## Sealed enclosure / Closed box / Acoustic suspension / Air suspension

These are the many names for the sealed enclosure. The explanation of the latter names is simple. Because the box is air tight, the air inside the cabinet acts like a spring. When the speaker moves, it pushes against the “spring” and then it is pushed by the “spring”, similar to a suspension, hence the term acoustic suspension  Logically, if the volume of the box is smaller, the “air spring” is stiffer. Inversely, if the volume gets bigger, the “air springs” effectiveness diminishes.

Increasing the volume too much, will lead to denying the effect of the spring, and the enclosure is an infinite baffle. Actually, the term infinite baffle is exactly what it sounds like, a baffle that extends indefinitely. This will lead to no resonances, no diffraction and other benefits. But in the real world, we can convene that the infinite baffle is just an oversized sealed box.

### Couple of relevant T/S parameters

Cms – The compliance of the suspension (the spider and the surround, to be exact). If the suspension is stiff, the driver is not compliant. So, the easy it is to move the speaker, the more compliant it is. Cms is measured in m/N.

Vas – The air inside the cabinet has its own compliance. If the box is small, the air is less compliant and if the box is larger, the air is more compliant. Vas describes the volume of the air inside the cabinet (measured in liters), where the compliance of the speaker matches the compliance of the air inside the box.

• This is an oversimplification:
• If (volume of the enclosure) < (Vas) then it’s an acoustic suspension enclosure.
• If (volume of the enclosure) >= (Vas) then it starts to become an infinite baffle.
• Example : If Vas = 30L and  I make a box of 29L or lower, the air inside the box starts to act like a suspension and I just made an acoustic suspension. I just like to keep it simple like that. Because if you want to get really technical, the term acoustic suspension is valid only when the compliance of the driver is 3 times (or more) larger than the compliance of the box.

### Why choose a sealed enclosure ?

There are many reasons why you would want to choose a sealed enclosure. Here are a few :

#### The roll-off is very smooth

Roll-off is about 12 db / octave. This is compared to other enclosures, like bass-reflex, which has a steep roll-off of about 24 db / octave. You can see from this graph, the frequency response of the driver. Blue is for sealed and red is for bass-reflex. Let’s consider, for argument’s sake, that they both play linear till 60 Hz, and then they start to roll-off. While the bass-reflex will play louder than the sealed counterpart, when it has reached the resonance frequency, it starts to roll-off quickly, while sealed will keep playing even the lowest notes (at an increasingly lower output, of course). You can see from the graph, that sealed plays louder at 30 Hz than bass reflex, because of this smooth roll-off. Please understand that this graph exists just to make a point, in real life things aren’t so perfect.

#### It has a great transient response

This means that the speaker is very “lively”. It can play with little effort short term sudden sound waves, like drums, for example. For a good transient response, the speaker needs to start and stop exactly when it needs to. The internal air “spring” that acts like a suspension, helps with achieving these good transients. Also, the fact that it has a gentle roll-off slope of 12 db / octave, helps as well.

#### The difficulty of construction is very easy.

You just have to make sure that the box doesn’t leak air, and you are pretty much set. The only thing you need to calculate beforehand is the internal volume of the box. Now, there is no particular best volume for each speaker. You just have to understand what you are using it for, what are your tastes in sound, and then you can calculate the volume of the box. Meddling with the volume affects another T/S parameter (called Q).

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We will talk about Q in a second and how does it affect the frequency response. Besides the fact that it is easy to build, if you get the volume wrong after you made the box, it’s not that big of a deal. Let’s say you wanted a 25 L sealed enclosure, and after it’s done, because of some building errors, it has 28 L. It will still sound good even with the 3 L extra. For a band-pass enclosure these kinds of errors are disastrous for the end result. You can even buy prefab boxes, since the only variable is the volume.

The major negative point for the sealed enclosure is the low efficiency. To make a comparison with bass-reflex : you would need a 200 W amplifier to drive a certain woofer in a sealed box, at the same output, you would only need 100 W, to drive the same woofer in a bass reflex box. Sealed will sound tight and deep, but not loud (unless you are pumping some serious watts). If you want loud, there are certainly better options out there.

### Stuffing / Filling of the box

It is common practice to stuff the box with absorbent material. Many materials can be used : polyurethane, fiberglass filling, bonded cellulose acetate fiber, long fiber wool etc  . The stuffing has various advantages :

#### Absorbing standing waves

The whole point is to separate the waves generated by the front of the speaker from the ones generated by the back. It is obvious that absorbing some of the back waves will do some good.

#### Diminishes panel resonances

Placing absorbent material on the walls of the enclosure, ensures low resonances. The thickness of the damping material is important, if you need to absorb sound waves of certain frequencies. The back panel is the one who needs this damping the most, because back waves reflect of the back panel, come back towards the speaker and come out through the speaker.

#### Increases the internal volume of the box

This is a bit harder to understand, but the technical term is isothermal propagation. Pressure and temperature are correlated (for example if pressure goes up, temperature goes up).  In our case, we talk about sound pressure. Now, when we add dampening material into the mix, it creates this isothermal environment to some degree. This material, although not a good temperature conductor, it conducts temperature better than air. In this case the pressure drops, which means the velocity of sound drops, which means the compliance of the box rises, which is the exact same thing as making the box bigger. Adding stuffing to your box will translate into 15 % – 25 % volume increase. We are talking about the effects, that happen when increasing the volume, because obviously the physical box size will remain the same.

#### Increases efficiency

If the damping of the box is done right, you are looking at up to 15% efficiency increase. Here is how a bag of poly fill (Amazon affiliate link) looks like.

### Q

When people talk about Q, they are trying to describe the damping of the driver, or the whole driver/box configuration. In reality, Q is a composite term, it takes into factor all the mechanical, electrical and pneumatic properties of the speaker/cabinet and describes how it affects resonance. So it actually describes damping in a reverse way. It is referred to as quality factor, but generally accepted that it describes damping.

• More to the point :
• When Q goes down => damping goes up.
• When Q goes up => damping does down.

#### What is this damping?

The cone tends to vibrate a lot at resonance and damping keeps this in check. Lets split damping into smaller parts :

• Qms : Mechanical Q. It describes the damping made by the suspension of the driver : the surround and the spider of the speaker.
• Qes : Electrical Q. It describes the damping made by the coil – magnet assembly. When the coil moves through the magnetic field it generated a current which opposes this motion (hence the electrical damping).
• Qts : Total Q. This is the number you will need when establishing the desired volume of the box: The formula is : 1/Qts = 1/Qms + 1/Qes.
• Qtc : This describes the total Q when you take into consideration the damping of the box as well.
• When Volume of the box goes up => Qtc goes down.
• When Volume of the box goes down => Qtc goes up.

#### Box-speaker damping (Qtc)

When you adjust the volume of the box, you are basically trying to hit certain values of Qtc, because these values translate into characteristics that have the following description :

• Qtc = 0.5 : Perfect transients, but low efficiency (over damped).
• Qtc = 0.707 : This is the number most people try to reach for, as it gives good transients and flat response with minimum cutoff.
• 0.7 < Qtc < 1.2 : Better efficiency, somewhat degraded transients, steeper roll off.
• Qtc > 1.2 : High efficiency, bad transients, bad frequency response (under damped).

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Regarding the value of Qtc, you can strive to get the 0.7 value, and you can’t go wrong. You can go a little up, like 0.8 – 0.9, to get a little more fun sound, which will translate into a few db more on the bass notes (at the expense of transient response). Going towards to Qtc of 1.2 is pushing it, and should do that only if space is an important factor and you need a small box. You should avoid going beyond 1.2, because you will end up with a “one note woofer”. This means it will play a very narrow frequency range, loud (see the graph), and it will overpower the rest of frequency spectrum.

To calculate Qtc, the volume of the box (Vc) according to desired Qtc, and resonant frequency of the box (fc) use these formulas :

• Qtc = Qts * (Vas / Vc + 1)1/2
• Vc = Vas / [(Qtc / Qts)2 -1]
• fc = fs * (Vas / Vc +1)1/2
• f3 = { { (1/Qtc2 -2) + [(1/Qtc2 -2)+ 4]1/2 } /2 }1/2 * fc

### Recommended speakers for sealed enclosure

If you want to build a sealed enclosure, picking the right woofer will be very easy. You are looking at low free air resonance (Fs), high cone mass and long voice coils. Don’t get too caught up by the actual values, because most of them will work fine in a sealed enclosure. If you really want to get more technical, you can calculate the Efficiency Bandwidth Product (EBP)

• EBP = Fs / Qes
• If EBP around 50 or less, then the woofer is suited for sealed.
• If EBP > 100 then the woofer is suited for bass reflex.
• If EBP is between 50 and 100, then it is good for either closed or bass reflex.

The length of the voice coil is something to consider also, because in a sealed enclosure, the woofer will have a longer excursion than the equivalent bass reflex.

• What are you looking for these Xmax values (please don’t stress too much on this) :
• For small woofers (6″ – 8″) Xmax should be 2-4 mm.
• For larger woofers (10″ – 12″) Xmax should be 5-8 mm.

### Conclusion

When you are building the enclosure, you should really focus on making the box air tight. You can ensure this by applying silicone sealant to all of the joints. If you do this, make sure you don’t place the speaker just yet, because the fumes from the fresh silicone will “attack” the speaker. Make sure you let it rest for at least 12 hours before placing in your speaker.

After figuring out which Qtc you want to hit for, you can find out the volume of the box. Take into consideration that after you calculated the net volume of the box, you should add the volume dislocated by the back of the driver (magnet assembly) , crossovers, bracing etc, so you get the gross volume of the box. Also, if you add stuffing, this will effectively increase the volume of the box, so keep that in mind also. If you are building your first speaker box, then the sealed enclosure is probably the safer bet.

#### References

1. Loudspeaker Design Cookbook 7th Edition by Vance Dickason (Audio Amateur Pubns, 2005). (Amazon affiliate link)
1. Newnes Audio and Hi-Fi Engineer’s Pocket Book by Vivian Capelm (Elsevier, 2016). (Amazon affiliate link)
1. The Audio Expert: Everything You Need to Know About Audio by Ethan Winer (Focal Press, 2012). (Amazon affiliate link)