What a shame. Volumes of acoustic design. Case size calculation

A characteristic feature of counter-aperture is that the sound coming to the listener from virtually all directions, although it creates an impressive presence effect, cannot fully convey information about the sound stage. Hence the stories from listeners about the feeling of a piano flying around the room and other wonders of virtual spaces.

Counterperture

Pros: A wide zone of spectacular volumetric perception, naturalistic timbres thanks to the non-trivial use of wave acoustic effects.

Cons: The acoustic space is noticeably different from the sound stage conceived when recording the phonogram.

And others...

If you think that this is the end of the list of speaker design options, then you greatly underestimate the design enthusiasm of electroacoustic speakers. I described only the most popular solutions, leaving behind the scenes a close relative of the labyrinth - a transmission line, a bandpass resonator, a housing with an acoustic resistance panel, load pipes...

This kind of exoticism is quite rare, but sometimes it materializes in a design with a truly unique sound. And sometimes not. The main thing is not to forget that masterpieces, like mediocrity, are found in all designs, no matter what the ideologists of a particular brand say.

Before you start designing and assembling the box, you need to decide on the choice of speaker. We recommend choosing 10-12 inch imported speakers, as they are most often used in car subwoofers and are best suited. We described in detail how to choose a speaker for a subwoofer in a previous article. The design of the box is also important: the quality and volume of low-frequency sound depends on it.

What types of subwoofer boxes are there?

There are several types of subwoofer boxes. The sound quality directly depends on the design of the box, which you will receive at the output. Below are the most popular types of subwoofers:

A closed box is the easiest to manufacture and design; its name speaks for itself. The woofer is housed in a sealed wooden housing, which improves its acoustic performance. Making a subwoofer in a car with such a housing is quite simple, but it has the lowest efficiency.

A 4th order bandpass is a type of subwoofer whose body is divided into chambers. The volumes of these chambers are different; in one of them there is a speaker, and in the second there is a bass reflex (air duct). One of the features of this type of subwoofer is the design's ability to limit the frequencies that the cone reproduces.

The 6th order bandpass differs from the 4th order by the presence of another bass reflex and another camera. There are two types of 6th order bandpasses - the first has one bass reflex, and the second has two (one of them is common to both cameras). This type of box is the most difficult to design, but provides maximum efficiency.

A bass reflex is a subwoofer with a special tube in the housing. It vents air and provides additional sound from the rear of the speaker. In terms of complexity in manufacturing and sound quality, this type is a cross between a closed box and a bandpass.

If you want to get the highest quality sound, you can opt for bandpasses. But a design of this type has many details that must be carefully designed and calculated. All this can be done using a special program WinlSD, which will not only determine the optimal size and volume of the subwoofer, but also create a 3D model of it, and also calculate the dimensions of all parts.

Unfortunately, this program requires at least minimal knowledge in this area and the average car enthusiast is unlikely to be able to do everything right the first time. Moreover, in order for the program to work correctly, it needs some speaker parameters, which are also not known to everyone. If you do not plan to take part in car audio competitions, we advise you to discard the bandpasses.

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A bass reflex will be the most optimal solution for a homemade subwoofer. This type of box is good because the tube (bass reflex) allows for better reproduction of the lowest frequencies. In fact, this is an additional sound source that contributes to the sound of the subwoofer and increases efficiency.

What materials do we need to assemble the subwoofer?

The material for making the subwoofer box must be durable, dense and well insulating sound. For this Multi-layer plywood or chipboard is perfect. The main advantages of these materials are their affordable price and ease of processing. They are quite durable and provide good sound insulation. We will make a subwoofer from 30 mm thick multilayer plywood.

To make a subwoofer box we will need:

• Wood screws (approximately 50-55 mm, 100 pieces)
• Soundproofing material (Shumka)
• Drill and screwdriver (or screwdriver)
• Jigsaw
• Liquid nails
• Sealant
• PVA glue
• Carpet, approximately 3 meters
• Klemnik

Subwoofer box drawings

In this article we will make a box for a subwoofer with a 12-inch speaker. Recommended box volume for one 10-12 inch speaker is 40-50 liters. Calculating a box for a subwoofer is not difficult, here is an approximate diagram with the dimensions of the panels.

It is worth paying attention to the minimum distance from the walls of the case to the speaker. It, like the volume of the entire box, is calculated based on the inner surface.

Video instruction: how to make a drawing for a subwoofer yourself

Assembling a subwoofer box with your own hands

You can start assembling. We use a 12-inch Lanzar VW-124 speaker.


Its diameter is 30 cm, and the first thing you need to do is cut a hole for the speaker. The minimum distance from the center of the diffuser to the subwoofer wall is 20 cm. We measured 23 cm (20 cm + 3 cm plywood width) from the edge of the panel and cut a hole with a jigsaw. Next, we cut a hole for the bass reflex slot; in our example, it has a size of 35*5 cm.


Instead of a slot, you can use a classic air duct - a tube. Now we assemble the bass reflex slot and attach it to the front panel of the subwoofer. We go along the joints with liquid nails and tighten them with self-tapping screws.

It is important to tighten the screws very tightly so as not to leave any voids. They will create resonant vibrations that will ruin the sound of the subwoofer.

Next, we assemble the side walls of the box, having previously lubricated them with liquid nails, and tighten them tightly with self-tapping screws.


On the back cover of the box you need to cut a small hole for the terminal block. We connect all parts of the body. We make sure that we cut and fastened all the parts correctly.


We insert the speaker. Let's look and admire.


Let's move on to the interior decoration of the box. The first thing you need to do is seal all the joints and cracks with epoxy glue or sealant. Next, using PVA glue, we glue soundproofing material onto the entire inner surface of the box.




Now we cover the entire outer plane of the box with carpet, including the bass reflex slot. You can attach it with epoxy glue or using a furniture stapler.


Next, insert and screw the speaker tightly. The subwoofer is almost ready, all that remains is to stretch the wires from the speaker to the terminal block and connect the amplifier.


We bought an additional amplifier, but you can also make it yourself. This is quite difficult, as it requires knowledge and practice in the field of radio engineering. You can also use ready-made kits and circuits for radio amateurs, like Master-KIT, and assemble the amplifier yourself. The only thing requirement for the amplifier - its maximum power must be less than the maximum power of the speaker.

See also a video report on making a homemade subwoofer for 2 speakers

Making a stealth subwoofer with your own hands

Tired of carrying a huge box in your trunk? Then the stealth subwoofer is just made for you. This unique type of case is more practical than the classic box. It doesn't sit in a square box in the middle of the trunk and takes up less space. Often, stealth is installed in the inner part of the wing, sometimes in a niche instead of a spare wheel. The minimum volume of the box that requires a 10-12 inch speaker for normal operation is 18 liters.

To make a passive stealth subwoofer we will need:

• subwoofer;
• protective grille and socket for connection to the amplifier;
• wire for connecting the speaker to the outlet;
• multilayer plywood or chipboard (thickness 20 mm);
• a small piece of fiberboard;
• epoxy glue;
• brush;
• fiberglass;
• mounting tape;
• polyethylene film;
• wood screws;
• drill, jigsaw.

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After choosing the place where the stealth will be installed, we empty the trunk and begin manufacturing the body. You can remove the trunk trim where the subwoofer will be installed to place it even closer to the fender. First of all, lay a plastic film on the floor of the trunk. It performs two functions at once: it protects the trunk lining from epoxy glue and allows us to make a mount to which we will screw the bottom of the subwoofer. Next, we cover the inside of the wing with mounting tape in two layers.


We cut the fiberglass into small pieces, approximately 20x20 cm. We put pieces of fiberglass onto masking tape and glue them with epoxy glue. It is better to overlap the fiberglass fabric so that there are no obvious joints and seams.


We sculpt layers of fiberglass on top of each other, simultaneously lubricating them with epoxy glue, until the thickness of the sheet reaches 10 mm (about 4-5 layers).


The material will harden in approximately 12 hours. To speed up the process, you can use a lamp. Now we cut out the bottom of the subwoofer and glue it to our body. The joint is treated with sealant or glued with epoxy resin.


In this particular case, the shape needs to be adjusted to the trunk hinges so that our homemade subwoofer does not interfere with its closing. After we cut off all the excess, we cut out the side walls and the top cover from chipboard. We make the rounded part from plywood, we did it “by eye”.

To make it easier to give the plywood a rounded shape, you must first wet it, give it the desired shape, secure it and let it dry.

Chipboard sheets must be glued with epoxy glue or sealant, and then fastened with self-tapping screws. We also glue the fiberglass box using epoxy resin, and when it dries, we fasten it with self-tapping screws.


For better sealing you can glue the seams again. We applied another layer of epoxy glue and pressed the structure with sand to help the glue adhere better.


Next we can measure the front panel and cut it out. Using a jigsaw, cut out a circle for the speaker. In order to securely attach the front panel to the body, you need to tighten it with self-tapping screws on all sides. That is, you need to install bars on the entire inside of the panel, at a distance slightly greater than the thickness of the plywood (in our case, we attached the bars at a distance of approximately 25 mm from the edge of the panel). Thanks to this, we will be able to secure the front part at the top, bottom, sides, and most importantly - securely attach it to the rounded element.


Cut a hole in the end for the socket.


In the end, it was decided to add two more layers of fiberglass and epoxy glue to the curved part of the body for the stealth subwoofer.


We carry out the final assembly: install the socket and connect the speaker to it, but do not screw it yet. Next There are two options - paint the subwoofer, or cover it with carpet. Painting is a little more difficult, since you must first level the surface. For this we used universal putty.


We level everything with sandpaper, prime and paint. The subwoofer is ready!

Subwoofer housing calculation

Calculating a housing for a subwoofer is not easy for every motorist, even one who is very passionate about music and understands various acoustic subtleties. A subwoofer is a complex and independent acoustic system designed to create high-quality sound inside a car.
However, few motorists know how to design a subwoofer housing correctly and without problems.

Hull and its calculations

So, directly the algorithm for calculating the subwoofer housing:

• There are four main types of subwoofer enclosures available today;
• Housing 3Ya is a closed type structure. This type, from the point of view of design and manufacturing, is the simplest. However, it has practically no efficiency. On top of that, it is leaky;
• The phase inverter (PI) has a complex calculation principle, but it has a high efficiency;
• The 4th and 6th order bandpass is the most difficult option from the point of view of design and practical manufacturing, but it has the highest efficiency within the range of low sound frequencies and at the same time completely suppresses high frequencies.

Note. Objectively, each of the options described above has a number of characteristic advantages and disadvantages, however, the choice must be made in accordance with the recommendations of the design program.

Program WinlSD 0.44

Before moving directly to the design process, you need to create an audio speaker in the database using the WinlSD 0.44 program:

• First, you need to move the computer mouse cursor to the New tab, after which you need to check Owndrivers and click on New again. After that, download the parameters selected in accordance with your own wishes and capabilities. At the end, just click OK, Close;
• Then you need to create a project based on the speaker and previously specified dimensions;
• Next, you need to repeat the above procedure many times, changing the type of case, having tried all four variations.

Direct algorithm for creating the housing itself for a car subwoofer

Here's what you need to know:

• The most optimal shape would be a truncated pyramid, since it is the most universal;
• The slope of the rear wall should be approximately 23 degrees, since the vast majority of modern passenger cars have an interior with the rear seat backs tilted at exactly this angle;
• It is imperative to calculate the volume of the case in accordance with the dimensions of the free space of the trunk (see).

Creating a closed enclosure

Let's start:

• All walls of the 3Ya case (closed type case) must be made of chipboard, and the front wall must be 23 mm thick, and the side wall must be 220 mm thick;
• Now you just need to cut out the walls of the specified size from chipboard with an accuracy of a millimeter, and then you can proceed to the direct assembly of the body;
• The connection should be made using glue and specialized screws with their further screwing in at a distance of 5 cm from each other;

• For the self-tapping screws, you need to create holes exactly 3 mm in size using drills, and for the heads of the self-tapping screws, you will need to create the corresponding recesses using a 10 mm drill;
• Now it's time to mark the holes for the acoustic terminal using a simple compass;
• Next you need to create the corresponding holes using an electronic jigsaw.

Note. If the acoustic terminal is constantly under high pressure conditions, then various kinds of overtones will regularly emanate from it. In order to avoid the effect described above, it is necessary to simply shield the acoustic terminal using a small box.

Let's continue:

• Before proceeding to screwing the pre-prepared screws, it is necessary to coat the entire surface of the joints with glue;
• The parts of the body that protrude after gluing just need to be carefully cut off using a plane;
• In a similar way, it is necessary to mark and cut the corresponding holes already on the front wall in order to ensure high-quality installation of the car speaker;
• Nitrolacquer for furniture must be applied to a wooden body in order to preserve the properties of anti-moisture and anti-condensation processes;
• To create a beautiful appearance, it is recommended to cover the outer part of the body with carpet (see);
• Now all that remains is to simply connect the acoustic terminal and the subwoofer speaker.

Note. It is extremely important to familiarize yourself with all stages of the instructions and understand the design program, as this will allow you to perform independent installation and individually design the box directly to the dimensions and capabilities of the luggage compartment of your car. Also, during absolutely all stages of work, a high degree of attentiveness and accuracy is important, because any inaccuracy will certainly affect the final result.

Self-construction instructions in combination with photo and video materials will allow you to complete the work quickly and efficiently. The price of the issue is minimal and is ten times different from the operation performed in the workshop.
It is quite possible to build a housing with your own hands. The main thing, we repeat, when creating and constructing for the first time, is to carefully read the detailed practical instructions.

Subwoofer housing - closed box (ZY)

As part of the general topic of choosing a subwoofer, let's consider this design or type of housing as a closed box (BY).

A closed box is the simplest and most widely used subwoofer design. It is a sealed box, that is, its name speaks for itself.

What kind of music is ZY suitable for?

The ZYa subwoofer is distinguished by fast and collected bass, punches well, has almost no delays and has a relatively even and smooth sound.

An example of the frequency response of a ground cell in a car interior

Based on these characteristics, a closed box is well suited for many and varied genres - popular, club and rock music, classical and various instrumental - jazz, acoustic compositions, etc.

ZY is not suitable for genres that have a lot of bass, where low frequencies are the basis of the composition. You shouldn't choose it for dubstep, rap, r&b and the like.

Choosing a speaker for the radio

To select a subwoofer speaker for a closed box, you need to start from. Usually this data is indicated in the accompanying documentation, but if you don’t have it, then the parameters can always be found on the Internet.

In order to understand whether a speaker is suitable for a radio cell, it is enough to carry out simple calculations. Need to divide by and if the value turns out to be less than 80, then such a sub is suitable for the subwoofer and will sound optimally in such a housing.

For example, the same speaker RE Audio SX PRO 15D2 Fs = 27.8 Hz, a Qts = 0.38.

Fs/Qts = 27.8 / 0.38 = 73.2 This sub is quite suitable for a closed box.

If the value for your speaker is more than 80, then you should find a different design for it using.

Features of manufacturing a closed box

This housing primarily requires tightness and absence of vibrations. For manufacturing materials, choose plywood or MDF with a thickness of 18 mm or more. If the walls are thin, they will rattle and vibrate, causing unnecessary waves to be transmitted into the cabin, which, when mixed with the sound waves of the playing speaker, will ultimately deteriorate the purity and quality of the bass. This is one of the reasons why ready-made subwoofers with thin cabinet walls made of low-quality material are not even considered for purchase.

See the table for verified box volumes.

Table of cell volumes for different speaker sizes

The net volume for the radio is the internal volume of the housing minus the volume occupied by the speaker.

More accurate results need to be calculated using the parameters of a specific model.

The more sealed the ZYa subwoofer, the higher its efficiency and the better the sound quality.

Example of subwoofers with rubber rims

Advantages and disadvantages of ZY

Pros:

• ease of calculation (you only need to calculate the volume);
• relative simplicity of design and manufacture;
• small dimensions;
• wide range of music genres, fast and clear bass without delays.

Cons:

• low efficiency (loudness);
• not suitable if you need a lot of bass.

Nuances

Despite the high requirements for tightness, some audiophiles drill a hole no larger than 2 mm in the housing. to equalize internal air pressure at different temperatures.

Lord, give me peace of mind,
To accept what I can't change
Courage to change what I can
And wisdom is to always distinguish one from the other.

The prayer of Rabbi Abraham-Malach, which almost turned into a banality from frequent quotation

PRAYER AND HUMILITY

Our designers really don’t like epigraphs, considering this literary form an atavism. However, I insisted on this; not only is it very necessary in life, it will come in handy several times today. Not everything we can change when designing a bass system in a car, and the main thing that we cannot do is the transfer function of the interior, which determines the final frequency response at lower frequencies as decisively and inevitably as the frequency response of the subwoofer itself, shown by him in free space.

What do we know about the transfer function, well, at least from the last issue? That in an extremely simplified form it consists of a horizontal section, in which it does not affect the final frequency response, and an inclined section, where the output of the bass loudspeaker grows at a rate of 12 dB/oct. with decreasing frequency. The frequency at which this progressive bass enhancement effect occurs depends on the maximum cabin size. The fine details of the transfer function depend on details including the width, height, geometry of the internal surfaces, their reflective properties, etc., but all of this ceases to affect the frequency response once we get really deep into the bass region. There are no reflections there, since there are no sound waves; the sound below the inflection frequency is created according to the compression principle, as if a piston was attached to the interior and with its help the pressure inside is changed with the required frequency. There is no absorption; low frequencies in this regard are extremely tenacious, unlike the upper ones, which readily die when sound waves fall on soft and porous surfaces. It is no coincidence that all measuring anechoic chambers in the world are certified to a certain frequency, below which even these rooms, lined inside with a half-meter layer of sound-absorbing material, cease to be anechoic. The best cameras in the world start lying below 30 Hz, those that are simpler (and yet cost like a cast-iron bridge) - below 50.

So it turns out: we cannot measure one of the two main components of the formation of the frequency response at low frequencies in the cabin, we must come to terms with this, showing the wisdom recommended in the epigraph.

Only SPL competition professionals do not want to resign themselves. They do the only thing that can influence the overall course of the transfer function: they cut the length of the cabin to a minimum. We're not going to go that far, and don't suggest...

From time to time, questions arise related to the individual transfer function for a particular car. We also periodically answer them: don’t worry more than absolutely necessary. Instead of sitting and grieving that no one removed this function for your beloved swallow, use a simple recipe that we have not only been using for a long time, but have also verified empirically: we use it correctly.

More than five years ago, we compared transfer functions in different machines, with dimensions statistically predominant in the total mass, on this basis we compiled our own universal transfer function and even published it, at the same time, in No. 8/2000. Since then, whenever we have the opportunity to compare predicted characteristics with real ones measured in the cabin (when testing cabinet subwoofers or when preparing reviews of systems, when there is comprehensive information on tuning the subwoofer), we compare our empirical curve with practice, invariably making sure that you can use it with sufficient accuracy for practice by entering the necessary numbers into the necessary cells of the “Speakershop”. For those who don’t even like this, we give an even simpler recipe, which is extremely slightly inferior in terms of the reliability of the results: in the same “Speakershop”, the frequency of the beginning of the rise in the frequency response is introduced, equal to 60 Hz. We compared: the main differences between the “proprietary car audio” universal function and the simplest one (Graph 1) appear at infra-low frequencies, where theory continues to drive the frequency response upward, and the inevitable in practice non-rigidity of body panels and leakage through cracks nails it downward. But, by and large, I don’t care about this, we are talking about frequencies below 15 - 20 Hz.

So: we humbly took the typical transfer function, which we cannot change, and began to shape the frequency response of the subwoofer so that in total we get the desired bass miracle. Armed, of course, with the courage to change what you can. Be prepared, however, for wisdom to be needed again - not everything can be changed when designing a subwoofer.

THIRD ONE

From this point onwards, of the three great Thiel-Small parameters, we will use two, completely ignoring the third. The two that are lucky are resonant frequency and quality factor. The third, it’s not hard to figure out, is the equivalent volume of the head. Why? Because, although they are used to walking in threes, the role of these parameters in the design is different. The resonant frequency and quality factor determine how the subwoofer will play. And the equivalent volume of the head - what it will look like.

Our task is when designing a subwoofer to reach the required value of the head resonance frequency in the design (remember: we are only talking about the “closed box” design, everything has its time) and, as will very soon become clear, the required value of the final quality factor. They will take the desired value when the speaker (with its Fs and Qts values) is in a box of a certain, required volume. And the required volume will be determined not by absolute numbers, but by the ratio with the equivalent volume of the speaker. Example: there are three heads with the same values ​​of the resonant frequency Fs and total quality factor Qts, but with different values ​​of the equivalent volume:

Speaker #1: Fs = 30 Hz; Qts = 0.5; Vas = 30 l.

Speaker #2: Fs = 30 Hz; Qts = 0.5; Vas = 60 l.

Speaker #3: Fs = 30 Hz; Qts = 0.5; Vas = 120 l.

We want (for example) that the subwoofer ultimately has a resonance frequency Fc = 45 Hz with a quality factor Qtc = 0.7. The first of the listed speakers will reach these parameters in a box with a volume of 22 liters, the second - 45 liters, the third will require about 90 liters, and the result, the frequency response, will be absolutely the same for all.

Therefore, now we will talk about what parameters in the design (finished dish) need to be prepared from the parameters of the head (initial raw materials), keeping silent about what the volume will be, this is the next step, an important one, but the next one. First we need to decide what we actually want.

BASS OF THE PEOPLE - BASS OF GOD

There was a kind of hint in the last issue, again in our traditions, based not on speculation, but on practice. We have derived the generalized frequency response of the bass, which is loved by the people, judging by the statistics, and the frequency response chosen for themselves by audiophiles and champions. Don’t be lazy, look in the last issue on page 35. These frequency responses are somewhat different, but both can be obtained using a closed box, and one (the champion) can be obtained almost exclusively using a closed box. The difference between the bass loved by the people and the bass favored by audiophiles is this: for audiophiles, the frequency response below 200 Hz is almost horizontal, while the majority of workers prefer a rise in the response below 80 Hz.

In the same issue, but on the next page, there is a hint for the second, practical step. Roughly speaking: unlike home acoustics, where the resonant frequency determines how low the speaker will play while maintaining a flat frequency response, in a car, due to the action of the transfer function, this will determine how loud the subwoofer will play. As a general rule, the lower the resonant frequency of a subwoofer in a box, the higher its frequency response will go below the frequency where the compression effect begins. Everything seems to be done, the issue is closed. We choose a fairly low (within possible) subwoofer frequency in the design and enjoy the divine bass. Agree, this would be too simple to be true. The truth is also quite simple, but not that simple. In addition to the resonant frequency, another parameter of the two left in the game is also important.

KINDNESS WILL SAVE BASS

In the sense - good quality. It will either save you or destroy you, as it goes. It primarily depends on what you want to get. Suppose you are attracted to the laurels of champions. Or your musical tastes require extremely delicate manipulations of the bass register (which is often the same thing). And you want to get the frequency response as smooth, horizontal, and without the slightest trace of extremism as possible. To do this, if we are still talking about a closed box (and it still is), it is necessary that the decline in the frequency response of the subwoofer in free space begins in the same place where the rise in the frequency response of the transfer function begins. Let's say at the already mentioned 60 Hz. A couple of hits on the keyboard - and now, the volume of the box in which the resonant frequency will reach the specified threshold has been obtained. And what kind of quality factor will come out of this? This is where the main pitfall lies. Take a look at graph 2. Taking obviously different heads, we built the frequency response in the cabin for the same final resonant frequency, but with different values ​​of the final quality factor of the head in the Qtc box.

At low Q values, the frequency response will be ungodly failed throughout the entire bass region, coming to life only where it is no longer needed: below 25 Hz. At high Q values, the hump at 50 - 60 Hz, which we so often observe in mediocre systems, appears. And with the famous Butterworth quality factor of 0.7, the frequency response is horizontal, like the surface of the world's oceans.

You see what happened: we introduced the resonant frequency by setting a certain volume of the box, and the quality factor itself went where it wanted. We can try to come from the other end, since it is the quality factor that is important to us. When calculating, set the Butterworth value, and the resonant frequency - as it turns out. This is what happens then (graph 3). At Fc = 60 Hz the results are naturally the same. If, at the required quality factor, the resonant frequency goes up, the frequency response will fail. If it goes down, we’ll get a natural rise, but not exactly where it’s needed, but at very, indecently low frequencies. It turns out that you need to get into two parameters of the head at once, and here everything turns out to be simpler than one might assume, guided by enlightened pessimism. When choosing a head for an audiophile, super-intelligent, neutral bass, you need to choose one whose ratio of the self-resonant frequency to the total quality factor is equal to (or close to) 80.

AND FINALLY, THE PRIME NUMBERS

This is the famous EBP (Enegry Bandwidth Product) parameter, which determines what acoustic design the head is suitable for. Only now we use it to solve other problems.

The charming simplicity of the approach is that the values ​​of Fs and Qts themselves, within certain limits, do not affect the choice. It is only their ratio that is important, and also that Fs should not be higher than 60 Hz. After all, in a closed box the resonant frequency can (even must) become higher, but never lower. The result of using the first of the “prime numbers”: let’s take, say, a head with Fs = 24 Hz and Qts = 0.3. By choosing the volume of the box, you can achieve Fc = 60 Hz and Qtc = 0.7. Let's take another: Fs = 36 Hz, Qts = 0.45. The result is the same, but in a different volume, which will also depend on your head, we do not touch on this. Let's take a head with Fs = 60 Hz at Qts = 0.7. She already has the necessary final parameters, which means she needs an infinitely large box, that is, an acoustic screen. Or free air, if you like. And that’s it: here it is, the audiophile prime number, 80.

What if we are not so sophisticated and want the bass to be somehow closer to the people? To do this, we will choose a lower resonant frequency, and, as we know, the frequency response in the bass will rise. What about quality factor? The same one? But no. Take a look at graph 4. With low quality factors it’s a real disaster, but even with Butterworth quality factors, not everything is smooth. The most logical, quite powerful, but not humpbacked frequency response is now obtained with a higher value of the final quality factor, in the region of 0.9 - 1.0. And graph 5, where we fixed the quality factor and varied the resonant frequency, shows: Fc = 40 Hz is truly the optimal resonance frequency. Below - we lose bass or gain a hump, above - we get an irrationally high output on infrasound, which will mean an increased stroke of the diffuser with all the ensuing (or rather, jumping-out) consequences.

What is the prime number for this option? It is equal (or approximately equal, we do not have accounting, but physics) 45. That is, if a “naked” speaker has Fs = 40 Hz, and the quality factor Qts = 0.9 (there are such, although rarely), it has one road : in free air. And if, say, Fs = 30 Hz at Qts = 0.65 (this happens much more often), the road lies in a closed box, and there will be happiness. Fans of extreme bass, who are not afraid to ruin the speaker with excessive amplitudes, can choose a “prime number” and lower, but at their own expense.

Are there “dead prime numbers”? But what about... Look: if you choose the resonance frequency of a subwoofer in a design that is obviously higher than the inflection frequency of the transfer function, say, 80 Hz, when we are talking about a not very small car, then whatever the quality factor, the frequency response will come out either humpbacked or failed, or, most tragically, both at the same time (Graph 6). But look at the curve corresponding to Qtc = 0.5. There are cases, however very rare, when the value of the subwoofer quality factor was chosen the same or slightly higher. At the same time, if a sufficiently high resonance frequency was selected at the same time, the frequency response turned out to be sluggish in response (graph 7), but smooth, and this was done in order to obtain the best impulse characteristics of the subwoofer at the cost of weakened bass sensitivity. For such systems, the “prime number” turns out to be large, 100 or higher, although, in general, such an indicator indicates that the head was born to work in a bass reflex. But if you want, please do so, we have no restrictions. As for bass reflexes, the day will come, we’ll talk about them too...

Prepared based on materials from the magazine "Avtozvuk", April 2006.www.avtozvuk.com