The TM arrangement proposes to use 4 subwoofers to achieve greater summation, and proposes to keep the acoustic centers nearby to maintain an omnidirectional coverage pattern.

Michael "Mija" Krieg Schreiber

Making designs of subwoofer systems is one of the most interesting and fun stages in the design of a system, the subs arrangements allow to change and control the directivity of low frequency energy. One of the needs in low frequency arrays is to achieve uniform coverage throughout an enclosure and avoid contamination onstage, for which TM arrangements were born.

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To achieve the above, we must understand the behavior of a single subwoofer at different frequencies, for this we can rely on acoustic prediction tools, such as Nexo's NS-1 software.

NS-1 allows you to create an acoustic space, place sound sources and finally predict their behavior. For this exercise we are going to use a square space only for the purpose of studying the behavior of the S118 subwoofer of the STM family.

Let's see the coverage of this subwoofer at different frequencies.

We can appreciate how a single subwoofer behaves as an omnidirectional element, although it seems to be more omnidirectional in the low frequency than in the high frequency. This change in directivity is related to the wavelength, remember that the wavelength of 31.5 Hz is equivalent to 10.8 meters while that of 120 Hz is equivalent to only 2.8 meters, so for 125 Hz the same speaker cabinet can represent an obstacle. This idea is a fundamental part of the TM arrangements, the question we can now ask is, how can we make the coverage omnidirectional for all frequencies?

If we add a second S118, back to back to the previous sub, we will have 2 sound sources working simultaneously and therefore we would expect to obtain higher sound pressure. But what about the coverage pattern?

The coverage is split in the form of a cross. This is because, for that frequency, the separation between the acoustic centers of the speakers equals a full wavelength. So if we wanted to avoid these cancellation corridors the separation between the acoustic centers should be minimized, preferably it should be less than 1 / 4 of the wavelength.

If we now do the same exercise, but rotate the speakers so that they are face to face, we can see how the destructive interaction is no longer present, even this coverage pattern seems to be more omnidirectional than the pattern of a single S118 in 125 Hz. turning the subwoofers we have achieved greater closeness between the acoustic centers of the speakers, this closeness results in a very consistent and uniform sum throughout the coverage of this arrangement.

We can also think that the acoustic center of this S118 subwoofer is located near the front of the speaker. This pattern of coverage is much more uniform than the pattern of a single speaker, but it is not yet completely omnidirectional, will it be possible to achieve an even more uniform pattern?

One of the challenges that Thomas Mundorf faced when developing this arrangement was to achieve a high SPL (sound pressure level) with a uniform coverage, thinking about the high SPL we know that the greater number of loudspeakers we will achieve greater summation. With this in mind the TM arrangement proposes to use 4 subwoofers to achieve greater summation, and proposes to keep the acoustic centers nearby to maintain an omnidirectional coverage pattern.

If we calculate the SPL gain that we achieved in this 4 subwoofer relationship, we could say that:
Sum of SPL = 20log⁡ ((Num of final subs) / (Num of original subs))
So that:
Sum of SPL = 20log⁡ (4 / 1)

So this configuration achieves 12dB SPL sum and an omnidirectional coverage pattern. It is because of this behavior that Thomas Mundorf says that this arrangement works as a point source in horizontal coverage, but Thomas also talks about this arrangement as an online array in vertical coverage. The line arrays, or LineArray, have very particular vertical coverage characteristics and the best way to study this behavior is by means of subwoofer lines.

Vertical directive control
If we now model the vertical coverage of the array we have created and add more subwoofers to each block or cluster, we can see that the vertical coverage narrows as we add elements.

This is actually the operating principle of online arrangements, the general idea of ​​this phenomenon is that having a line of omnidirectional sources the coverage pattern will be related to the length of the arrangement and the frequency that is reproduced. Once again we can associate this phenomenon with the wavelength and the phase.

If we imagine the subs line and place ourselves below it, it will be evident that all the elements will reach our listening position at different times, this causes that in that position the signal of the different subwoofers is added with phase differences so that there will be considerable attenuations. On the other hand, if we position ourselves in front of the arrangement, the time and phase differences of each element will be minimal and therefore we will have good summation in the front part of the arrangement.

The coverage of a subs line is subject to the frequency. When the subs line has the same size as the wavelength of a frequency, for that frequency the array will have approximately 72 ° coverage. When the subs line has twice the length of a frequency, for that frequency the array will have 36 ° of coverage. So the coverage of a line is proportional to the frequency.

That is to say. If we have a subwoofer line that measures 3.4 meters, which is the 100 Hz wavelength, we will have 72 ° coverage for 100 Hz. If we analyze the coverage of that same line for 200 Hz, which has a wavelength of 1.7 meters, we will see that the coverage is 36 °. On the other hand, if we analyze the coverage of 50 Hz, which has a wavelength of 6.8 meters, we will see that the coverage is 144 °.

If we now analyze the coverage of our TM array with 7 S118 subwoofers we can confirm that:
Under the arrangement there is considerable attenuation and we have achieved managerial control.
For higher frequencies, the directive control is lower
For higher frequencies, direct control is greater

These arrangements have great advantages when making 360 ° assemblies, since they allow to achieve a uniform coverage throughout large enclosures and at the same time they manage to eliminate low frequency contamination on the stage, so that achieving a good mix will be easier.

Here is an example of a TM arrangement for an 360 ° assembly at the Mexico City Arena.

* Michael "Mija" Krieg Schreiber, has worked in various companies, productions, discotheques and installations as designer, technician and operator of sound systems gathering 8 date of years of experience. Among others are Audio Representations, Meyer Sound Mexico, Hi tech Audio, the Papal Mass in San Cristóbal de las Casas 2016, Corona Capital 2014, National Auditorium, among others. Nowadays he concentrates his career in educational activities offering different presentations and professional audio courses. Among the schools and organizations with which he has collaborated are: AES Mexico, IPN National Polytechnic Institute, Technological Institute and Higher Studies of Monterrey, UNITEC Technological University of Mexico, SAE INSTITUTE Mexico, EMEH School of Music of the State of Hidalgo, G Martell, Pro Audio Puebla, among others.

Richard St.
Author: Richard St.
Journalist from the University of Antioquia (2010), with experience in technology and economics. Editor of the magazines TVyVideo + Radio and AVI Latin America. Academic Coordinator of TecnoTelevisión & Radio.


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