Calculation of speakers with bass reflex. A simple way to set up speaker systems with a bass reflex. Video: how to calculate round bass reflex ports

Any car owner can build a full-fledged sound system in the car interior. Many people install front speakers. This is where quality sound begins. They provide natural sound even at low frequencies. When this becomes not enough, they think about using a subwoofer. It emphasizes the depth of bass and increases sound pressure. With the help of a properly selected and installed subwoofer, you can completely change the sound.

Description of the bass reflex

Subwoofers come in a variety of types and quality. But to achieve the highest quality acoustics, it is recommended to design their enclosures. The most popular design method is a closed box and bass reflex. Sometimes sound fans prefer bandpass, passive radiators or acoustic loads. What is a bass reflex and how is it installed? Let’s look at it in detail.

A closed box (box) is the speaker housing. Its volume is comparable to the volume of the column.

A bass reflex for a subwoofer is a design that is a special housing hole. Also, it can be a pipe built inside it that connects the internal volume and the external space. It is otherwise called a bass reflex port. This system differs from a closed box in that it does not dampen vibrations emanating from the back of the diffuser. On the contrary, in this way it complements the radiation. This gives a significant increase in sound.

The bass reflex has another type - a passive radiator. The port here is a special system or a simple speaker that is not connected to an amplifier.

Box calculation

The acoustic system, as well as subwoofers, can be easily calculated using online programs. You can simply download them from the Internet. Automatic calculation is carried out by substituting data on sound elements. Here you need to find out information about the technical characteristics necessary for the calculation.

All information can be obtained from the built-in database program. If the characteristics are already known, they are entered manually. The online program is also convenient because it makes it possible to select speakers that will provide the best output.

The simplest forms of acoustics are a closed box and a bass reflex. It is not necessary for them to know the exact data. Calculation using formulas is enough.

How to calculate a closed box

You will need to find out three main indicators of the dynamics. The result will be the selection of the internal volume of the column. Pay attention to the ratio of the resonant frequency in the passport to the quality factor. If the indicator is less than 100, it is not recommended to install this speaker in a closed box. Since the air is compressed in a locked body, the stiffness of the suspension increases.

Special formulas have been derived that relate the resonant frequency, quality factor and volume: Fc, Qtc, Vb, respectively, with the same parameters in the passport. The formulas can be carefully examined in the photo.

Using formulas, the required volume of the case is selected. It is important to ensure that the resonant frequency of the speakers is not higher than 50 Hz. And the quality factor was approaching 0.7.

How is the bass reflex calculated?

The phase inverter is calculated by selecting speakers whose quality factor is from 0.3 to 0.5, and the resonant frequency ratio is 50 (not less).

In this case, it is necessary to calculate the following parameters:

Subwoofer volume.
Sectional area.
Pipe length and diameter.
Bass reflex port.

Information about the box is selected using the same formulas as when calculating a closed box. Only here the quality factor of the column differs: from 0.6 to 0.65. The port data is determined using the frequency value at which the bass reflex is tuned. It is selected along with the resonant frequency of the speaker. But it could be less. The calculation is carried out using the formulas that are also in the photo.

The calculated length is sometimes longer than the recommended maximum value. But there are ways to help reduce this length. The output of the round bass reflex is placed on the panel plane. This allows for a length gain of approximately 0.85. And the bass reflex pipe has flanges at the end, which can enhance the effect to a greater extent.

Approximately 15% of the length can be saved by placing the bass reflex close to one side of the speaker. If you use the port as a truncated cone (round or rectangular), this will make it possible to reduce the length by 35%.

The above methods are quite simple and do not require complex measuring instruments and mathematical calculations. It is important to consider a few more points:

the resonance frequency should be slightly lower than the resonance frequency of the speakers located in the box;
The bass reflex expands the reproduced frequencies towards low frequencies. you need to be able to choose the right one;

If you select too low frequencies, the output of the speakers will decrease.

In order to configure the bass reflex online, in one of the programs, you will need very accurate data on all parameters. But the program can still produce a large error. Therefore, most users try to adjust the acoustics themselves.

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, s 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. 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 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:

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 actual jet noise, 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...

The calculation of the bass reflex enclosure (box) can be divided into 3 parts, but before that you need to find the Thiel-Smol parameters for the subwoofer speaker, otherwise nothing will come of it. To calculate the FI of a box, three parameters Fs, Vas and Qts are sufficient

Fs – resonant frequency of the speaker, indicated in Hz (hertz).
Vas is the equivalent volume, indicated in liters.
Qts – total quality factor of the speaker.

These parameters can be found in the instructions for the subwoofer speaker or on the manufacturer’s website.

1. Calculation of the net volume and tuning frequency of the bass reflex port.

Net volume (Vb) is the internal volume of the box, excluding the volume of the bass reflex port and the volume displaced by the speaker.

Port settings (Fb)– this is the configuration of the port (length, width, height) relative to the net volume of the housing, tuned to a certain frequency to amplify it, which leads to the formation of the desired frequency response.

We can make this calculation in the JBL SpeakerShop or BassBox 6 pro programs. I recommend using the first one, it is simpler and much clearer. In the program we enter the parameters Fs, Vas and Qts, then by changing the values of Vb (volume) and Fb (port setting) we achieve the desired frequency response graph. For a universal box, the graph should not be very humpbacked with a peak in the region of 35Hz - 40Hz. If you encounter any difficulties with the program, you can view the instructions for it.

In the program we found out what net volume of the box and port settings we need, in this example Vb - 45l. Fb- 36Hz.

2. Calculation of the bass reflex port.

We will perform the calculations of the bass reflex port in the BassPort program.

Enter in the program:

Required frequency of setting the FI port (Fb)
Previously obtained net volume of the box (Vb)
Effective area of the subwoofer speaker cone (measured as the length at the center of the speaker from one center of the suspension to the opposite center of the suspension)
Maximum diffuser stroke in one direction (indicated in the instructions or on the manufacturer’s website as Xmax, can be indicated in one direction or in both directions at once)
Enter port dimensions W And h
Click the recalculate button.

In this example, a slot port is calculated, 35 cm high and 4 cm wide, the length of which is 61 cm and has a volume 8.5l. (rounded)

When selecting port sizes, it is impossible that the length of the port L exceeds 1000 mm, and the maximum air speed at the outlet is red.

3. We calculate the total volume of the FI body and make a drawing.

We have the following data that needs to be added up to get the total volume of the box (dirty volume) - clean volume 45 liters, port volume 8.5 liters, and we also add here the volume that will displace the speaker itself, this is within 2-4 liters . Let’s take 3L in this case, but since this is a slot port and one of the walls will also displace some volume, it also needs to be taken into account, but here it will be 4L.

To calculate the displacement of the wall, multiply the length of the inner wall of the port by its height and thickness, then divide by 1000.

We count: 45+8.5+3+4= 60.5l.

In total, we need a box with a total volume 60.5l.

Let's move on to the drawing of the box.

We have a volume of 60.5 liters. We measure the trunk, see what dimensions suit us, for example: height - 39cm, length - 50cm, we just need to find out the width. We subtract the thickness of the walls from the height and length, in this case it is 2 cm and we get: height - 35 cm, length 46 cm.

Now we calculate the width of the box: 60,5 1000 ÷ 35 ÷ 46 = 37.57 cm(round up to 38cm) – width of the body, excluding walls, with walls it will be 42cm.

This is how the calculation of a bass reflex enclosure looks like for a specific subwoofer speaker that will play as we need.

I didn't vote either up or down. I can’t for reasons of lack of faith in the device. Against because
feelings of camaraderie. You can brand me with disgrace for the second.
I can say right away that I have not used or even assembled a resonant frequency generator (RFG). I don’t know how it works in practice. The reason is that at that time I already had a generator and a millivoltmeter, and after reading Golunchikov’s article I didn’t understand how the FI could be configured correctly using the GRF. And now I don’t understand. Familiar, but practically did not work.
Let's think about it and carefully read what is written in the articles:
V. Burundukov writes that using this device you can quickly measure the resonant frequency of an acoustic unit. Okay, but how? We started the generator, it generated, so what? How can you determine this frequency? By ear? Exactly how many hertz are there?
Can anyone answer?
He further writes that resonant frequencies are determined using appropriate measuring instruments. We've arrived. The resonant frequencies are already known. Most likely dynamics without a box. And we are most likely talking about comparing this and that. That is, the meaning of using the device is not completely clear.
As for setting up the FI, everything is clear; all the articles clearly state: lasing occurs at the resonance frequency of the loudspeaker in the corresponding volume. That is, it's not
The resonant frequency of the speaker in open space is the resonance of the system. We put the din in a large volume - resonance one, take a smaller volume, resonance another.
Right or wrong?
The times were long ago, few people knew about Thiel and Small, at least the mathematical calculation of FI was inaccessible. There were different methods, it doesn’t matter.
Speaker Golunchikova it is possible and can be adjusted acceptably, after all, the volume of the box is not small, and even filled to capacity with a sound absorber. that is, the resonance of the dyne in the box should increase slightly. Apparently the same applies to other large speakers.
Let's move on. We are asked to tune the FI to the resonant frequency of the speaker in the box.
Let it be. Let Fs (resonance in free space), equal to about 30 Hz, become equal in the box to, well, 40 Hz. We denote the resonance in the box as Fc. In principle, it’s normal; by tuning the FI to this frequency, nothing nasty will happen. It will work, no question. Not entirely accurate, but if you also take into account the room and location of the speaker, everything is fine. The not-smooth theoretical frequency response is not scary; anyway, indoors it resembles mountains at low frequencies.

Now let's take another example and try to configure Saltykov's AS in the same way.
Volume about 9l. Din 6GD-6 or 10GD-34. The resonance (Fs) of these dins is about 80 Hz. Rare examples below. But rare. So, in a 9 liter box the resonance will go above 80 Hz.
I hope no one will argue with this? It is to this frequency that the FI is tuned when using this device. And it is necessary, as you remember, it is necessary (in my opinion) about 50-55Hz.
How do you like it?
Tell me what I'm doing wrong?

Now about the modern one. According to authoritative sources (Vinogradova and Aldoshina are quite authoritative, if not legendary), there is a total quality factor equal to 0.383 , in which the FI is tuned to the resonant frequency of the dyne in open space (not in a box). In this case, the volume of the box is taken to be 1.41 times less than the equivalent volume of the dyne.
That is, the flexibility of the air in the box is less than the corresponding dynamic parameter.
It is probably possible to calculate cases when the FI needs to be tuned to the resonance of the dyne in the box, I think these cases are combinations of unit parameters.
If the quality factor is greater than 0.383, then FI is always adjusted lower than Fs. Without fail.
By and large, FI will always work, the only exception being when it is set so low that FI becomes a closed box with a hole. But this is an unlikely case.
If the entire chain (amplifier, cable to the speakers, and speakers) is built normally, there may even be a hump
It won't hurt the frequency response. Maybe even the increased quality factor of the dyne is not a hindrance. If the other components (PA and cable) can cope with this, there is nothing wrong with the frequency response curve.
If, of course, the ear likes it. All the same, everywhere the final tuning of FI is done by ear.

Something like this. In my opinion, it turns out that the device is useless. Neither quickly measure nor adjust.

Sound at the end of the tunnel

“Volodya, if you’re in the warehouse, grab the ports for the phasics...”
(overheard in one of the Moscow installation studios)

In general, in the first issue of any magazine, the reader usually does not expect to see a continuation of any series of articles. But you see, it happens. When Autozvuk was still small and sat under the wing of Salon AV, the first two parts of a trilogy about subwoofers were published - about what to expect from different types of acoustic design and how to choose a speaker for a closed box. (“AV Salon” No. 4 and 5 - 6, 1998).
A significant portion of those who, contemplating life, decided to treat the bass armament of their car with understanding, in principle, could already get by with this. But not all. Because there is at least one more, extremely popular type of acoustic design, which is not inferior in popularity to a closed box. Bass reflex in Russian literature, bass reflex, ported box, vented box in English - all this is, in fact, a sound engineering implementation of the Helmholtz resonator idea. The idea is simple: a closed volume is connected to the surrounding space through an opening containing a certain mass of air. It is precisely the existence of this mass - that very column of air that, according to Ostap Bender, puts pressure on any worker, and produces miracles when the Helmholtz resonator is hired to work as part of a subwoofer. Here the sophisticated thing named after the German physicist takes on the prosaic name of a tunnel (in bourgeois - port or vent). How does a bass reflex work? Why does the presence of a neatly made hole of a certain size in the loudspeaker body suddenly have a dramatic effect on the work of the entire ensemble? As already mentioned in passing in the previous parts of this epic canvas, the bass reflex tunnel serves to delay the sound wave arising inside the speaker box for a strictly defined time and release it outside in the same phase as that created by the “front” side of the speaker. Here, in the wild, they will combine their decibels and hit your ears (if calculated correctly) so that it will not seem too little. This is, in fact, why they love the bass reflex - for its increased efficiency compared to a closed box. But not only that. Brute force is not an argument unless it is supported by the accuracy of signal reproduction. Here we mean another, much less trivial feature of the bass reflex - its ability to produce the required sound pressure with a significantly smaller amplitude of vibration of the diffuser. This sounds somewhat paradoxical. Everyone knows that it is the presence of a closed volume behind the diffuser that restrains the vibrations of the diffuser, so why will they suddenly appear smaller in a “leaky” housing? And because of the mass, as was said. That's why the hole in the phase converter body is made like a fairly long tunnel - a pipe, in other words, to keep a certain mass of air inside. At relatively high frequencies, above 200 Hz, the inertia of the air mass in the tunnel causes it to be acoustically completely opaque. It's like it's completely blocked.

Lower in frequency, the air plug in the tunnel begins to come to life and move, as it is pushed from behind by the pulsating pressure inside the box. The inertia of the air mass leads to the fact that it does not move in time with the wave acting on it, but with some shift. It reaches 180 degrees in phase, that is, it begins to be antiphase to the sound wave emanating from the back side of the diffuser at a certain frequency, which is called the bass reflex tuning frequency.

Here, almost all the efforts of the speaker go towards rocking the intractable air mass inside the tunnel, so that there is almost nothing left for natural vibrations, and the amplitude of the diffuser’s vibrations is minimal. (And the sound is coming, and what a sound! It’s just that at this frequency almost all of it comes out of the tunnel). And since it is the large amplitudes of vibration of the diffuser that give rise to distortions noticeable to the ear, the situation, in terms of sound, is the most favorable. Even lower in frequency, however, things begin to change for the worse. For very slow low-frequency oscillations, the air mass in the tunnel no longer has any inertia, and the back side of the diffuser pumps it back and forth like a pump.

In this case, a situation arises as if the speaker was not installed in the housing at all, that is, the waves from the back side of the diffuser and from the front side meet in antiphase and largely eat each other up, as in a normal acoustic short circuit. That is why, below the tuning frequency, the bass reflex output drops twice as fast as that of a closed box. However, something else is worse - the diffuser no longer slows down anything, and the amplitude of its oscillations at very low frequencies begins to grow simply catastrophically. The subsonic filters found on some, usually thoroughbred, crossovers and amplifiers are made almost exclusively to counteract this bad habit of bass reflexes. So, what exactly do we get by choosing a bass reflex for our project as an acoustic design? I want to warn you right away: calculating a bass reflex without computer programs designed for this is possible, and there are calculation formulas and nomograms for it. However, on the threshold of the third millennium, I cannot classify such methods as anything other than masochism. And I promised not to let formulas appear on the pages of this magazine, and so far I’m sticking to it. So for those interested, at the end of the article I place the address on the WWW, where there is an annotated selection of proven programs of varying degrees of complexity and sophistication. Here's a picture that explains (almost) everything. A 10-inch speaker was taken, its parameters suitable for installation in a bass reflex, and the characteristics that would be obtained when installed in the optimal bass reflex for it (20 l, tuned to 42 Hz) and a closed box of the same volume were simulated.

The upper of the two black curves is, of course, ours. Compared to a closed box, the response is significantly higher throughout the entire frequency band below about 150 Hz. What does "substantially" mean? Take a look: at a frequency of, say, 60 Hz, the difference is about 4 dB. And this is equivalent to increasing the amplifier power by 2.5 times. That is, with a modest 100-watt amplifier, such a sub will play as if 250 watts were supplied to it. For the same money. But of the red curves depicting the dependence of the amplitude of vibrations of the diffuser on frequency, ours is the lower one. Just where most of the bass energy is concentrated - below 100 Hz, the amplitude begins to drop and remains much lower than that of a closed box, although the sound pressure generated is twice as high! In a closed box, the amplitude of oscillations increases steadily and, when the power indicated as maximum is applied, it goes beyond the operating range (red dotted line) already at 70 Hz, and below that it’s a disaster. This is where the familiar wheezing sounds that accompany the bass notes will be generated. With a bass reflex, grace with amplitudes continues up to about 30 Hz, and there the amplitude begins to grow irrepressibly. However, there is almost no sound there, so the direct meaning is to “strangle” this part of the spectrum with a subtonal filter (if there is one) and enjoy impact efficiency with a minimum of distortion in the actual audio range. "Great!" - the impatient and decibel-hungry reader will exclaim, slam the magazine shut and immediately go to fix the holes in his own subwoofer. Comrade, stop! See what might happen next. Let us leave everything unchanged, take the old speaker out of our 20-liter box and install another one - designed to work specifically in a closed case.

His performance in the closed, native box (lower on the graph) was very nice. And after converting it into a bass reflex, it will become like the top one, that is, it will give a pronounced “pop” between 50 and 100 Hz. It was as a result of the creation of such combinations that bass reflexes at one time received the offensive nickname boom-box (“booze”), which was later used, this time quite rightly, for some kind of portable radio. What was the difference between the two speakers? In two parameters that must be in a certain harmony for a given acoustic design, otherwise, everyone who sounds here, give up hope, so to speak. These parameters are the resonant frequency Fs and the total quality factor Qts. For the “closed” speaker they were Fs=25 Hz, Qts=0.4. And the “bass reflex” one has 30 Hz and 0.3. It seems that the difference is not so great, but the results differ significantly. The energy bandwidth parameter Fs/Qts, invented at one time, immediately shows who is who: its value for the first speaker is 62.5, and for the second - 100. The rule is simple: if Fs/Qts is noticeably less than 100, forget the word “bass reflex” . If it’s close or more, remember again, and forget about the closed box. In the region of 90 - 100 there is a “twilight zone”, where, with certain concessions, one or the other can be used. But what happens if you insist on your own and push the speaker into a design that is unusual for it? Let's try, fortunately while the drama is unfolding on paper and a computer screen, that is, “with little loss, on foreign territory.” To begin with, we put the “bass reflex speaker” in a closed box and try to vary the only parameter we have - the volume of this box.

There are three curves on the graph. The flattest is the result of installation in a box with a volume of 50 liters, the steepest drop below 100 Hz is the result of installation in a box with a volume of 10 liters. And in the middle is our original characteristic in a 20-liter volume. We see: the volume changes from indecently small to impractically large, but a good characteristic does not come out - it either begins to fall off too early, or falls off too quickly. A speaker designed for a closed box, as can be seen from the following graph, has the opportunity to either hit the optimum (middle curve), or “cut” on the volume, thereby obtaining a rather noticeably “buzzing” characteristic (the upper curve, plotted in volume 10 l).

What about the other way around? When installing a “closed” speaker into a bass reflex, is it possible to configure it in such a way as to obtain an even frequency response? Theoretically, yes, fortunately, with a bass reflex, you can adjust the frequency at a constant volume by changing the diameter and length of the tunnel (in practice, always the length, of course). We start the experiment with the upper, absolutely terrible curve (volume 20 liters, tuning frequency 50 Hz) and, gradually rebuilding the bass reflex, suddenly at a tuning frequency of 20 Hz we notice that we have arrived at a very nice curve (lower on the graph).

Oops, let's now figure out which tunnel is needed for this - and go ahead! After half a second of computer time, we receive data that in order to tune a 20-liter volume to a frequency of 20 Hz, you need a tunnel with a diameter of 75 mm and a length of 1 m 65 cm. That is, the height of a miniature lady, and not the size of a compact subwoofer part. But a “bass reflex” speaker will allow you to adjust the frequency with minimal hassle (push in or out the pipe) no worse than using an equalizer. The graph shows the results of such activity in the tunnel tuning frequency range from 35 to 52 Hz, which required a tunnel length from 190 to 400 mm - God knows what, even at the highest value.

In the next part of the saga about subwoofers (of course, not the last - the topic is boundless, and God is merciful and, perhaps, will extend the years of the author), we will directly address the issue of the practical implementation of the plan - for those who want to do it themselves, or for those who want to be able to distinguish the work of a competent installer from the efforts of an ignorant hack. Agree, even when traveling in a taxi, it is useful to know that the path from Sokolniki to Izmailovo passes somehow away from Chertanovo... For those with access to the Internet, as promised, the coordinates of the rookery of subwoofer calculation programs. Search in the “Information Resources” section and, I promise, you will find it.

See you in the bass range...