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#### Patrick Bateman

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Has anyone on this forum studied cabin gain?

This is JBL's measurement of cabin gain. I've used this jpg a million times, but I think I made some fundamental mistakes in my understanding of room gain. If what I've studied yesterday is correct, it leads to some surprising conclusions!

These conclusions include:

#1 - There's no good reason to use a ported sub box in car
#2 - There's no good reason to use a tapped horn sub in a car
#3 - Our estimates of 'cabin gain' cannot be applied to all box types - they only apply to sealed subs, single reflex bandpass subs, and front loaded horn subs.

I literally re-read my acoustics books in the past day, so I may be making some type of fundamental mistake here. But based on a re-read, I've found the following:

• All rooms have a fundamental resonance, and below that resonance, a monopole will pressurize a room. A dipole WILL NOT. That's the key. (And vented boxes, tapped horns, and back loaded horns are dipoles below their passband.)
• In a sedan, the lowest fundamental resonance is about sixty hertz. I calculated this figure using my Accord as an example. The longest dimension of the cabin is 110". According to page 110 of the Audio Recording Handbook, we calculate the frequency like this:
room fundamental = frequency / 2 * length
= 13500 inches per second / 220"
= 61hz
Now at this point, plenty of people will say "I've heard vented boxes produce tons of bass in a car."

But I think there's *another* thing going on here, which further complicates cabin gain. And that is standing waves.

The car's cabin is excited by a series of standing waves. These standing waves begin at one quarter wavelength, and occur at odd multiples. Both monopoles and dipoles are effected by standing waves.

So I think that's the key. If I'm grokking my acoustic texts properly, both affects are laid on top of each other.

But the key to all of this is that only a monopole will pressurize the cabin below 61hz, using the dimensions listed above.

The effect of standing waves is not subtle, and in the example of a Honda Accord, the standing waves will occur at odd multiples of one quarter wavelength. For a 110" long cabin, those frequencies are 30.7hz, 92hz, 153hz, etc.

Complicating this further, standing waves are created by from side to side, and top to bottom as well. With a width of 55", there are also side-to-side standing waves at 61hz, 183hz, 305hz, etc.

And just to really blow your mind, this all happens in three dimensions.

If you tried to visualize it, the car cabin is almost like a pressure map, with varying areas of high and low pressure. And this is why you can move a microphone (or your ears) a couple of inches and the frequency response changes dramatically.

But the main thing, is that any type of dipole box has limited use as subwoofer in a car. This includes vented boxes, tapped horns, and back loaded horns. YES, these box types can see an efficiency bump from the rear wave, but that efficiency gain will be swamped by the effect of cabin pressurization. If I'm reading my numbers right, pressurization would add 12dB at 30hz for a monopole, and 0dB for a dipole. The dipole subs would only become compelling if the vehicle was very large, or if the tuning was extremely low (sub 30hz, likely) But even that last case is dubious, due to the monopole's size advantage.

If anyone wants to fact check this, here's some reading:

John K explores pressurization on dipoles : http://www.musicanddesign.com/roomgain.html

standing waves : http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html#c3

Geddes weighs in : http://www.diyaudio.com/forums/gedlee/161630-geddes-bandpass-subs-multi-sub-approach-3.html

Aaron Clinton

#### thehatedguy

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That might explain why the "unhorn" on DIYA acted the way it did.

Ported can be useful for exciting a room mode...ala what the SPL guys are doing.

#### Andy Wehmeyer

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Patrick,
I think you're on the right track, but there are a bunch of other things to consider and I'm not sure about the calculation of "room resonance"--that appears to me to be a calculation of some mode, not resonance. The resonance of the room MUST include all of the things that contribute to sustaining the energy that's applied. A square balloon that's been inflated would likely NOT have the same resonance as a cinder block box of the ssame dimensions--as Geddes suggests, leaks have to be considered and anything that isn't completely rigid is a leak. IF there are multiple surfaces that vibrate differently when the "room resonance" is excited, then those would contribute to the "spread the chaos around" idea and would serve to obscure the fundamental frequency and the Q of the fundamental. This will be exceptionally difficult in the car, since the seat is a filter between the cavity of the trunk (box appears to be larger at lower frequencies), the windows are MUCH stiffer than the sheet metal. Windows are also suspended using a rubber gasket or flexible glue--so they're passive radiators each with mass and compliance, and so on and so forth.

I suppose this would be easy enough to try to determine the resonance. Put a mic in the car and close it up. Make a recording of the sound inside the car when you:
1. Whack the window with your hand
2. Whack the sheet metal with your hand
3. Whack the windshield with your hand.

If you notice that there's a fundamental frequency at which the sound decays, then you've found the resonance of the car. If the fundamental is different depending on which surface you whack, then the fundamental depends on the surface that's used to excite the resonance. I don't know if this will be the case, as I've never done this.

I also don't buy the idea that a vented box doesn't pressurize the cabin. I do, however buy the idea that the vented box doesn't do a good job of pressurizing anything far below Fb. The pressure inside the vented box is MUCH higher at Fb than the pressure inside a sealed at the same frequency--Richard Small wrote a paper that indicates that the anechoic response of the speaker can be modeled by measuring the pressure inside the box. I'll see if I can find it. I have it somewhere. It's no mystery why dipoles don't pressurize the room at low frequencies--there's no displacement at frequencies below the point at which the radiation patterns meet. At low frequencies, they radiate in all angles. Same for a woofer and a port--far below Fb. Same for a 6x9" speaker thrown onto the rear package tray of the car.

Vented boxes are beneficial in cars for other reasons, so let's be careful not to categorically rule them out simply because of what happens below Fb (in the same way that ALL AMPLIIFERS DO NOT SOUND THE SAME, despite the misunderstanding by so many of RC's "experiment").

In my experience, bass in the car is so easy that it really doesn't warrant much experimentation or explanation. It's between 60Hz and 1kHz Hz where all of the thinking and reading ought to be applied.

#### asota

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Have a perhaps dumb question but how does a true infinate baffle sub (vented outside) effect cabin gain?

#### Mirage_Man

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I always enjoy reading your posts Patrick. I try my best to follow what you're saying. I have one question though regarding this one. When you talk about "dipole" would it also refer to two sealed subs mounted in different locations (ala two corner loaded subs)? My guess is no because there is no back wave. However they should be exciting different but symmetrically the same points, yes?

My current build in my Accord coupe:

#### BigRed

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Floyd Toole's book is awesome. thanks for the suggestion Andy. It has changed my whole perspective about near field listening.

#### BlackFx4InTn

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Hmm... Can't get to the subscribe button. Thanks for sharing, can't wait to see what comes out of this.

#### The Baron Groog

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Has anyone on this forum studied cabin gain?

Not extensively, but I did use the graph below when designing my system. I implimented a Linkwitz Transform enclosure design and used the cabin gain for the LT EQ. F3 of enclosure is around 74Hz, Fb around 76Hz sub crossed at 63Hz. 1st pocket RTA of the setup showed flat to 30Hz-150Hz with zero tuning. Box volume 0.126cf and in the front kickwell of a 2003 Cooper S.

This is JBL's measurement of cabin gain. I've used this jpg a million times, but I think I made some fundamental mistakes in my understanding of room gain. If what I've studied yesterday is correct, it leads to some surprising conclusions!

These conclusions include:

#1 - There's no good reason to use a ported sub box in car
#2 - There's no good reason to use a tapped horn sub in a car
#3 - Our estimates of 'cabin gain' cannot be applied to all box types - they only apply to sealed subs, single reflex bandpass subs, and front loaded horn subs.

I literally re-read my acoustics books in the past day, so I may be making some type of fundamental mistake here. But based on a re-read, I've found the following:

• All rooms have a fundamental resonance, and below that resonance, a monopole will pressurize a room. A dipole WILL NOT. That's the key. (And vented boxes, tapped horns, and back loaded horns are dipoles below their passband.)
• In a sedan, the lowest fundamental resonance is about sixty hertz. I calculated this figure using my Accord as an example. The longest dimension of the cabin is 110". According to page 110 of the Audio Recording Handbook, we calculate the frequency like this:
room fundamental = frequency / 2 * length
= 13500 inches per second / 220"
= 61hz
Now at this point, plenty of people will say "I've heard vented boxes produce tons of bass in a car."

But I think there's *another* thing going on here, which further complicates cabin gain. And that is standing waves.

The car's cabin is excited by a series of standing waves. These standing waves begin at one quarter wavelength, and occur at odd multiples. Both monopoles and dipoles are effected by standing waves.

So I think that's the key. If I'm grokking my acoustic texts properly, both affects are laid on top of each other.

But the key to all of this is that only a monopole will pressurize the cabin below 61hz, using the dimensions listed above.

The effect of standing waves is not subtle, and in the example of a Honda Accord, the standing waves will occur at odd multiples of one quarter wavelength. For a 110" long cabin, those frequencies are 30.7hz, 92hz, 153hz, etc.

Complicating this further, standing waves are created by from side to side, and top to bottom as well. With a width of 55", there are also side-to-side standing waves at 61hz, 183hz, 305hz, etc.

And just to really blow your mind, this all happens in three dimensions.

If you tried to visualize it, the car cabin is almost like a pressure map, with varying areas of high and low pressure. And this is why you can move a microphone (or your ears) a couple of inches and the frequency response changes dramatically.

But the main thing, is that any type of dipole box has limited use as subwoofer in a car. This includes vented boxes, tapped horns, and back loaded horns. YES, these box types can see an efficiency bump from the rear wave, but that efficiency gain will be swamped by the effect of cabin pressurization. If I'm reading my numbers right, pressurization would add 12dB at 30hz for a monopole, and 0dB for a dipole. The dipole subs would only become compelling if the vehicle was very large, or if the tuning was extremely low (sub 30hz, likely) But even that last case is dubious, due to the monopole's size advantage.

If anyone wants to fact check this, here's some reading:

Audio Recording Handbook : The audio recording handbook - Alan P. Kefauver - Google Books

John K explores pressurization on dipoles : roomgain

standing waves : Fundamental and Harmonic Resonances

Geddes weighs in : Geddes Bandpass Subs and the Multi-sub approach - Page 3 - diyAudio

So large vented boxes will still have their place if tuned below the fundamental of the vehicle-but the gains below the fundamental will largely be from standing waves and the gains above the car fundamental will be from pressurisation of the cabin.

Is extremrevolution (SP) still knocking about? He had some software for factoring in the vehicle boundaries when designing an enclosure-so perhaps he has a better understanding of standing waves within vehicles? (or maybe he just gets the softeware to crunch the numbers)

#### The Baron Groog

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Have a perhaps dumb question but how does a true infinate baffle sub (vented outside) effect cabin gain?
Under PB's proposed idea it would act as a sealed enclosure as you aren't using any of the back wave for increased output

#### thehatedguy

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60-1k is where I think a distributed system like Geddes and Toole recommend for subbass in the home should work in the car.

#### Andy Wehmeyer

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Under PB's proposed idea it would act as a sealed enclosure as you aren't using any of the back wave for increased output
Right. And using the backwave is only a "not able to pressurize the cabin" condition when the front and back wave play the same thing out of phase at the same level.

This is NOT the case AT Fb in a vented box. The port and the woofer do NOT play the same thing out of phase. At Fb, almost all the output comes from the port (if the port islarge enough) and almost nothing comes from the woofer. They are 2 separate radiators.

Below Fb, the port passes the backwave basically unobstructed and this is both the reason for the steep rolloff and the reason why a subsonic (infrasonic--whatever) filter ought to be used.

#### fish

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60-1k is where I think a distributed system like Geddes and Toole recommend for subbass in the home should work in the car.
Are you thinking along the lines of an MS-8?

#### Andy Wehmeyer

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60-1k is where I think a distributed system like Geddes and Toole recommend for subbass in the home should work in the car.

We actually tried this but there's one HUGE drawback that renders it useless--distributing the drivers to eliminate the modes doesn't necessarily place those drivers in spots that preserve the stereo image. Doesn't work. For subs or for a mono system and one in which imaging doesn't matter, it's fine.

#### stills

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sealed isobaric makin' a comeback

one thing not mentioned for the SPL'er

on the cabin gain chart look at the gap @ 60-70hz almost everything has.

many people run very low tuned ported boxes and wonder why their mids can't keep up.
or think they need 10'' mids up front.

when maybe all they need are sealed enclosures.

#### Hanatsu

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Interesting post. Done extensive measurements on different boxes in my car. Small ported designs with low Fb (~30Hz) and sealed designs tend to work best. Cabin gain was more linear with the sealed enclosure than the ported even though they modeled pretty much alike in WinISD (same rolloff slope but lower f3 point). Cabin gain became more unpredictable as I increased tuning frequency, with more dips/peaks below 60Hz or so (still manageable though). Car's well damped btw... I measured FR outside the car and I was able to differentiate the in-car FR with the "anechoic" freq response and discovered that the sealed design had a very smooth and predictable FR below 30Hz, where the ported design had a narrow dip with like 10dB amplitude directly below Fb but went up again at normal levels around 25Hz. Must have been caused some cancellation of some kind, no idea if its related to this phenomena though.

It's close to impossible to integrate 6,5" and smaller midbasses with ported subs in my experience. They simply don't have enough output at lower frequencies and as you increase highpass, sub localisation becomes an issue. You probably need a pair of 8"s to keep up, another reason to go with sealed designs... or bigger mids hm.

#### Andy Wehmeyer

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Re: sealed isobaric makin' a comeback

one thing not mentioned for the SPL'er

on the cabin gain chart look at the gap @ 60-70hz almost everything has.

many people run very low tuned ported boxes and wonder why their mids can't keep up.
or think they need 10'' mids up front.

when maybe all they need are sealed enclosures.
What does a sealed sub enclosure have to do with midbass?

#### thehatedguy

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Just seems like that extra set of speakers in the center really changes the output of the system.

#### Andy Wehmeyer

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Just seems like that extra set of speakers in the center really changes the output of the system.
What? Oh, a center channel? Wll, sure, especially since the signal is steered and not just the acoustic sum of right and left. That's not the same as placing drivers in antinodes.

#### stills

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i was thinking along the lines of using a higher lowpass freq w/ a sealed subs than ported basically.

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