What to make a bass reflex with your own hands. DIY speaker system with bass reflex. How to Know Which Car Speakers Are Right for You

I started doing “column construction” in the early 80s. And if at first it was just a “speaker in a box,” then, naturally, the study of the influence of the parameters of the box (and bass reflex) on the sound of the speaker began.

There are many "subwoofer builders" out there, but for the vast majority it is simply a "speaker in a box" and the bigger the better. Yes, to some extent, this is correct for a closed box. But for a bass reflex...

The bass reflex requires careful adjustment. What do we see in practice? As a bass reflex, people install sewer pipes of arbitrary length, make “slotted bass reflexes” in the image: “Vasya made them according to these dimensions,” while installing another speaker. Anyone who imagines this is limited to making a closed box (and rightly so!).

Of course, there are great modeling programs, such as JBL SpeakerShop. But they all require the introduction of a bunch of initial parameters. And even knowing them, a discrepancy with practice usually results - huge(the speaker turned out to be slightly different, the box is slightly different in size, we don’t know what filler and how much, the bass reflex pipe is slightly different, we don’t know the acoustic resistance, etc.)

There is a simple technique for setting up a bass reflex, which does not require knowing the exact source data of the speakers, boxes, and also does not require complex measuring instruments or mathematical calculations. Everything has already been thought out and tested in practice!

I want to talk about a simple method for setting up a bass reflex, which gives an error of no more than 5%. A technique that has existed for more than 30 years. I used it when I was a schoolboy.

How does a box with a bass reflex differ from a closed box?

Any speaker, like a mechanical system, has its own resonant frequency. Above this frequency the speaker sounds “pretty smooth”, and below this frequency the level of sound pressure it creates drops. Drops at a rate of 12 dB per octave (i.e., 4 times per twofold decrease in frequency). The “lower limit of reproducible frequencies” is considered to be the frequency at which the level drops by 6 dB (i.e., 2 times).

Frequency response of dynamics in open space

By installing the speaker in a box, its resonant frequency will increase slightly due to the fact that the elasticity of the air compressed in the box will be added to the elasticity of the diffuser suspension. A rise in the resonant frequency will inevitably “pull with it” the lower limit of the reproduced frequencies. The smaller the volume of air in the box, the higher its elasticity, and, consequently, the higher the resonant frequency. Hence the desire to “make the box bigger.”

Yellow line – frequency response of the speaker in a closed box

It is possible to make the box “larger” to some extent without increasing its physical dimensions. To do this, the box is filled with absorbent material. We will not go into the physics of this process, but as the amount of filler increases, the resonant frequency of the speaker in the box decreases (the “equivalent volume” of the box increases). If there is too much filler, the resonant frequency begins to rise again.

Let us omit the influence of box size on other parameters, such as quality factor. Let's leave this to experienced "column builders". In most practical cases, due to limited space, the volume of the box is quite close to optimal (we are not building cabinet-sized speakers). And the point of the article is not to burden you with complex formulas and calculations.

We got distracted. With a closed box everything is clear, but what does a bass reflex give us? A bass reflex is a “pipe” (not necessarily round, maybe rectangular in cross-section and a narrow slot) of a certain length, which, together with the volume of air in the box, has its own resonance. At this “second resonance” the sound output of the speaker rises. The resonance frequency is chosen slightly lower than the resonance frequency of the speaker in the box, i.e. in the area where the speaker begins to decline in sound pressure. Consequently, where the speaker experiences a decline, a rise appears, which to some extent compensates for this decline, expanding the lower limit frequency of reproduced frequencies.

Red line – frequency response of the speaker in a closed box with a bass reflex

It is worth noting that below the bass reflex resonance frequency the sound pressure drop will be steeper than that of a closed box and will be 24 dB per octave.

Thus, the bass reflex allows you to expand the range of reproduced frequencies towards lower frequencies. So how to choose the bass reflex resonance frequency?

If the bass reflex resonance frequency is higher than optimal, i.e. it will be close to the resonant frequency of the speaker in the box, then we will get “overcompensation” in the form of a protruding hump in the frequency response. The sound will be barrel-shaped. If the frequency is chosen too low, then the level rise will not be felt, because at low frequencies the speaker output drops too much (undercompensated).

Blue lines – not optimal bass reflex setting

This is a very delicate point - either the bass reflex will give an effect, or will not give any effect, or, on the contrary, will spoil the sound! The bass reflex frequency must be chosen very accurately! But where can you get this accuracy in a garage or home environment?

In fact, the proportionality coefficient between the resonance frequency of the speaker in the box and the resonance frequency of the bass reflex, in the vast majority of real designs, is 0.61 - 0.65, and if we take it equal to 0.63, then the error will be no more than 5%.

1. Vinogradova E.L. “Design of loudspeakers with smoothed frequency characteristics”, Moscow, ed. Energy, 1978

2. “More about the calculation and manufacture of a loudspeaker,” g. Radio, 1984, No. 10

3. “Setting up bass reflexes”, g. Radio, 1986, No. 8

Now let’s transfer theory to practice - it’s closer to us.

How to measure the resonant frequency of a box speaker? As is known, at the resonant frequency, the “modulus of total electrical resistance” (Impedance) of the voice coil increases. Roughly speaking, resistance is growing. If for direct current it is, for example, 4 Ohms, then at the resonant frequency it will increase Ohms to 20 - 60. How to measure this?

To do this, you need to connect a resistor in series with the speaker with a value an order of magnitude higher than the speaker’s own resistance. A resistor with a nominal value of 100 - 1000 Ohms is suitable for us. By measuring the voltage across this resistor, we can estimate the "impedance modulus" of the speaker's voice coil. At frequencies where the speaker impedance is high, the voltage across the resistor will be minimal, and vice versa. So, how to measure it?

Measuring speaker impedance

The absolute values are not important to us, we just need to find the maximum resistance (minimum voltage across the resistor), the frequencies are quite low, so you can use a regular tester (multimeter) in AC voltage measurement mode. Where to get the source of sound frequencies?

Of course, it’s better to use an audio frequency generator as a source... But let’s leave that to the professionals. “Nobody forbids us” to create a CD with a recorded range of audio frequencies, created in some computer program, for example, CoolEdit or Adobe Audition. Even I, having measuring instruments at home, created a CD of 99 tracks, a few seconds each, with a range of frequencies from 21 to 119 Hz, in 1 Hz steps. Very comfortably! I put it in the radio, you jump through the tracks and change the frequency. The frequency is equal to the track number + 20. Very simple!

The process of measuring the resonant frequency of a speaker in a box is as follows: we “plug” the bass reflex hole (a piece of plywood and plasticine), turn on the CD to play, set an acceptable volume, and, without changing it, “jump” along the tracks and find a track on which the voltage is at resistor is minimal. That's it - we know the frequency.

By the way, in parallel, by measuring the resonant frequency of the speaker in the box, we can select the optimal amount of filler for the box! Gradually adding the amount of filler, we look at the change in the resonant frequency. We find the optimal quantity at which the resonant frequency is minimal.

Knowing the value of the “resonant frequency of the speaker in a box with filler” it is easy to find the optimal resonant frequency of the bass reflex. Just multiply it by 0.63. For example, we obtained the resonant frequency of the speaker in the box as 62 Hz - therefore, the optimal resonance frequency of the bass reflex will be about 39 Hz.

Now we “open” the bass reflex hole, and by changing the length of the pipe (tunnel) or its cross-section, we tune the bass reflex to the required frequency. How to do it?

Yes, using the same resistor, tester and CD! You just need to remember that at the resonance frequency of the bass reflex, on the contrary, the “modulus of total electrical resistance” of the speaker coil drops to a minimum. Therefore, we need to look not for the minimum voltage across the resistor, but, on the contrary, for the maximum - the first maximum, located below the resonance frequency of the speaker in the box.

Naturally, the bass reflex tuning frequency will differ from the required one. And believe me - very much... Usually, towards low frequencies (undercompensation). To increase the bass reflex tuning frequency, it is necessary to shorten the tunnel or reduce its cross-sectional area. This needs to be done gradually, half a centimeter at a time...

This is what the speaker impedance module in a box with an optimally tuned bass reflex will look like in the low-frequency region:

That's the whole technique. Very simple, and at the same time, giving a fairly accurate result.

Magic formulas

One of the most common requests in the author's e-mail is to provide a “magic formula” by which the ACS reader could calculate the bass reflex himself. This is, in principle, not difficult. A bass reflex is one of the cases of implementing a device called a “Helmholtz resonator”. The formula for calculating it is not much more complicated than the most common and accessible model of such a resonator. An empty Coca-Cola bottle (just a bottle, not an aluminum can) is just such a resonator, tuned to a frequency of 185 Hz, this has been verified. However, the Helmholtz resonator is much older than even this packaging of the popular drink, which is gradually going out of use. However, the classical Helmholtz resonator circuit is similar to a bottle (Fig. 1). In order for such a resonator to work, it is important that it has a volume V and a tunnel with a cross-sectional area S and a length L. Knowing this, the tuning frequency of the Helmholtz resonator (or bass reflex, which is the same thing) can now be calculated using the formula:

where Fb is the tuning frequency in Hz, c is the speed of sound equal to 344 m/s, S is the tunnel area in square meters. m, L is the length of the tunnel in m, V is the volume of the box in cubic meters. m. = 3.14, that goes without saying.

This formula is truly magical, in the sense that the bass reflex setting does not depend on the parameters of the speaker that will be installed in it. The volume of the box and the dimensions of the tunnel and the frequency of tuning are determined once and for all. Everything, it would seem, is done. Let's get started. Let us have a box with a volume of 50 liters. We want to turn it into a bass reflex enclosure with a 50Hz setting. They decided to make the diameter of the tunnel 8 cm. According to the formula just given, the tuning frequency of 50 Hz will be obtained if the length of the tunnel is 12.05 cm. We carefully manufacture all the parts and assemble them into a structure, as in Fig. 2, and to check we measure the actual resulting resonant frequency of the bass reflex. And we see, to our surprise, that it is not equal to 50 Hz, as the formula would suggest, but 41 Hz. What's the matter and where did we go wrong? Nowhere. Our newly built bass reflex would be tuned to a frequency close to that obtained by the Helmholtz formula if it were made as shown in Fig. 3. This case is closest to the ideal model that the formula describes: here both ends of the tunnel “hang in the air,” relatively far from any obstacles. In our design, one of the ends of the tunnel mates with the wall of the box. For the air oscillating in the tunnel, this is not indifferent; due to the influence of the “flange” at the end of the tunnel, a virtual elongation occurs. The bass reflex will be configured as if the length of the tunnel was 18 cm, and not 12, as in reality.

Note that the same thing will happen if the tunnel is placed completely outside the box, again aligning one end with the wall (Fig. 4). There is an empirical relationship between the “virtual lengthening” of a tunnel depending on its size. For a circular tunnel, one section of which is located far enough from the walls of the box (or other obstacles), and the other is in the plane of the wall, this elongation is approximately equal to 0.85D.

Now, if we substitute all the constants into the Helmholtz formula, introduce a correction for the “virtual elongation”, and express all dimensions in conventional units, the final formula for the length of a tunnel with a diameter D, ensuring the tuning of a box of volume V to the frequency Fb, will look like this:

Here the frequency is in hertz, the volume is in liters, and the length and diameter of the tunnel is in millimeters, as we are more familiar with.

The obtained result is valuable not only because it allows, at the calculation stage, to obtain a length value close to the final one, giving the required value of the tuning frequency, but also because it opens up certain reserves for shortening the tunnel. We have already won almost one diameter. You can shorten the tunnel even further while maintaining the same tuning frequency by making flanges at both ends, as shown in Fig. 5.

Now, it seems, everything has been taken into account, and, armed with this formula, we imagine ourselves as omnipotent. This is where difficulties await us.

First difficulties

The first (and main) difficulty is this: if a relatively small-volume box needs to be tuned to a fairly low frequency, then by substituting a large diameter into the formula for the length of the tunnel, we will get a larger length. Let's try to substitute a smaller diameter - and everything works out fine. A large diameter requires a long length, and a small one requires just a short length. What's wrong with that? Here's what. While moving, the rear side of the speaker diffuser “pushes” practically incompressible air through the bass reflex tunnel. Since the volume of oscillating air is constant, the air speed in the tunnel will be as many times greater than the oscillatory speed of the diffuser, how many times the cross-sectional area of the tunnel is less than the area of the diffuser. If you make a tunnel tens of times smaller than the diffuser, the flow speed in it will be high, and when it reaches 25 - 27 meters per second, the appearance of turbulence and jet noise is inevitable. The great researcher of acoustic systems R. Small showed that the minimum cross-section of the tunnel depends on the diameter of the speaker, the maximum stroke of its diffuser and the tuning frequency of the bass reflex. Small proposed a completely empirical, but trouble-free formula for calculating the minimum tunnel size:

Small derived his formula in his usual units, so that the speaker diameter Ds, the maximum cone stroke Xmax and the minimum tunnel diameter Dmin are expressed in inches. The bass reflex tuning frequency is, as usual, in hertz.

Now things don't look as rosy as before. It often turns out that if you choose the right tunnel diameter, it turns out to be incredibly long. And if you reduce the diameter, there is a chance that the tunnel will “whistle” even at medium power. In addition to the jet noise itself, small-diameter tunnels also have a tendency to so-called “organ resonances,” the frequency of which is much higher than the bass reflex tuning frequency and which are excited in the tunnel by turbulence at high flow rates.

When faced with such a dilemma, ACS readers usually call the editor and ask for a solution. I have three of them: simple, medium and extreme.

Simple solution for small problems

When the calculated length of the tunnel is such that it almost fits in the housing and only a slight reduction in its length is required with the same setting and cross-sectional area, I recommend using a slotted tunnel instead of a round one, and placing it not in the middle of the front wall of the housing (as in Fig. 6 ), but close to one of the side walls (as in Fig. 7). Then at the end of the tunnel, located inside the box, the effect of “virtual lengthening” will be affected due to the wall located next to it. Experiments show that, with a constant cross-sectional area and tuning frequency, the tunnel shown in Fig. 7, turns out to be approximately 15% shorter than with the design as in Fig. 6. A slotted bass reflex, in principle, is less prone to organ resonances than a round one, but to protect yourself even more, I recommend installing sound-absorbing elements inside the tunnel, in the form of narrow strips of felt, glued to the inner surface of the tunnel in the region of a third of its length. This is a simple solution. If it is not enough, you will have to go to the middle one.

Average solution for bigger problems

A solution of intermediate complexity is to use a tunnel in the shape of a truncated cone, as in Fig. 8. My experiments with such tunnels have shown that here it is possible to reduce the cross-sectional area of the inlet in comparison with the minimum allowable according to Small’s formula without the risk of jet noise. In addition, a conical tunnel is much less prone to organ resonances than a cylindrical one.

In 1995, I wrote a program to calculate conical tunnels. It replaces a conical tunnel with a series of cylindrical ones and, by successive approximations, calculates the length required to replace a conventional tunnel of constant cross-section. This program is made for everyone, and it can be downloaded from the ACS magazine website http://www.audiocarstereo.it in the ACS Software section. A small program that runs under DOS, you can download and calculate it yourself. But you can do it differently. When preparing the Russian edition of this article, the results of calculations using the CONICO program were compiled into a table from which the finished version can be taken. The table is compiled for a tunnel with a diameter of 80 mm. This diameter value is suitable for most subwoofers with a cone diameter of 250 mm. Having calculated the required tunnel length using the formula, find this value in the first column. For example, according to your calculations, it turned out that a tunnel 400 mm long is needed, for example, to tune a box with a volume of 30 liters to a frequency of 33 Hz. The project is non-trivial, and placing such a tunnel inside such a box will not be easy. Now look at the next three columns. It shows the dimensions of an equivalent conical tunnel calculated by the program, the length of which will no longer be 400, but only 250 mm. It's a completely different matter. What the dimensions in the table mean is shown in Fig. 9.

Table 2 is compiled for an initial tunnel with a diameter of 100 mm. This will fit most subwoofers with a 300mm driver.

If you decide to use the program yourself, remember: a tunnel in the shape of a truncated cone is made with an inclination angle of the generatrix a from 2 to 4 degrees. It is not recommended to make this angle greater than 6 - 8 degrees; in this case, turbulence and jet noise may occur at the entrance (narrow) end of the tunnel. However, even with a small taper, the reduction in tunnel length is quite significant.

A tunnel in the shape of a truncated cone does not necessarily have a circular cross-section. Like a regular cylindrical one, it is sometimes more convenient to make it in the form of a slotted one. It is even, as a rule, more convenient, because then it is assembled from flat parts. The dimensions of the slotted version of the conical tunnel are given in the following columns of the table, and what these dimensions mean is shown in Fig. 10.

Replacing a conventional tunnel with a conical one can solve many problems. But not all. Sometimes the length of the tunnel turns out to be so long that shortening it even by 30 - 35% is not enough. For such severe cases there is...

Extreme solution for big problems

An extreme solution is to use a tunnel with exponential contours, as shown in Fig. 11. For such a tunnel, the cross-sectional area first gradually decreases, and then just as smoothly increases to the maximum. From the point of view of compactness for a given tuning frequency, resistance to jet noise and organ resonances, the exponential tunnel has no equal. But it has no equal in terms of manufacturing complexity, even if its contours are calculated according to the same principle as was done in the case of a conical tunnel. In order to still be able to take advantage of the benefits of the exponential tunnel in practice, I came up with a modification of it: a tunnel that I called the “hourglass” (Fig. 12). The hourglass tunnel consists of a cylindrical section and two conical ones, hence the external resemblance to an ancient device for measuring time. This geometry makes it possible to shorten the tunnel compared to the original one, with a constant cross-section, by at least one and a half times, or even more. I also wrote a program to calculate the hourglass; it can be found there, on the ACS website. And just like for a conical tunnel, here is a table with ready-made calculation options.

What the dimensions in tables 3 and 4 mean will become clear from Fig. 13. D and d are the diameter of the cylindrical section and the largest diameter of the conical section, respectively, L1 and L2 are the lengths of the sections. Lmax is the total length of the hourglass-shaped tunnel, it is given simply for comparison, how much shorter it was possible to make, but in general, it is L1 + 2L2.

Technologically, it is not always easy or convenient to make an hourglass with a round cross-section. Therefore, here too you can make it in the form of a profiled slot, it will turn out as in Fig. 14. To replace a tunnel with a diameter of 80 mm, I recommend choosing the slot height equal to 50 mm, and to replace a 100 mm cylindrical tunnel - equal to 60 mm. Then the width of the constant section section Wmin and the maximum width at the entrance and exit of the tunnel Wmax will be the same as in the table (the lengths of sections L1 and L2 - as in the case of a circular section, nothing changes here). If necessary, the height of the slot tunnel h can be changed, simultaneously adjusting Wmin, Wmax so that the values of the cross-sectional area (h.Wmin, h.Wmax) remain unchanged.

I used the bass reflex version with an hourglass-shaped tunnel, for example, when I made a subwoofer for a home theater with a tuning frequency of 17 Hz. The estimated length of the tunnel turned out to be more than a meter, and by calculating the hourglass, I was able to reduce it by almost half, and there was no noise even with a power of about 100 W. Hope this helps you too...

Subwoofer housing - bass reflex (FI)

As part of the discussion of choosing a subwoofer, we will consider such a housing as a bass reflex.

The bass reflex, unlike, has a port with the help of which it reverses the phase of the signal from the rear side of the speaker, thus increasing the efficiency by 2 times.

The principle of operation of the bass reflex

What kind of music is a bass reflex suitable for?

features powerful and spacious bass, and in the region of the tuning frequency it has a hump (a significant increase in sound volume).

Example of bass reflex frequency response

According to this FI suitable for music, in which there is a lot of slow bass, where low frequencies are the basis of compositions. Choose a bass reflex if you like dubstep, triphop, other slow electronic music, rap, R&B, etc.

Note: the bass reflex setting is the frequency at which the peak falls, and is regulated by changing the length and area of the port, as well as the ratio of the port volume to the body volume.

Which speaker is suitable for a bass reflex

To choose a subwoofer for a bass reflex, you need to start from. Usually this data is in the documents, but if you don’t have it, the parameters can be found on the Internet.

In order to understand whether the speaker is suitable for FI, carry out some simple calculations. Divide the value to the value and if the answer is between 60 and 100, then such a sub will be optimal for a bass reflex.

For example, at the speaker SUNDOWN AUDIO E-12 V3 Fs = 32.4 Hz, a Qts = 0.37.

Fs/Qts = 32.4 / 0.37 = 87,6 — such a subwoofer is quite suitable for FI.

If the value for your speaker is outside the range of 60-100, it may be worth finding a different design for it using. Please note that the table above does not prohibit the use of speaker enclosures that do not comply with meaning Fs/Qts. It shows options that will definitely work well.

Types of bass reflexes

Bass reflex port- the main element of the body, it can be round (pipe) or rectangular (slot).

Slot port

Round port (pipe)

It is impossible to say for sure which of these ports is better. They do what is more convenient or what they like best. The only point is that In sports(sound pressure competition) pipes are more often used, since with their use it is easier to change the bass reflex setting by changing the length of the port.

Separately, it is worth noting this type as a passive radiator. (more correctly - passive reflector) there is the same bass reflex and the principle of its operation is the same. It is used in cases where the desired port for the FI does not suit the dimensions. In a passive radiator instead of a port used.

speaker without magnetic system

Operating principle of a passive radiator

Advantages and disadvantages of FI

Pros:
High efficiency (roughly - 2 times louder than the ZYa);
Can produce a lot of loud bass;

Can be customized to suit your music preferences.

Minuses:
Large dimensions (compared to ZYa);

Relative complexity of calculation.

Peculiarities

Materials

Requirements for materials and assembly are standard. The bass reflex box must be strong, sealed and not vibrate. Material - plywood or MDF from 18 mm. and thicker. Please note that, all wire entry channels, terminal blocks, etc. must be securely sealed internal partitions (port walls).

should not have gaps

Rounding of the bass reflex port If the slot port is long and has turns, then stagnation zones may occur in the corners, to avoid this bends are smoothed out - as a result, efficiency increases, since air resistance is reduced

. It is quite difficult to determine the improvement in quality by ear, but for the fight for a high result in sound pressure, this solution works.

The logical ending to the saga of the bass reflex will be the practical aspects of its implementation. The key element here is the pipe, which is also a tunnel, which, as a result of slavish transliteration from English, is also a port. It is this, the pipe, that will make it possible to implement in practice two main parameters that determine the acoustic appearance of the conceived bass reflex: the volume of the housing and its tuning frequency. These two quantities, one in liters, the second in hertz, are the result of either an independent calculation or following previously made calculations. Their source may be the speaker manufacturers, our tests, or expert advice based on their practice. In all three cases, it happens that ready-made tunnel dimensions are given, ensuring the tuning of a known volume to the desired frequency, but, firstly, not every time, and secondly, blind copying is not always possible and is always not commendable. So the following formulation of the problem will be more general and much more productive: the volume and frequency are known, and we will solve the question of their physical, material, implementation on our own. Part of the story will be organized according to the principle of questions and answers: the nomenclature of questions is known, in the editorial mail they are repeated with regularity, giving rise to statistical calculations that our testing department loves so much. I won’t take away their favorite toy, or ours. So, what first, do we calculate the tunnel or buy the pipe that will become this tunnel? In theory, you need to buy it first - pipes do not come in any diameter, but from a certain range of values, if you take ready-made ones, and do not wind them yourself from paper with glue, like a pioneer from a young cosmonaut's circle. But you still have to start with at least a rough estimate, and the point here is that...

Thickness matters

If the tunnel is really a pipe (there are options, after all), what diameter should it be? The most general and crudest answer is: the more, the better. The advice is really radical and can cause a protest reaction: what if I take and make a tunnel with a diameter twice the size of the speaker? You won’t take it and won’t do it, no matter how hard you try, this was taken care of more than a hundred years ago by a certain Hermann Helmholtz, whose resonator name the bass reflex is, and later by the creators of cars, who made them smaller in size than the steam locomotives that existed at that time. So, in order, why more and why something will stop this process.

During operation near the tuning frequency, where, in fact, the bass reflex tunnel performs its functions, adding to the sound waves generated by the vibrations of the diffuser, air moves inside the tunnel. It moves oscillatingly, back and forth. The volume of moving air is exactly the same as that driven by the diffuser during each oscillation; it is equal to the product of the diffuser area and its stroke. For a tunnel, this volume is the product of the cross-sectional area and the air flow inside the tunnel. The cross-sectional area is actually always smaller than the diffuser area (if anyone has not yet given up the threat to make the same, or even larger, they will soon not go anywhere and refuse), and in order to move the same volume, the air needs to move faster, the speed in the tunnel decreases diameter increases in proportion to the decrease in its cross-sectional area. Why is this bad? Everyone at once. First of all, the Helmholtz resonator model, on which everything is based, assumes that there is no energy loss due to air friction against the tunnel walls. This, of course, is an ideal case, but the further we move away from it, the less the bass reflex operation will resemble what we expect from it. And the higher the air speed inside the tunnel, the higher the friction losses in the tunnel. Theoretically, the formula, and even the simple program based on it, does not take these losses into account and will meekly give you the estimated length of the tunnel with a diameter of even a finger, but such a bass reflex will not work, everything will die in the turbulence of the air trying to quickly fly backwards through the tight tunnel. forward. The text of a traffic police propaganda poster I once saw, “Speed is death,” certainly applies to the movement of air in a tunnel, if death is attributed to the effectiveness of the bass reflex.

However, much before the phasic dies as a means of sound reproduction, it will become a source of sounds for which it is not intended; vortices arising from excessively high air speeds will create jet noise that disrupts the harmony of bass sounds in the most unscrupulous and unaesthetic way.

What should be taken as the minimum cross-sectional area of the tunnel? You will find different recommendations in different sources, not all of them have ever been tested by the authors, even through a computational experiment, let alone others. As a rule, such recommendations include two values: the diameter of the diffuser and the maximum value of its stroke, that is, Xmax. This is reasonable and logical, but it fully applies only to the operation of the subwoofer at the maximum mode, when it is already a little late to talk about sound quality. Based on numerous practical observations, you can adopt a much simpler rule; it is not perfect and not entirely universal, but it works: for an 8-inch head, the tunnel must be at least 5 cm in diameter, for a 10-inch -

7 cm, for 12 and more - 10 cm. Is it possible to have more? It’s even necessary, but right now something will stop us. Namely, the length of the tunnel. The fact is that...

Length matters

As was said, she will be commanded by the great Hermann von Helmholtz. Here he is, at the blackboard at the University of Heidelberg, and on the blackboard is the same formula. Well, okay, this time I wrote it, but I made it up - he would have written it exactly the same way. This simple dependence, since it was derived for the ideal case, shows what the resonance frequency of a certain cavity will be (we are more familiar with a box, although Hermann von made some kind of bubbles with pipe tails) depending on the volume V, length L and cross-sectional area of the tail. Please note: there are no speaker options here, and it would be strange if there were. In any case, it is useful to remember and never succumb to provocations: the bass reflex setting is completely and exhaustively determined by the size of the box and the characteristics of the tunnel connecting this box with the environment. In addition, the formula includes only the speed of sound in the atmosphere of planet Earth, designated “c,” and the number “pi,” which does not even depend on the planet.

For practical purposes, namely, calculating the length of the tunnel using known data, the formula can be easily transformed by remembering your native school, and the constants can be substituted in the form of numbers. Many people did this. Many people published the results of this exciting process, and the author is a little surprised how it was possible to screw up spectacularly during an operation with three or four numbers. In general, a third of the converted formulas published on paper and on the Internet are incomprehensibly nonsense. The correct one is given here if you substitute the values in the units shown in black.

The same formula, plus some corrections, is included in all known programs for calculating bass reflexes, but right now the formula is more convenient for us, everything is in sight. Look: what will happen if, instead of the minimalist tunnel, we install another, larger one (and therefore better)? The required length will increase in proportion to the square of the diameter (or in proportion to the area, but we were going to buy a pipe by diameter, they don’t sell it any other way). We switched from a 5-centimeter pipe to a 7-centimeter one, for example, the length with the same setting will need twice as much. We moved to 10 cm - four times. Trouble? So far - not so bad. The fact is that...

Caliber matters

There will be trouble now. Let's look at the formula again, this time - at the denominator, focus your vision. All other things being equal, the length of the tunnel will be greater, the smaller the volume of the box. If, in order to tune a 100-liter volume to 30 Hz, having a 100-mm plumbing pipe at your disposal, you need to open and paste a 25-centimeter piece of shit pipe into the box, then with a box volume of 50 liters it will be half a meter (which is no less, than not so bad), and with the fairly common 25 liters, a tunnel of this thickness will have to be a meter long. This is already a disaster, there are no options.

In our practical conditions, the volume of the box is primarily determined by the parameters of the speaker, and for reasons already well known to readers of this series, for 8-inch heads the optimal volume rarely exceeds 20 liters, for “tens” - 30 - 40, only when it comes to reaches 12-inch caliber, we begin to deal with volumes of the order of 50 - 60 liters, and even then not always.

So we get some kind of parade of sovereignties: the tuning frequency of the FI is determined by the bass that we want to get from it, whether it’s on the “eight” or on the “fifteen” - it doesn’t matter. And the tuning frequency of the box again does not depend on the speaker; the smaller the volume, the longer the tunnel. The result of the parade: as we have repeatedly noticed in tests of small-caliber subwoofers, the desired and promising design option in FI is physically impossible (or difficult) to implement. Even if you don’t mind the space in the trunk, you cannot make the volume of the FI box larger than the optimal one, and the optimal one often turns out to be so small that setting it to a frequency of 30 - 40 Hz, which is invariant to other factors, is unthinkable. Here is an example from a recent test of 10-inch subwoofer heads (“A3” No. 11/2006): if we take a pipe diameter of 7 cm as an axiom, then in order to make a bass reflex on the Boston head, a piece of it 50 cm long would be needed, for Rainbow - 70 cm, and for Rockford Fosgate and Lightning Audio - about a meter. Compare with the recommendations in the test of this issue relating to 15-inch heads: none of these problems were noted. Why? Not because of the speaker, as such, but because of the initial volume selected according to the speaker parameters. What to do? Meet adversity head-on. Generations of specialists (and others) forged our weapons. Do you know what's the matter?

Shape matters

You could hardly fail to notice: I really like to delve into patents, because I believe that even though the road from invention to real life is not so short, a patent is a reflection of thought in the form of a vector, that is, taking into account the direction. Most of the innovations proposed (and steadily proposed) by tireless minds in relation to the bass reflex are concentrated on combating two interfering factors: the length of the tunnel, when its cross-section is large, and jet noise, when they tried to reduce its cross-section, trying to reduce the length. The first, simplest solution, the admissibility of which we are asked in our editorial mail about five times a month: is it possible to place the tunnel not inside the box, but outside? Here is the answer, final, factual and real, like a paper for Professor Preobrazhensky’s apartment: you can. At least partially, at least entirely, the tunnel was pushed inside the box solely for aesthetic reasons; von Helmholtz had it sticking out outside, and nothing, he survived it. And our modern times provide examples: for example, car audio veterans cannot help but remember (many, frankly speaking, cannot forget) the “bass pipes” of the SAS Bazooka company. They started with a patent for a subwoofer that could be conveniently placed behind the seat of a truck, America's favorite vehicle. To do this, the inventor stretched the bass reflex pipe along the body from the outside, at the same time giving it a shape spread out over the surface of the cylindrical body. This is one example, there is another: some companies that produce built-in subwoofers for home theaters bring out a pipe-tunnel of a bandpass subwoofer. The type of subwoofer in this case does not matter: it is the same resonator named after you know who. Judging by the letters, they are also looking for another solution, but they are afraid. “Is it possible to bend a tunnel?” The answer is in the style of Philip Philipovich and is obvious. Otherwise, several companies (DLS, JL Audio, Autoleads, etc. etc.) would not have produced flexible pipes specifically for this purpose. And in the field of patent documentation there is even an interesting hint on how this problem can be solved not without grace and material savings: at one time a design was proposed for a model tunnel that would be assembled from standard elements in any desired form; the illustration will tell the rest. I’ll add on my own behalf: most of the details depicted in the patent are touchingly reminiscent of the nomenclature of elements of local sewer networks, which is a practical recipe for introducing the intellectual excess of the American inventor.

When struggling with the inappropriate length of the tunnel, they often take the path of constructing so-called “slot ports”, their advantage lies in their constructive integration with the body, which allows, with a certain imagination, to make the tunnel quite long; in the attached diagram there are several options at once, which the question is, Of course, it is far from being exhausted (the three top sketches belong to the pen of the famous high-end designer Alexander Klyachin, the rest was a matter of technique).

The disadvantage of the slots is that it is difficult to adjust the length, this is not plumbing PVC - waved the saw, and that was it. But there are solutions here too: not so long ago, one of the heroes of the “Own Game” column, Permian Alexander Sultanbekov (it’s not a sin to once again remind the country of the names of its heroes) demonstrated in practice how a slot port can be adjusted by changing its cross-section while maintaining a constant length, he I did it by placing plywood spacers inside, as shown in the photo somewhere nearby, look for it.

In folding the bass reflex tunnel, some bright minds went to extremes: one bright one suggested, for example, folding the tunnel in the form of a spiral around a cylindrical loudspeaker body, another responded to Helmholtz’s cunning formula with a screw tunnel, this concept is familiar to us here in Russia...

But in general, all these solutions (even with a propeller) are frontal; here a tunnel of constant length is simply attached or folded so that it does not interfere. Implementations of another principle are known (and even sold in commercial quantities). Here's the thing.

Section matters

Not the area as such, but the nature of its change along the length of the tunnel. Until now, we, guided by the teachings of von Helmholtz in its simplest, school form, have considered it indispensable that the cross-section of the tunnel is constant. But there were people who violated this condition and even made money from it.

Experienced readers will remember, for example, the article by our Italian colleague Professor Matarazzi, where he offers effective solutions for reducing the length of the tunnel by giving it a conical or double-conical, hourglass shape. In “A3” No. 10/2001, calculations for the professor’s programs are presented in the form of tables, and the sir recently found and sent the programs themselves, at our request. By the time this issue comes out of print, we will post them on the website in the “Appendices” section. True, the absent-minded professor lost the source code forever, so the programs remain in Italian, if anyone knows how to translate without having the code, we will accept help with gratitude.

For now, let us note: the professor is neither the first nor the only one in his research. Even tragedies occurred in this direction. Long-time readers of the magazine may remember the article in “A3” No. 2/2003 about a lawsuit regarding a bass reflex tunnel; let me remind you not so long ago: the Bose corporation noticed that another corporation, JBL, had used bass reflex tunnels with a curved generatrix in its speakers, called Linear-A has seriously infringed the intellectual property of Bose Corp. As evidence, a US patent was cited, which mentioned, among other things, that it would be nice to make the tunnel with an elliptical generatrix; then it would be shorter and quieter in terms of jet noise. In vain, JBL tried to explain to the court that Bose has an ellipse, and JBL has an exponential one. The court explained that ellipses-schmellipses are a minor matter, and they sold a lot of speakers; Bose’s accounting department calculated: JBL’s profit amounted to 5,676,718 dollars and 32 cents, which was proposed to be deposited into the cash register of the offended party. They brought it in like nice little ones, including coppers, and in all the columns the tunnels were changed to others, FreeFlow, like an improved model. This is how it happens...

Many, many people have proposed moving away from the cylinder as a form of tunnel. Some - in the Matarazzi style with variations, others - on a modest, local scale, limiting themselves to giving curved contours to the ends of the cylindrical tunnel in order to reduce jet noise from turbulence. The most radical means of combating both length and noise was not only invented, but also exclusively used for many years by Matthew Polk, the founder of a company named after him. The essence of the device called PowerPort is this: part of the functions of the tunnel is taken over by one or two, at each end of the pipe, an annular slot between the wall of the box and a “fungus” placed at a strictly calculated distance from it, however, everything is visible in the figure. Almost all Polk Audio home speakers are equipped with such tunnels. And if someone encroaches, they pay him 32 cents plus something else. For yourself, your loved ones, no one will forbid you to try such a thing, especially since once upon a time Polk posted a table in Excel on his corporate website, according to which you can calculate everything, I then downloaded it from this site (having received later, in hindsight, the author’s blessing - I’m not doing it for profit) and even translated the accompanying instructions into the great and mighty one, it’s all on our website.

A propos, both the works of Professor Matarazzi and the revolutionary development of Matthew Polk remind us of this: Helmholtz’s gymnasium formula, among other things, does not take into account an effect that is very significant for practice: in the vast majority of cases (almost always) one of the ends of the tunnel is adjacent to the wall subwoofer body, this applies to both round pipes cut flush with the wall and pipes equipped with an aerodynamic end, and to an even greater extent - slotted ports attached to the wall. The proximity of the wall creates an end effect reminiscent of what the author of PowerPort intentionally sought - a virtual extension of the tunnel. That is why modern applied specialists recommend introducing an amendment to the formula directly derived from the works of von Helmholtz, which is purely empirical, but no less necessary; it is highlighted in red so that it is clear where is the classic of the 19th century and where is the practice of the 20th.

But actually, dear friends, it’s time to get down to business, it’s not an age to dig through paperwork. This is exactly the point...

On the issue of thickness: pushing the same volume of air through a tighter tunnel, it will have to be accelerated to a higher speed. And “speed is death”

Helmholtz would have written his formula in exactly the same way, but there was no photographer at that moment

The final and actual formula replacing the computer program. It is correct, it has been checked several times. The meaning of the “tail” highlighted in red will be explained in the text

Could the tunnel be outside the box? Yes, a whole company built its business on this, the patent for an easy-to-place subwoofer was replicated by thousands of SAS Bazooka bass tubes. And manufacturers of built-in subwoofers for home theaters don’t give a damn...

Is it possible to leave the tunnel inside, but bend it as it is more convenient? Here's your answer

Exotic, desperate solutions: roll up the tunnel with a spiral or screw

The slot tunnel is integrated with the box, which makes it possible to make it longer than the usual “plug-in” one; adjusting the length, however, is much more difficult...

This means that it is necessary to adjust not the length, but the cross-section: this is how one resident of the capital of the Perm Territory did it

A move away from the cylindrical shape of the tunnel was proposed both to reduce its length and in the form of local “aerodynamic treatment” to reduce jet noise

The most impressive solution in this area: Matthew Polk's PowerPort. The invention did not remain on paper, it is an integral part of almost all Polk Audio acoustics

Prepared based on materials from the magazine "Avtozvuk", February 2007.www.avtozvuk.com

Editor's note: The article by an Italian acoustician, reproduced here with the author's blessing, was originally titled Teoria e pratica del condotto di accordo. That is, literally translated – “Theory and practice of a bass reflex”. This title, in our opinion, corresponded to the content of the article only formally. Indeed, we are talking about the relationship between the simplest theoretical model of a bass reflex and the surprises that practice prepares. But this is only formal and superficial. But in essence, the article contains an answer to questions that, judging by the editorial mail, often arise when calculating and manufacturing a bass reflex subwoofer. Question one: “If you calculate a bass reflex according to a formula known a long time ago, will the finished bass reflex have the calculated frequency?” Our Italian colleague, who has eaten about a dozen dogs on bass reflexes in his time, answers: “No, it won’t work.” And then he explains why and, most importantly, how exactly it won’t work. Question two: “I calculated the tunnel, but it’s so long that it doesn’t fit anywhere. What should I do? And here the signor offers such original solutions that we put this side of his work in the title. So the key word in the new title should be understood not in New Russian (otherwise we would write: “in short - bass reflex”), but quite literally. Geometrically. And now Signor Matarazzo has the floor to speak.

Bass reflex: in short!

Jean-Pierrot MATARAZZO Translation from Italian by E. Zhurkova

About the author: Jean-Piero Matarazzo was born in 1953 in Avellino, Italy. Since the early 70s he has been working in the field of professional acoustics. For many years he was responsible for testing acoustic systems for the magazine "Suono" ("Sound"). In the 90s, he developed a number of new mathematical models of the process of sound emission from loudspeaker diffusers and several projects for acoustic systems for industry, including the “Opera” model, popular in Italy. Since the late 90s, he has been actively collaborating with the magazines “Audio Review”, “Digital Video” and, most importantly for us, “ACS” (“Audio Car Stereo”). In all three, he is the chief for measuring parameters and testing acoustics. What else?.. Married. Two sons are growing up, 7 years old and 10.

Fig 1. Diagram of a Helmholtz resonator. That's where everything comes from.

Fig 2. Classic bass reflex design. In this case, the influence of the wall is often not taken into account.

Fig 3. Bass reflex with a tunnel, the ends of which are in free space. There is no influence of walls here.

Figure 4. The tunnel can be brought completely outside. Here again a “virtual extension” will occur.

Figure 5. You can get a “virtual extension” at both ends of the tunnel by making another flange.

Figure 6. Slot tunnel located far from the walls of the box.

Figure 7. Slot tunnel located near the wall. As a result of the influence of the wall, its “acoustic” length turns out to be longer than the geometric one.

Fig. 8. Tunnel in the shape of a truncated cone.

Figure 9. Main dimensions of a conical tunnel.

Figure 10. Dimensions of the slotted version of the conical tunnel.

Figure 11. Exponential tunnel.

Figure 12. Hourglass-shaped tunnel.

Figure 13. Main dimensions of the hourglass-shaped tunnel.

Fig 14. Slotted version of the hourglass.

Magic formulas

One of the most common requests in the author’s e-mail is to provide a “magic formula” by which the ACS reader could calculate the bass reflex himself. This is, in principle, not difficult. A bass reflex is one of the cases of implementing a device called a “Helmholtz resonator”. The formula for calculating it is not much more complicated than the most common and accessible model of such a resonator. An empty Coca-Cola bottle (just a bottle, not an aluminum can) is just such a resonator, tuned to a frequency of 185 Hz, this has been tested. However, the Helmholtz resonator is much older than even this packaging of the popular drink, which is gradually going out of use. However, the classical Helmholtz resonator circuit is similar to a bottle (Fig. 1). In order for such a resonator to work, it is important that it has a volume V and a tunnel with a cross-sectional area S and a length L. Knowing this, the tuning frequency of the Helmholtz resonator (or bass reflex, which is the same thing) can now be calculated using the formula:

where Fb is the tuning frequency in Hz, c is the speed of sound equal to 344 m/s, S is the tunnel area in square meters. m, L – length of the tunnel in m, V – volume of the box in cubic meters. m. = 3.14, that goes without saying.

Here the frequency is in hertz, the volume is in liters, and the length and diameter of the tunnel is in millimeters, as we are more familiar with.

Now, it seems, everything has been taken into account, and, armed with this formula, we imagine ourselves as omnipotent. This is where difficulties await us.

First difficulties

The first (and main) difficulty is this: if a relatively small-volume box needs to be tuned to a fairly low frequency, then by substituting a large diameter into the formula for the length of the tunnel, we will get a larger length. Let's try to substitute a smaller diameter - and everything turns out great. A large diameter requires a long length, and a small one requires just a small one. What's wrong with that? Here's what. While moving, the rear side of the speaker diffuser “pushes” practically incompressible air through the bass reflex tunnel. Since the volume of oscillating air is constant, the air speed in the tunnel will be as many times greater than the oscillatory speed of the diffuser, how many times the cross-sectional area of the tunnel is less than the area of the diffuser. If you make a tunnel tens of times smaller than the diffuser, the flow speed in it will be high, and when it reaches 25 - 27 meters per second, turbulence and jet noise will inevitably appear. The great researcher of acoustic systems R. Small showed that the minimum cross-section of the tunnel depends on the diameter of the speaker, the maximum stroke of its diffuser and the tuning frequency of the bass reflex. Small proposed a completely empirical, but trouble-free formula for calculating the minimum tunnel size:

When faced with such a dilemma, ACS readers usually call the editor and ask for a solution. I have three of them: simple, medium and extreme.

Simple solution for small problems

Average solution for bigger problems

In 1995, I wrote a program to calculate conical tunnels. It replaces a conical tunnel with a series of cylindrical ones and, by successive approximations, calculates the length required to replace a conventional tunnel of constant cross-section. This program is made for everyone, and it can be downloaded from the ACS magazine website http://www.audiocarstereo.it/ in the ACS Software section. A small program that runs under DOS, you can download and calculate it yourself. But you can do it differently. When preparing the Russian edition of this article, the results of calculations using the CONICO program were compiled into a table from which the finished version can be taken. The table is compiled for a tunnel with a diameter of 80 mm. This diameter value is suitable for most subwoofers with a cone diameter of 250 mm. Having calculated the required tunnel length using the formula, find this value in the first column. For example, according to your calculations, it turned out that a tunnel 400 mm long is needed, for example, to tune a box with a volume of 30 liters to a frequency of 33 Hz. The project is non-trivial, and placing such a tunnel inside such a box will not be easy. Now look at the next three columns. It shows the dimensions of an equivalent conical tunnel calculated by the program, the length of which will no longer be 400, but only 250 mm. It's a completely different matter. What the dimensions in the table mean is shown in Fig. 9.

Table 2 is compiled for an initial tunnel with a diameter of 100 mm. This will fit most subwoofers with a 300mm driver.

Extreme solution for big problems

Technologically, it is not always easy or convenient to make an hourglass with a round cross-section. Therefore, here too you can make it in the form of a profiled slot, it will turn out as in Fig. 14. To replace a tunnel with a diameter of 80 mm, I recommend choosing the slot height equal to 50 mm, and to replace a 100 mm cylindrical tunnel - equal to 60 mm. Then the width of the section of constant cross-section Wmin and the maximum width at the entrance and exit of the tunnel Wmax will be the same as in the table (the lengths of sections L1 and L2 - as in the case of a circular section, nothing changes here). If necessary, the height of the slot tunnel h can be changed, simultaneously adjusting Wmin, Wmax so that the values of the cross-sectional area (h.Wmin, h.Wmax) remain unchanged.