q) does not interact well with the local environment.”
Other papers from Krevskovsky which might e interesting: http://musicanddesign.speakerdesign.net/tech.html
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I was long of the opinion that the -3dB point was not very important, and just a carryover artifact from electrical filter theory used for mathematical convenience. It was gratifying to actually meet Richard Small at Harman in Indiana on a business trip-he agreed that was so and that the -6 and -10 points were probably more relevant in rooms. Due to "Room gain" which (semantics aside) does exist, but many only at the lowest frequencies in big/leaky spaces. I have also begun to feel that just having a low resonance is a merit-for transient response, maybe having a low resonance is actually more important than the Q. I would love to find a way to simulate tone bursts out of a box simulation to explore this more. This used to be possible within LMS but I don't have that board any more, nor hardware that will run LEAP to export a response to it. (I want to see actual tone burst response at like 40 Hz, 80 Hz, whatever. A more visual thing than just perusing an impulse response or group delay curve).
It may be a helmholtz resonance, it doesn't follow the theoretical 12dB/oct of room gain..
http://www.geocities.ws/kreskovs/Box-Q.html
Hmm, AVAST initially blocked this site due to a URL:scam virus, so clicked it off, then a 'am i a robot' screen popped up, but afraid to click OK. 🙁 Bummer as I have this as a saved link.
Hmm, AVAST initially blocked this site due to a URL:scam virus, so clicked it off, then a 'am i a robot' screen popped up, but afraid to click OK. 🙁 Bummer as I have this as a saved link.
Yes.
That's the point of the article. It only follows that smooth theoretical slope at very low frequencies. Above about 10Hz, there is plenty of measured (non-mythical) gain, but it is very irregular due to room modes.
The relevance is that, in your (somewhat niche) case:
- a fixed build
- big enclosure(s) are OK
- you are after response well below Fs (i.e a pro woofer down to 16Hz
In practice, you probably won't notice a lot of difference, Pretty much any large LF system that is operating well within its limits will sound good 🙂
Ah OK, to clarify 16Hz is the ideal but I accept the fact that a high efficiency main speaker is not going to be able to pull that off in any reasonable fashion so I settle for an 8va higher in mains which appears to be doable. That way for most listening the mains alone are adequate and reasonabley good output transformers should be able to keep up. No sense trying to get 16Hz out of the OPTs. A sub can handle the last 8va when needed.
For size I think I can get 95dB/W/m (which would be good enough to start) with a woofer enclosure of only 250 to 350 liters. It would need to be a good bit bigger to start nipping on the heels of 100dB plus it starts to get hard to get a mid/full range with the stones to keep up without going full horn. My KT88 amp is good for around 7 or 8WPC which would be fine for 95dB sensitivity as I have driven much less efficient to reasonable loudness. A 6EM7 amp should even do alright in my small room.