non-conventional alternative approaches to low frequency...
TRANSCRIPT
Non-conventional alternative
approaches to low frequency coverage
in sound reinforcement of small venues.
Daniel Nielsen
Ljudteknik, kandidat
2017
Luleå tekniska universitet
Institutionen för konst, kommunikation och lärande
During sound reinforcement of small venues the low bass frequencies are one of the hardest things
to control. Due to the limitations of sightlines, space and time consumption to optimize and integrate
subwoofer arrays, alternative configurations might be desirable for a specific type of event. Five
configurations are tested, one conventional stereo configuration and four non-conventional
subwoofer configurations. An experiment with measurements was performed. The four non-
conventional configurations are compared to the stereo reference, to see if they have any
advantages over a more conventional approach that can be utilized in sound reinforcement of small
venues. It is concluded that the each non-conventional configuration has its advantages and
disadvantages to the stereo reference that can be desirable for some scenarios.
Table of Contents 1. Introduction ......................................................................................................................................... 1
1.1 Research question ......................................................................................................................... 1
2. Background .......................................................................................................................................... 2
2.1 Subwoofers .................................................................................................................................... 2
2.2 Modal Frequencies ........................................................................................................................ 2
2.3 Sub-Arrays and Low Frequency Directivity ................................................................................... 3
2.4 System Design Goals...................................................................................................................... 3
3. Method ................................................................................................................................................ 4
3.1 Equipment and Signal Flow ........................................................................................................... 4
3.2 The Venue...................................................................................................................................... 5
3.3 Measurement Positions ................................................................................................................ 6
3.4 Configurations ............................................................................................................................... 7
3.4.1 Traditional Stereo Reference (TSR) ........................................................................................ 7
3.4.2 Four Unit Cluster (FUC)........................................................................................................... 8
3.4.3 The Vortex (VTX) ..................................................................................................................... 9
3.4.4 Rear Wall Cancellation (RWC) .............................................................................................. 10
3.4.5 Surrounding the Audience (STA) .......................................................................................... 11
4. Results & Analysis .............................................................................................................................. 12
4.1 Traditional Stereo Reference (TSR) ............................................................................................. 13
4.2 Four Unit Cluster (FUC)................................................................................................................ 16
4.3 The Vortex (VTX) .......................................................................................................................... 19
4.4 Rear Wall Cancellation (RWC) ..................................................................................................... 22
4.5 Surrounding the Audience (STA) ................................................................................................. 25
4.6 Configuration comparison ........................................................................................................... 28
5. Discussion .......................................................................................................................................... 34
5.1 Low Frequency Directivity ........................................................................................................... 34
5.2 Low Frequency Coverage ............................................................................................................ 34
5.3 Comparison ................................................................................................................................. 35
5.4 Strengths and weaknesses .......................................................................................................... 35
5.5 Critique of the method ................................................................................................................ 36
6. Conclusion ......................................................................................................................................... 37
6.1 Further research .......................................................................................................................... 37
References ............................................................................................................................................. 38
Appendix A – Standard Deviation ......................................................................................................... 40
Appendig B – Configurations and Measurements ................................................................................ 43
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1. Introduction When designing a modern sound reinforcement system for a live sound event, one of the hardest
things to control is the lower bass frequencies (Hill, Hawksford, Rosenthal, & Gand, 2010). The
lower you go in the audible frequency range, the subwoofers usually shapes the lower bass
directivity to a more omnidirectional polar pattern. (Rumsey, & McCormick, 2013). This becomes a
problem since this also means that there will be an equal amount of LFC (Low Frequency Content) on
the stage as well as in the targeted audience area. To solve this problem a certain amount of
directivity of the lower frequencies is desired (Hill et al., 2010).
1.1 Research question
This research project will investigate if one can achieve a more even low frequency coverage solution
by using non-conventional alternative subwoofer configurations. Can such configurations provide a
more even coverage of low frequency energy in a smaller venue than a more commonly used
configuration? Are there any clear benefits or is it more disruptive than beneficial?
During the course of this experiment it’s necessary to determine which qualities that might be
preferable, and must therefore define some key aspects to consider during the course of the
experiment. These aspects being:
Even coverage of the audience area without too much LFC on stage.
System design for a specific type of music/event.
Physical limitations of sight lines/cost/transport space and stage/performance areas.
2
2. Background
2.1 Subwoofers
From a single speaker or speaker array, it is difficult to achieve a flat response that favours both high
efficiency and a good bass response (Rumsey, & McCormick, 2013). For example, sub-bass
information often ranges from 20 – 100 Hz, which means that the wavelength of these frequencies
will vary from roughly 17 m to 3,4 m. This would in turn mean that the speaker cabinet necessary to
reproduce these frequencies would need to be quite large, as well as the driver actually moving the
air (Nicklasson, 2006). Referring to the equal loudness contours (first developed by Fletcher &
Munson in 1933, since then further refined by others), show that the SPL (Sound Pressure Level)
varies with different frequencies as compared to its 1 kHz loudness reference for each curve. Looking
at the curves shows us that the human ear is much less sensitive at lower frequencies and must
therefore be further amplified to be perceived as equally loud as its reference (Everest, & Pohlmann,
2009). It therefore makes perfect sense to leave the LFC reproduction to a separate speaker system
designed to handle only low frequencies, than to rely on a speaker that cannot guarantee sufficient
efficiency (Colloms, 1991). Hence the subwoofer came into play. By dividing the low frequency
information from the main signal and sending it to a separate system handling only LFC, this offers
the opportunity for better efficiency and reproduction of LFC, as well as allowing the main PA to be
smaller (thus improving audience sight lines) and focus on the mid to high range of the signal. By
properly calibrating and integrating the subwoofer/sub-array into the main PA system, it can
enhance the overall quality and experience significantly (Rumsey, & McCormick, 2013).
2.2 Modal Frequencies
A short description of room modes is they are the result of reflections from surrounding surfaces that
reinforce each other (Toole, 2008). The modal responses present in indoor environments can if
serious enough contribute to a severe degradation of frequency response and uneven SPL coverage.
When performing a measurement at a point in a room, the mode can easily be identified by its shape
of a peak or dip visible at the frequency response curve. (Toole, 2008). Another phenomenon created
by reflections is standing waves. They exist and can be created by reflections in-between two parallel
surfaces at a certain distance from one another. When this distance corresponds to the wavelength
of a certain frequency, the reflections from the surfaces causes a summation and results in a stronger
SPL at that point (Everest, & Pohlmann, 2009). The same problem and phenomenon is most likely
present in “power alleys” created where the SPL produced by two or more subwoofers meet and
creates a large area of stronger SPL (Hill et al., 2010).
Sound reinforcement of smaller venues can to some extent be considered the same as with larger
venues. With the exception of that the smaller the venue is, the modal responses in the LFC region
are going to get bigger and more common (DellaSala, 2015) especially if the venue is indoors and of a
rectangular shape. If so, alternative placement methods might be of importance (Welti, 2002).
3
2.3 Sub-Arrays and Low Frequency Directivity
Low frequency coverage is one of the most important aspects to consider when system designing a
modern day sound reinforcement system. LFC on stage is important to keep at a minimum SPL in
order to provide musicians, technicians and stage monitoring systems a well functioning and proper
working environment (Hill et al., 2010). A certain amount of directivity is therefore necessary reduce
LFC on stage and to aim as much LFC out to the audience as possible.
The only way to properly control the dispersion of the lower frequencies is to use multiple sounds
sources (Shabalina, Ramuscak, & Vorländer, 2011). Typically these multiple source solutions are
called Sub-arrays and can be placed processed in a number of different settings and array
configurations to achieve wanted directivity of LFC. The amount of subwoofers necessary to provide
an even distribution of SPL is also an important aspect to consider, since it isn't always a question of
optimum performance, but more of the cost of using many subwoofers.
In research made by Welti (2002), he investigates if there is any correlation between the number of
subwoofers distributed along a room and the desirability of frequency response over a desired
listening area. This experiment is focused around a 5.1 surround configuration in a small to medium
sized rooms. However, one can see that both surround sound and sound reinforcement shares the
same goal to cover a larger listening area for multiple listeners. In his study Welti seeks the answer to
how many subwoofers are enough and what their optimal placements are. He arrives at the
conclusion that a large number of subwoofers seem to cancel out many of the room modes.
However, the large number of subwoofers necessary is not reasonable and it turns out that
configurations of 4 subwoofers yielded the best results in the bigger picture. . It seems that one
subwoofer at each wall at midpoint is the best placement in terms of measurement. It is then
reasonable to assume that the techniques and findings of his paper can be applicable to modern day
sound reinforcement as well as surround sound setups.
In 1973 Harry F. Olson came up with the concept of gradient loudspeakers, which he based on what
was known about directionality of microphones, and treated loudspeakers the same way working in
reverse. The definition of gradient loudspeakers is:
"…consisting of two or more loudspeakers separated in space and operating with a difference in phase or powers of the difference in phase between the loudspeakers…"(Olsson, 1973, pp. 86).
These speakers which are also called "Differential loudspeakers", can be used to achieve different polar patterns simply by using several subwoofers with different positions, delay and phase settings.
There is no single obvious solution of how to distribute subwoofers for best coverage of LFC, but the
venue itself and its properties has to be taken into account and consideration. Compromises have
almost always to be done to achieve LFC optimization. It is through careful positioning, orientation
and calibration that we can achieve enhanced Low-frequency coverage. (Hill et al., 2010).
2.4 System Design Goals
There are as described many things to keep in mind and aim for when optimizing a subwoofer array.
A few of the main goals being equal SPL across the targeted listening area, an equally distributed
frequency response throughout the area and the impulse response (time Structure) of the array
(Shabalina et al., 2011). The necessary complex design of larger sound reinforcement systems is
often simplified for convenience. The ideal sound reinforcement scenario can’t always be considered
and compromises has to be made due to the fact of lack of truck space, system efficiency, audience
sight lines and the time it takes to manually calibrate the subwoofers to fit each new world venue.
4
This is even more important when dealing with smaller venues, since there most likely is no space for
large subwoofer-arrays. However, consistently good coverage, regardless of the differences between
venues, can be achieved by keeping certain aspects in mind when designing the system. These
considerations include orientation, delay and proper spacing of the subwoofers. (Hill et al., 2010)
3. Method The primary source of data for this experiment relies on information collected from live
measurements of subwoofer configurations, and the analysis and discussion deriving from this data.
Since two of the configurations explored focuses on low frequency directivity, and two aiming for low
frequency coverage, these two pairs will be discussed together and compared to the TSR before
being compared to the other configurations.
Every measurement was performed with only subwoofers playing in the room and no main PA
aligned with it. The aim of this research is to only focus on the low frequencies reproduced by the
subwoofers and how they propagate in the room. Therefore leaving out how the configurations
under investigation can be aligned with a main PA.
3.1 Equipment and Signal Flow
The equipment used in this experiment was:
4x Nexo LS 1200 Subwoofer (NEXO Innovate, n.d.)
A computer with CLIO v.10 measuring program with Interface and related microphone
(Audiomatica Electrical and Acoustical Measuring Systems, n.d.)
2 x Crown Macro-tech 3600vz Amplifiers (Crown by HARMAN, 2017)
BSS Minidrive FDS-336T Loudspeaker management system (BSS by HARMAN, 2017)
From the CLIO interface a Pink noise was sent to the BSS Minidrive processor unit, and out from its
outputs the signal went into the Macro-tech Amplifiers. Out from the amplifiers the signal went to
the 4 NEXO LS 1200 Subwoofers. Each measurement was then performed with the supplied
microphone from the CLIO system, into the CLIO interface.
5
3.2 The Venue
The Venue of choice for this experiment was Black box, Studio Acusticum, Piteå, Sweden (Figure 1).
One of the reasons for choosing this venue is because a black box theatre is a common performance
area that exists in many different locations and shares many of the same features (Education
Facilities Specifications, 2001). Also, its square design is an important factor for some of the
configuration done in this experiment to work.
What qualifies a room as a black box theater is that it´s designed as a box, often with black walls and
many adjustable features to enable it to host a number of different configurations suitable for many
varying performances and shows. (“What is a Black Box Theater?”, n.d.)
Due to an inconvenience with the room of choice the decision was made to rotate the configurations
and place them alongside the length of the room instead of the width. This because the right short
side wall had a permanent installation of telescopic seats mounted along the complete length of the
wall. During the course of the measurements taken the telescopic seats was withdrawn to their full
capacity to minimize their influence on the experiment.
21,866 m
11
,86
6 m
Black Box Telescopic
Seats
1,5 m
Figure 1: Black box layout and measurements.
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3.3 Measurement Positions
The measuring positions was randomly placed and divided throughout the room with the most
positions outside in the audience area, and a few by the stage area, resulting in 17 different
measurement positions (Figure 2). The measuring microphone was placed on a microphone stand at
the height of 1,6 m, to simulate the average ear height of a standing audience member.
Stage area
1
13
6
7
8
2
3
4
5
9
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16
Audience area
Figure 2: Plot of measuring points.
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3.4 Configurations
3.4.1 Traditional Stereo Reference (TSR)
This configuration of two separate subwoofers to either side of the stage (Figure 3) is one of the
most commonly used techniques and will serve as a reference to the other non-conventional
configurations. Consisting of two subwoofers at equal spacing from the walls so that they are time
aligned with each other.
Stage
R L
8 m 8 m
2 m 2 m
Figure 3: Stage plot for the traditional stereo reference. Two subwoofers at either side of the stage.
8
3.4.2 Four Unit Cluster (FUC)
Deriving from tested configurations created by Rat (2009) and the further researched by Hill et al.
(2010), this four unit subwoofer mono cluster was placed in the centre of the width of the room, and
in front of the stage. By maintaining consistent spacing and placing the four subwoofers in a square,
turned 45° from the middle of the stage and applying delay and phase reversal, this four unit cluster
(FUC) is meant to aim the LFC out towards the audience area with 180° dispersion (Figure 4).
Unit 1 has correct phase and no delay. (unprocessed)
Unit 2 has reversed polarity and a 5 ms delay applied to it.
Unit 3 has the exact same processing as unit 2.
Unit 4 has reversed polarity but without delay.
The target frequency of 50 Hz was chosen to optimize the setup for. The temperature of the room
was 20° Celsius at the time, which means that the speed of sound in the room equals approximately
343 m/s. The spacing distance was then calculated by dividing the wavelength (λ) by four. To
calculate the quarter wavelength of 50 Hz the formulas below was used:
==>
Lastly the delay time for the wavelength of 1,715 m needs to be calculated. This can be done using
the formula below. The delay time will be added to unit 2 & 3.
Stage
4
1
2 3
¼ λ ¼ λ
Figure 4: Stage plot for the four unit cluster and vortex configurations. each unit spaced for a 1/4 wavelength of 50 Hz.
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3.4.3 The Vortex (VTX)
This configuration was created by Dave Rat (2009) of Rat Sound and originally consisting of four
cardioid subwoofers arrays with 3 units each (Figure 5). This experiment uses omnidirectional
subwoofers and is therefore not dependent on the same setup angles as in the original configuration
using cardioid subwoofers. This configuration utilizes the same layout as the previous FUC
configuration (see figure 4). Each unit is spaced to match the quarter wavelength of 50 Hz, keeping
the same distance of 1,715 m towards the closest two subwoofers. The only thing different from the
previous configuration is that this configuration is processed differently.
Unit 1 has no processing applied to it.
Unit 2 has a 5 ms delay applied to it against unit 1 to increase
LFC to the side and cancellations towards the stage area.
Unit 3 has the same settings as unit 2.
Unit 4 has a 10 ms delay applied to it, set to be double the
delay of unit 2 and 3. As recommended by Rat D. (2009)
1
3
2
4
Figure 5: Original Vortex layout. Originally consisting of cardioid subwoofers.
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3.4.4 Rear Wall Cancellation (RWC)
This configuration was inspired by the work of Nielsen and Celestions (2011). These two subwoofers
(L and R) are placed adjacent to the front short side wall, at an equal distance of a 1/4 length of the
wall feeding the same signal to both speakers. On the opposite wall the same kind of configuration is
setup, but with reversed phase and adjusted in time and level to cancel out the plane wave created
at the front wall (Figure 6).
"For two waves to cancel each other totally they need to travel in the same direction with the same radiation pattern and with precisely the same amplitude but in opposite phase." (Nielsen & Celestions, 2011, p. 4)
The goal of this technique is if configured properly, to cancel out the reflections from the rear wall and result in a homogenous plane wave originating from the front wall.
To calibrate the level of the polarity reversed subwoofers a pink noise was played through the front wall speakers one at a time, and measured in front of the opposing subwoofer. The SPL received by the opposing subwoofers (originating from the front wall units) was used to calculate the level reduction applied to match the primary subwoofers.
-
The delay time was then calculated using the distance between the two opposing subwoofers, with the addition of the short distance from the wall to the middle of the speaker, divided by the speed of sound.
1/4
1/4 1/4
1/4 ØR
L
R
ØL
Figure 6: Stage plot for the Rear Wall Cancellation configuration. Each unit spaced a 1/4 distance of the length of the wall.
Stage
11
3.4.5 Surrounding the Audience (STA)
This configuration has been inspired by work done by Welti (2002). In his research he concluded that
2 - 4 Subwoofers was the optimal number of subwoofers necessary to reproduce LFC properly. In
fact, his research showed that more subwoofers actually caused the LF factor measured to go down.
The LF Factor is described as the sum of the energy over his bandwidth of interest at 20-80 Hz.
In his conclusion for the question "What is the optimal placement?" he writes:
"One subwoofer at each wall midpoint is the best in terms of Std, Max-ave and Max-min but does not support low frequencies particularly well. Two subwoofers, at opposing wall midpoints, performs very nearly as well as four at the midpoints and gives a much better LF factor." (Welti, 2002, p.15)
This information is what this configuration is based upon. Placing a subwoofer at midpoint to each
wall in the venue, without further processing each unit reproduces the same signal (Figure 7).
Stage
2
3 1
4
Figure 7: Stage plot for the surrounding the audience configuration. Each unit place midpoint at the length of each wall.
12
4. Results & Analysis Since the NEXO LS 1200 subwoofers are specified to be able to reproduce LFC between 30 – 120 Hz,
the analysis won’t focus on the contents below 30 Hz or above 120 Hz. Most subwoofers can
however reproduce content outside of their specified range, but the response is not guaranteed to
be flat (Dicomo, P., 2005).
For every configuration a graph will follow containing five chosen frequencies inside of this range.
The frequencies was chosen as 1/3 octave band, and since most subwoofers aren’t supposed to
reproduce any content above 100 Hz, this frequency was chosen as highest frequency.
Since over a third of the measuring points were in the audience area, leaving only five measuring
points in a small area, called the stage area, the mean SPL of the audience area will be very similar to
that of the stage area.
13
4.1 Traditional Stereo Reference (TSR)
These two graphs shows the mean of the SPL for 1/6 octave measurements of the TSR configuration.
Red = Mean Blue dotted = Mean ± standard deviation
Figure 8: Traditional Stereo Reference – mean of the audience area.
Figure 9: Traditional Stereo Reference - Mean of the stage area.
As one can see from the shapes of these two graphs (Figure 8 & 9) they are quite similar, only with a
few variations in-between them. Interestingly the stage (Figure 9) has slightly higher SPL values
overall, especially in the low end response of 20 – 80 Hz. This is to be expected since the subwoofers
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Traditional Stereo - Audience - Mean
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Traditional Stereo - Stage - Mean
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are omnidirectional and all five measuring points in the stage area are closer to the source, than the
sum of the measuring points divided throughout the audience area. One of the most noticeable
differences is that the stage graph has a small dip present at 140 Hz. This is most likely the result of
cancelations since the wavelength of 140 Hz is roughly 2,45 m. This is close to the same distance as
that of in-between the measuring points of the stage area, and the subwoofer units.
Figure 10: Traditional Stereo Reference - Total mean of the entire venue.
Looking at the mean of the total collection of measuring points (Figure 10) one can see that the
majority of energy is gathered in-between 30 – 120 Hz, which is within the usable range of the LS
1200 subwoofer as specified by NEXO (NEXO Innovate, n.d.). The strongest point at 63 Hz is the only
clear peak from an otherwise flat response. However, the peak is most likely the result of room
modes.
As one can see by looking at the frequency comparison below (Figure 11), 63 Hz seems to be the
dominant frequency with the loudest SPL at every measuring point. The largest exception is at
measuring point X6, X7 and X8, were 50 Hz dominates. These measuring points are located close
together in the middle of the stage area behind the subwoofers (Figure 12), which would indicate
that 50 Hz could be a summation of the direct sound from subwoofers and reflections from the rear
wall. The biggest differences in the frequency curves seem to be at the lower frequencies. The 80 Hz
and 100 Hz curves are relatively even in comparison to the 40 Hz and 50 Hz curves.
40
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dB
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Traditional Stereo - Total - Mean
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Figure 11: Traditional Stereo Reference - Frequency Comparison.
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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
Traditional Stereo - Frequency comparison
40 Hz 50 Hz 63 Hz 80 Hz 100 Hz
STAGE 1
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R L
8 m 8 m
2 m 2 m
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Figure 12: the traditional stereo stage plot with measuring points.
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4.2 Four Unit Cluster (FUC)
These two graphs show the mean of the SPL for 1/6 octave measurements of the FUC configuration.
Red = Mean Blue dotted = Mean ± standard deviation
Figure 13: Four Unit Cluster - Mean of the audience area.
Figure 14: Four Unit Cluster - Mean of the stage area.
As seen by the above graphs there are some differences between the first graph of the audience area
(figure 13), and the second graph of the stage area (Figure 14). The stage graph has a more uneven
representation with a larger cancelation around 56 - 90 Hz. The cancelations actually begin slightly
earlier close to 40 Hz. Since this configuration is optimized for 50 Hz this shows indications that these
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Four Unit Cluster - Audience - Mean
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Four Unit Cluster - Stage - Mean
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frequencies actually might be out of phase behind the setup and resulting in lower SPL towards the
stage (see Figure 17).
Figure 15: Four Unit Cluster - Total mean of the entire venue.
As seen above (Figure 15) the total frequency response of this configuration is quite linear with an
upwards rising angle. From 31,5 - 125 Hz the difference is only ≈ 6 dBSPL, with most of the energy
gathered at 80 - 125 Hz. This could indicate good LFC dispersion throughout the venue.
Looking at the frequency comparison (Figure 16), one can see that the lower sub frequencies of 40
Hz and 50 Hz are more consistent and doesn’t differ as much as the middle sub frequency of 63 Hz.
The same goes for the upper sub frequencies which also are more aligned at each measuring point.
The reason why 63 Hz differ so much form the others are hard to say for sure. It could be that it has
to do with the room modal frequencies, or it could be a bi-effect of the configurations optimization
for 50 Hz.
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Four Unit Cluster - Total - Mean
18
Figure 16: Four Unit Cluster - Frequency comparison.
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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
Four Unit Cluster - Frequency comparison
40 Hz 50 Hz 63 Hz 80 Hz 100 Hz
STAGE 1
2
3
4
5
6
7
8
9
10
11
12
13
15
14
17
4
1
2 3
¼ λ ¼ λ
16
Figure 17: Stage plot for the four unit cluster and vortex configuration with measuring points plotted.
19
4.3 The Vortex (VTX)
These two graphs shows the mean of the SPL for 1/6 octave measurements for the VTX
configuration.
Red = Mean Blue dotted = Mean ± standard deviation
Figure 18: The Vortex - Mean of the audience area.
Figure 19: The Vortex - Mean of the stage area.
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The Vortex - Audience - Mean
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The Vortex - Stage - Mean
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By analyzing the audience curve (Figure 18) and focusing on the frequency range 30 - 120 Hz, one can
see that it’s not completely linear. The difference between the lowest point at 50 Hz and the loudest
at 100 Hz is that of 11 dBSPL. Since 100 Hz is a complete octave above 50 Hz this could indicate that
there are a few cancelations present at 50 Hz and summations at 100 Hz. By looking at the frequency
comparison (Figure 21) the 100 Hz curve is clearly different from the other curves in terms of SPL.
This could be either because of room modes or that the configuration is not properly optimized. Also
important to notice is that the standard deviation is quite large in comparison to the stage area
(Figure 19).
Looking at the stage graph it shows the opposite of the audience graph. When the audience graph
shows a rising trend of SPL, the stage graph shows a declining trend of SPL. The stage mean also
shows a more non linear graph, which most likely means more cancelations.
Figure 20: The Vortex - Total mean of the entire venue.
When looking at the total mean SPL (Figure 20) one can see the same trend as in the audience graph,
but with slight alterations. Overall the configurations promise a relatively linear frequency
distribution across the venue. However the standard deviation is still quite large. As one can see at
for example 56 Hz, the average SPL can vary with as much as ≈ 12 dBSPL throughout the venue.
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The Vortex - Total - Mean
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Figure 21: The Vortex - Frequency comparison.
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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
The Vortex - Frequency comparison
40 Hz 50 Hz 63 Hz 80 Hz 100 Hz
22
4.4 Rear Wall Cancellation (RWC)
These two graphs shows the mean of the SPL for 1/6 octave measurements of the RWC
configuration.
Red = Mean Blue dotted = Mean ± standard deviation
Figure 22: Rear Wall Cancellation - Mean of the audience area.
Figure 23: Rear Wall Cancellation - Mean of the stage area.
These two graphs (Figure 22 & 23) clearly have a major difference, and that is what can be seen from
the stage curve (Figure 23), the clear peak at 63 Hz. The is most likely a boost received from the room
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Rear Wall Cancellation - Audience - Mean
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Rear Wall Cancellation - Stage - Mean
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modal frequencies and the two measuring points which are located very close to the two primary
subwoofers (Figure 26). The spacing of the subwoofers for this configuration is based upon the ¼
distance of the walls length, which is roughly 5,5 m. Since the wavelength of 63 Hz equals to ≈ 5,4 m,
the reflections from the side walls most likely results in a boost of 63 Hz at these locations. Using the
online tool amroc – the room mode calculator (n.d.) to calculate the room modes, one can see that
this is the case, and a room mode is present at 62,71 Hz. Further strengthening this hypothesis is that
the other three measuring points are located close together in-between the two subwoofers close ½
distance of the room, where the two sound waves of 63 Hz meet.
Looking at the audience curve (Figure 22) there are some fluctuations in SPL present, but not with
such a drastic peak as in the stage graph. The two most noticeable peaks are ≈ 75 dBSPL at 63 Hz, and
≈ 65 dBSPL at 90 Hz. These two peaks could be the result of cancelations and summations due to the
modal frequencies of the room, indicating that the polarity reversed rear wall subwoofers might not
be properly configured. Also worth noticing is that between the frequency range of 31,5 Hz to 125 Hz
the average SPL varies between +-5 dBSPL. This means that it’s not completely flat, but still
somewhat linear.
Figure 24: Rear Wall Cancellation - Total mean of the entire venue.
The above graph of the total mean (Figure 24) shows that the lower bass from 31,5 - 63 Hz is most
linear sequence varying only with +-3 dBSPL. However, the standard deviation shows that the actual
SPL can vary with certain frequencies with approximately 10 dB at its most. From 63 Hz and up to 120
Hz a decline of average SPL is clearly visible. Whether this is a result of the room or cancelations
caused by subwoofer interference is hard to say.
The frequency comparison (Figure 25) seems to be very uneven, with peaks at approximately 85
dBSPL at 65 Hz at point X1, X6, X7, X8 and X13. However looking at the measuring plot for this
configuration (figure 10) this is not that odd since all five measuring positions are located either on,
or in between the primary speakers, resulting in a very strong SPL. Keeping this in mind the
frequency response across the room looks more even and follows a clear pattern. as also visible in
40
45
50
55
60
65
70
75
80
85
90
dB
SPL
Hz
Rear Wall Cancellation - Total - Mean
24
previous graphs, 63 Hz is the strongest frequency in terms of SPL and clearly shows that there is
something going on at this frequency.
Figure 25: Rear Wall Cancellation - Frequency comparison.
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
Rear Wall Cancellation - Frequency comparison
40 Hz 50 Hz 63 Hz 80 Hz 100 Hz
1/4
1/4 1/4
1/4 ØL ØR
L
R
STAGE 1
13
6
7
8
2
3
4
5
9
10
11
12
15
14
17
16
Figure 26: Stage plot for the Rear Wall Cancellation configuration with measuring points plotted.
25
4.5 Surrounding the Audience (STA)
These two graphs shows the mean of the SPL for 1/6 octave measurements for the STA
configuration.
Red = Mean Blue dotted = Mean ± standard deviation
Figure 27: Surrounding the Audience - Mean of the audience area.
Figure 28: Surrounding the Audience - Mean of the stage area.
Judging by looking at the audience curve (Figure 27) and stage curve (Figure 28) one can see that
there are no significantly big differences between the two areas, thus indicating that the average SPL
40
45
50
55
60
65
70
75
80
85
90
dB
SPL
Hz
Surrounding the Audience - Audience - Mean
40
45
50
55
60
65
70
75
80
85
90
dB
SPL
Hz
Surrounding the Audience - Stage - Mean
26
are quite even throughout both room areas. This can also be verified by looking at the graph for the
entire venue (Figure 29), which is quite identical to the audience graph.
Figure 29: Surrounding the Audience - Total mean of the entire venue.
The mean of the total graph shows that there are very small deviations from the mean with very few
larger variations. The larger part of the energy is located between 31,5 Hz to 80 Hz, with a slowly
declining tail throughout the upper bass frequencies. Since this curve is quite even it indicates good
frequency distribution throughout the venue. If by looking at (Figure 30) one can see that the
average SPL for every frequency at every measuring point (Figure 31) is also very consistent, with
only a few variations present.
40
45
50
55
60
65
70
75
80
85
90
dB
SPL
Hz
Surrounding the Audience - Total - Mean
27
Figure 30: Surrounding the Audience - Frequency comparison.
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
Surrounding the Audience - Frequency comparison
40 Hz 50 Hz 63 Hz 80 Hz 100 Hz
Stage
2
3 1
4
1
13
6
8
7
2
3
4
5
9
10
11
12
15
14
17
16
Figure 31: Stage plot for the surrounding the audience configuration with measuring points plotted.
28
4.6 Configuration comparison
Figure 32: Comparison of the mean for every configuration.
When comparing the 4 configurations too the TSR, one can see that they all have their similarities.
Both the RWC configuration and the STA configuration are very close to the reference. The biggest
difference is that STA has a higher SPL of ≈ 3-4 dB in-between the range of 31,5 Hz to 125 Hz.
Interesting to notice is that the VTX and FUC is very similar in frequency response. The biggest
difference can be seen at the low end under 45 Hz, were the VTX is approximately 4 dBSPL higher
than the FUC. Since these two configurations share the same layout, but with different processing,
their differences are what make them more suitable for different purposes. Comparing these two
configurations with the TSR one can see that the VTX and FUC is much more linear in their frequency
response than the FUC, which for example has a clear rise in SPL surrounding the frequency 63 Hz.
50
55
60
65
70
75
80
85
90 d
BSP
L
Hz
Mean SPL Comparison (Total)
Traditional Stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding the Audience
29
Figure 33: Comparison of the mean of the audience area for every configuration.
Focusing on the audience area (Figure 33) one can see that the differences become a little bit more
apparent. Comparing them to the reference almost all of them have a higher SPL. One of the biggest
differences is that of the RWC configuration. Between 71 Hz to 100 Hz there is a visible lack of power
at 90 Hz which does stand out a bit from the other configurations. While the VTX and FUC have a
much more even response they both suffer a tiny lack of power at the lower end frequencies. In this
aspect the STA configurations promises better low end reproduction.
50
55
60
65
70
75
80
85
90 d
BSP
L
Hz
Mean SPL Comparison (Audience)
Traditional Stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding the Audience
30
Figure 34: Comparison of the mean of the stage area, for every configuration.
The biggest differences can however be seen from the above graph of the stage area (Figure 34). The
only two configurations that shows some lower SPL on stage is the VTX and FUC, which both show
promising reduction at stage between the frequencies 40 – 90 Hz. 90 Hz seems to be a common SPL
occurrence for all non-conventional configurations. At this point and forward, they all seem to
behave similarly.
It is only natural that the STA and RWC configurations doesn’t show signs of cancelations and are
louder than the reference, since both of them has subwoofers located inside of the stage area and
are meant to excite the entire venue.
50
55
60
65
70
75
80
85
90 d
BSP
L
Hz
Mean SPL Comparison (Stage)
Traditional Stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding the Audience
31
Figure 35: Comparison at 40 Hz for every configuration.
Figure 36: Comparison at 50 Hz for every configuration.
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
40 Hz
Traditional stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding The Audience
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
50 Hz
Traditional stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding The Audience
32
Figure 37: Comparison at 63 Hz for every configuration.
Figure 38: Comparison at 80 Hz for every configuration.
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
63 Hz
Traditional stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding The Audience
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
80 Hz
Traditional stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding The Audience
33
Figure 39: Comparison at 100 Hz for every configuration.
Dividing the configurations into 1/3 octave band representations and analyzing each frequency gives
a different overview what is happening at each measuring point. At 40 Hz (Figure 35) one can see
that at point X15 there is a significant difference between the configurations. Looking back at the
measuring point position chart (Figure 2) one can see that X15 is located close to midpoint at the far
right wall. This is right beside one of the subwoofers placed in the STA configuration. This would
explain the peak of SPL at this measuring point. Furthermore, looking at the same measuring position
one can see some significant cancelations at 40 Hz for the VTX and FUC configuration. This
cancelation is most likely caused by a bi-effect of the processing for these configurations, since they
are optimized to cancel out sound waves behind the configuration. It could be that it causes
cancelations to the sides as well, or cancelations caused by wall reflections.
At 50 Hz (figure 36) one can see that the VTX, FUC and STA configurations has a very even frequency
response throughout the venue, in comparison to the TSR. The RWC configuration has a very similar
response to the reference, which most likely has its roots in the similarities of their layout in the
venue. The similarities being that the RWC configuration basically is a stereo configuration placed
alongside the wall, with the addition of a corresponding pair of subwoofers at the opposite wall with
reversed polarity.
What 63 Hz (Figure 37) demonstrates well is that the vertex and FUC configurations cancel very well
behind them. Position 1,6,7,8 and 13 are all located behind the subwoofers and is clearly visible on
the graph at these positions. Moving on to the two highest frequencies of 80 Hz (Figure 38) and 100
Hz (Figure 39) one can see that the TSR frequency response propagates more evenly throughout the
room resulting in a more even SPL at each measuring position, which is most visible at 100 Hz (Figure
39).
50
55
60
65
70
75
80
85
90
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
dB
SPL
Measuring Points
100 Hz
Traditional stereo Four Unit Cluster The Vortex
Rear Wall Cancellation Surrounding The Audience
34
5. Discussion Judging by the data collected from this experiment it is clear that these configurations are very
different from one another. Each and every configurations layout is often far from the reference, but
all with their different characteristics and suitability for a wide range of purposes. This is to be
expected as all four tested configurations are quite drastically different from conventional stereo
setup. Since these configurations are so different from one another, both in processing and physical
layout, it is only natural that some irregularities will be present on different measuring points. For
example on the RWC configuration the right primary subwoofer happened to be located on top of a
measuring point (figure 10), resulting in a significantly higher SPL at that location.
However, because these configurations are so different is exactly why they were chosen to begin
with. Each setup has its own strengths and weaknesses, which could make it more suitable for one
occasion than another.
5.1 Low Frequency Directivity
Out of the five configurations tested only two of them were suited for the purpose of keeping the SPL
down on stage, while giving the audience sufficient SPL. Both the FUC and VTX showed promising
results in this area. However, the cancelations were most noticeable at and around 50 - 63 Hz. This
can be seen by looking at the mean of the stage are for the FUC (Figure 14), where a clear change in
the curve at 63 Hz can be seen. Important to notice when reading these graphs is that by the looks of
it the SPL isn’t that much different between the stage and audience area. Either this means that
there isn’t much of a difference between the stage and audience area, or this could have to do with
that the few measuring points located behind the configurations often are much closer to the
subwoofers than the average audience points (Figure 2).
Overall the VTX and FUC are very similar in their respective frequency response. Which is to be
expected of the since the idea of the FUC came from the VTX (Hill et al., 2010). What does however
make them different from one another, apart from their processing, is that their frequency response
shows that the VTX has a more even and solid low end (31,5 – 45 Hz), than the FUC (Figure 32). The
FUC has in turn a flatter high end frequency response (90 – 125 Hz) than the VTX. This would perhaps
indicate that the VTX is more naturally suitable for purposes where more power in the low end
frequencies of 30 – 45 Hz is desired. The FUC would then in turn be a better choice for a smaller
venue, where too much low end might blur the sound and create more problems than be of aid. Its
flat high end could then make the highest low frequencies more Intelligible.
5.2 Low Frequency Coverage
What the RWC configuration has in common with the STA setup is that they both focuses on an even
coverage throughout the venue, with quite high disregard to keeping the SPL on stage as low as
possible. This might not always be the goal for a traditional live audio reinforcement scenario with
many microphones on stage, since they would in fact be in front of the subwoofers, instead of
behind them. However, these configurations could be very well suited for reinforcement of
electronic ally produced music or DJ-concerts, since these events often don’t require microphones on
stage. This does not exclude the possibility of microphones on stage as long as they are not required
to reproduce any content below the crossover frequency for the subwoofers.
Ruling out the reduced SPL on stage factor and focusing on the coverage in total, one can see from
the SPL comparison graph (Figure 32) that both configurations has a more linear frequency response
from 31,5 Hz to roughly that of 63 Hz than the TSR. After 63 Hz and upwards they share a similar
response to the TSR, but with the difference that the STA configuration has a slightly higher SPL value
35
than the others. The reason for the higher SPL value is most likely because all four subwoofers
located midpoint at every wall reproducing the same output content and with the same SPL, which
naturally would make the mean SPL a few dB stronger. Their flat low end frequency response does
make them more linear than the TSR. However, it comes with the drawback of higher SPL on stage as
can be seen on Figure 34.
5.3 Comparison
As the total frequency response show (Figure 32) most configurations measured can to some extent
be considered more linear than the TSR. The FUC and VTX configuration are the two most linear
through the entire range of 31,5 – 125 Hz. The STA configuration has the third most linear frequency
response, followed by the RWC configuration, which in terms of frequency response is the most
similar to the TSR. What’s interesting with the latter is that it is the only configuration with a strong
dip at 90 Hz in the audience area (Figure 22). What’s causing this cancelation is hard to say for sure. It
could be from modal frequencies or it could be that the polarity reversed speakers at the opposing
wall aren’t optimized completely, which causes the cancellations. If this is the result of poor
optimization it would have taken more time to optimize it correctly, time that one might not have at
hand when setting up the configuration for a sound reinforcement scenario. Never the less, these
small non linear irregularities present is not always a big problem since most likely some form of
equalization is going to be applied by the system designer, to even out the curve when optimizing the
array.
5.4 Strengths and weaknesses
The FUC is a very linear configuration and better suited for keeping down stage SPL than the TSR. Its
coverage extends well throughout the audience area and shows signs of cancellations both behind
and to the sides for its optimized frequency of 50 Hz and nearby frequencies. This configuration
needs relatively little processing, but requires in turn more time and space to set it up properly with
the correct spacing in-between each unit. However, if configured properly it promises better
directivity than the TSR. Since this configuration does require a relatively large space in front of the
stage, it might not be the best choice of subwoofer configuration if there is a lack of audience space
in the venue. If the height of the stage allows for it, half of the configuration could be hid under it to
save space. This would most likely result in higher SPL on stage than if it were in front of it, and
would require more time and research to optimize for.
The results for the VTX is very similar to that of the FUC, which is only natural since they derive from
each other and share the same spacing and layout. The biggest difference between them is that this
configuration doesn’t rely on polarity reversed subwoofers, but only time differences and proper
spacing. This does in turn mean even less processing than the FUC. Although this configuration isn’t
using cardioid subwoofers as the original version of the VTX was made for, it still shows signs of good
cancelations behind and to the sides of the configuration. Its frequency response is very linear with a
solid low end. This configuration shares the same physical limitations as the FUC and is dependent on
the same amount of subwoofers and dedicated channels of subwoofer processing.
The RWC configuration is as previously mentioned very similar to the TSR in its frequency response
and linearity. However, it does promise better coverage for a larger area. This in turns comes with
the drawback of the primary subwoofers being located behind the stage, as is necessary for this
configuration to work properly. There is still some dips in the frequency response curve that might
indicate that the rear wall subwoofers purpose of cancelling out rear wall reflections might not be
working properly. A theory why they might not be working properly could be because they are too
low in level, to properly cancel out reflections, which means that the room modal frequencies are too
36
strong to be cancelled out. The physical layout of the subwoofers alongside two opposing walls gives
the audience more space and envelops them more. A big problem however is the strong SPL on stage
where the homogenous wave front starts is necessary to ensure that it covers the audience with
sufficient SPL, which causes the working environment on stage to suffer what might be unnecessarily
high SPL. This might indicate that this configuration would be more suitable for smaller venues,
where the desired SPL isn’t necessarily to high.
The last configuration tested is the STA configuration, and just as the RWC configuration it has
potential for solid and linear low end up to 80 Hz (Figure 32). Its four subwoofer units placed
midpoint at each wall in the room does provide a good coverage across the room, but just as the
RWC it comes with the price of also targeting the stage area with high SPL. However as previously
mentioned, if it isn’t necessary for the event to have microphones present on stage and the SPL
doesn’t get too loud for the working environment, it might be a very good configuration choice. Its
physical layout also enables more room for the audience to be on.
5.5 Critique of the method
Each and every configuration was measured at the same measuring positions as the others In order
to make the results as just as possible. However, this does mean that some measurements was
performed directly above a subwoofer during some configurations, resulting in a significant rise in
SPL at that given position. This has been taken into consideration during the analysis of the results
and should not compromise the discussion. Another factor that could have affected the results is the
orchestral ditch in the middle of the room, which basically is a 33 m3 box covered by a thick wooden
lid (Studio Acusticum, n.d.).
Throughout this experiment the same equipment has been used with the same output level from
every subwoofer to eliminate any outside interference that could have otherwise influenced the
results. Except for the RWC configuration, which relied on that two units were adjusted in SPL to
cancel out rear wall reflections.
The output level for every subwoofer unit was measured using the measuring microphone placed
directly in front of the subwoofer, and then compensating the amplifier level to match the others.
This was done to eliminate any differences in power from the amplifiers. The first subwoofer
measured was used as a reference to the others, with the amplifier knob turned 50% of maximum
output. This value was chosen at random as a default value, and it could be argued that some
thought behind it should have been applied. For example if a measurement of a live music
performance, or live playback of music in the venue was done before the experiment, that value
could have been used as a reference and the same settings be applied when performing the
experiment.
37
6. Conclusion
Measurements was performed to compare and investigate if a more non-conventional subwoofer
configurations could be preferable to a more conventional stereo configuration, in terms of
coverage, linearity, Physical limitations of sight lines/ cost/ transport space and stage performance
areas. These criteria are often decisive for choosing subwoofer placements. An experiment was
done where four non-conventional and one more conventional stereo configurations were tested,
measured and compared to one another.
It was concluded that each non-conventional configuration had something to offer that was
preferable over the stereo reference, however their drawbacks might not always be acceptable
depending on the circumstances of their intended use. Never the less the results of the experiment
shows that there are more prominent solutions accessible if a conventional stereo configuration isn’t
desirable for a specific event.
6.1 Further research
In sound reinforcement there is always need to optimize the low end response for the system in use
at every new world venue. As most live events are hosted at temporary locations in a venue that
might not have been built with sound in thought, the need for different subwoofer configurations
and arrays are of utmost importance. Which in turns mean that there is always room for
improvement and further research into new and prominent ways to improve the low frequency
directivity and coverage with easy and adjustable solutions.
For the one interested it might be worth looking into different ways to reduce space requirements
and leakage onto the stage of the FUC or VTX configuration tried in this experiment. Perhaps by
adjusting output level or time for different units in an approach to create more directivity or increase
cancelations backwards.
38
References Amrock – the room mode calculator. (n.d.). [Website]. Retrieved from: http://amroc.andymel.eu/?l=2188&w=1188&h=900&st=false&so=false&fo=100&fu=20&re=DIN%2018041%20-%20Music Audiomatica electrical and acoustical measuring systems. (n.d.). CLIO 10 FW [Website]. Retrieved from: http://www.audiomatica.com/wp/?page_id=51 BSS by HARMAN. (n.d.). BSS Minidrive FDS-336T [Website]. Retrieved from: http://bssaudio.com/en/products/fds-336t Colloms, M. (1991). High Performance Loudspeakers (4th ed.). London, GB: Pentech Press Limited Crown by HARMAN. (2017). Macro-Tech 3600VZ [Service Manual]. Retrieved from: https://3e7777c294b9bcaa5486-bc95634e606bab3d0a267a5a7901c44d.ssl.cf2.rackcdn.com/product_documents/documents/2736_1432925253/130366-1_11-00_ma3600vz_service_manual_original.pdf DellaSala, G. (2015, September 17). Early Reflections and Bass for Small Room Acoustics. Audioholics [Online Article]. Retrieved from: http://www.audioholics.com/room-acoustics/small-room-acoustics Dicomo, P. (2005, april 9). Understanding Speaker Frequency Response. Ecoustics [Online Article]. Retrieved from: http://www.ecoustics.com/articles/understanding-speaker-frequency-response/ Education Facilities Specifications. (2001, December 1). Space Types & Requirements [Website]. Retrieved from: http://www.dodea.edu/edSpecs/upload/Performance-Space-01-Dec-11.pdf Everest, F.A., & Pohlmann, K.c. (2009). Master Handbook of Acoustics (5th ed.). New York, USA: The McGraw-Hill Companies, Inc. Hill, A.J., Hawksford, M.O., Rosenthal, A.P., & Gand, G. (2010, May 22-25). Subwoofer positioning, orientation and calibration for large-scale sound reinforcement. Paper presented at the 128th AES Convention, London, UK. Retrieved from: http://www.aes.org/e-lib/browse.cfm?elib=15268 Mapp, P., & Associates. (2007, April 11). Psychoacoustics in Sound Reinforcement and PA Design. Paper presented at the 22nd AES Conference: Illusions in Sound, Cambridge, UK. Retrieved from: http://www.aes.org/e-lib/browse.cfm?elib=17284 Milán, N., & Amate, J. (2011, May 13-16). Time Alignment of Subwoofers in Large PA Systems. Paper presented at the 130th AES convention, London, UK. Retrieved from: http://www.aes.org/e-lib/browse.cfm?elib=16562 NEXO Innovate. (n.d.). PS15 LS 1200 Subwoofer [Data Sheet]. Retrieved from: http://www.jpb-audiovisuel.fr/pdf/caissondebassels1200.pdf Nielsen, S.B., & Celestinos, A. (2011). Low frequency sound field control in rectangular listening rooms using CABS (Controlled Acoustic Bass System) will also reduce sound transmission to neighbour rooms. Paper published in: Acustica United with Acta Acustica, 97(Supplement 1), pp.37. Nicklasson, H. (2006). Jakten på det perfekta PA-ljudet (1th ed.). Ljungskilje, Sweden: HN ljuddesign Olsson, H.F. (1973, March 1). Gradient Loudspeakers. Journal of Audio Engineering Society. 21( 2) , pp.86-93. Retrieved from: http://www.aes.org/e-lib/browse.cfm?elib=2006 Rumsey, F., & McCormick, T. (2013). Sound and Recording (6th ed.). Burlington, UK: Focal Press Taylor & Francis Group Rat, D. (2009, 30 July). Going Deeper, Rodies in the Midst [Blogg]. Retrieved from: http://www.ratsound.com/cblog/archives/337-Going-Deeper.html Shabalina, E., Ramuscak, J., & Vorländer, M. (2011, May 13). A Study of Human Perception of Temporal and Spectral Distortion Caused by Subwoofer Array. Paper presented at the 130th AES Convention, London, UK. Retrieved from: http://www.aes.org/e-lib/browse.cfm?elib=15836 Studio Acusticum. (n.d.). Black Box [Technical Specification]. Retrieved from: http://studioacusticum.com/wp-content/uploads/2012/04/BlackBox.pdf Toole, F.E. (2008). Sound reproduction: loudspeakers and rooms. Amsterdam, NL: Elsevier. Welti, T. (2002, April 1). How Many Subwoofers are Enough, Paper presented at the 112th AES Convention, Munich, Germany. Retrieved from: http://www.aes.org/e-lib/browse.cfm?elib=11355 “What is a Black Box Theater?”. (n.d.) [Website]. Retrieved from: http://www.wisegeek.com/what-is-a-black-box-theater.htm
39
List of Acknowledgments
The author would like to thank each and every one who has helped to contribute to this study in any
way.
Thanks to my supervisor Roger Johnsson, who’ve guided me throughout this project and answered
questions where they’ve risen.
Gratitude goes out to my wonderful girlfriend Angelica Larsson. Who’ve been a huge emotional
support and have put up with me being away on many a late night of subwoofer bliss.
A huge special thank you to my good friend and partner in crime, Liv “The Bass Queen” Lindström,
Who’ve helped me make the hard decisions and come up with great solutions to all the problems
which at the time seemed impossible to solve. You’ve been a great support and there is nothing you
can’t do if you put your mind to it! Liv long and prosper!
40
Appendix A – Standard Deviation Standard deviation for each configuration
0
1
2
3
4
5
6
7
8
9
10
Stan
dar
d D
evi
atio
n
Hz
Traditional Stereo - St.Dev
0
1
2
3
4
5
6
7
8
9
10
Stan
dar
d D
evi
atio
n
Hz
Four Unit Cluster - St.Dev
41
0
1
2
3
4
5
6
7
8
9
10 St
and
ard
De
viat
ion
Hz
The Vortex - St.Dev
0
1
2
3
4
5
6
7
8
9
10
Stan
dar
d D
evi
atio
n
Hz
Nielsen & Celestions - St.Dev
42
0
1
2
3
4
5
6
7
8
9
10 St
and
ard
De
viat
ion
Hz
Surrounding the Audience - St.Dev
43
Appendig B – Configurations and Measurements Configuration Specifications
Rear Wall Cancellation
SPL measured in front of each unit:
1. 99 dBSPL 2. 99 dBSPL 3. 78 dBSPL 4. 69 dBSPL
Vortex and four unit cluster
Configuration layout. Each unit turned 45°
Unit Length (m) Width (m)
1 10,920 3,318
2 9,574 4,359
3 11,967 4,728
4 10,585 5,702
Picture 1: Vortex and four unit configuration layout
44
Measuring positions and microphone height
Measuring Points Length (m) Width (m)
X1 2,968 1,113
X2 2,582 4,059
X3 1,655 7,901
X4 5,930 5,323
X5 5,009 9,468
X6 8,000 0,874
X7 10,695 1,464
X8 13,978 0,532
X9 8,815 6,123
X10 9,153 10,139
X11 13,665 6,327
X12 13,449 8,699
X13 16,581 1,042
X14 18,598 3,043
X15 17,563 5,319
X16 18,514 7,671
X17 17,640 10,041
Microphone Height 1,6 m
Microphone height was chosen to simulate an average person’s ear height when standing up.
45
Measurements
Traditional Stereo Reference measurement positions [dBSPL]
FREQ[Hz] X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
20,0 53,09 53,40 56,89 54,28 56,76 55,88 53,80 54,49 56,21 56,47 51,15 54,93 51,23 53,83 51,79 54,37 55,56
22,4 63,46 59,32 59,09 54,75 60,45 61,78 61,24 63,97 55,64 60,23 57,50 58,18 63,32 61,52 51,69 54,46 57,99
25,0 64,70 58,31 63,79 54,85 57,75 65,54 66,29 66,13 60,95 63,59 62,00 63,12 62,17 57,78 51,19 55,76 52,92
28,0 60,86 50,35 59,38 57,93 56,72 68,07 71,36 66,95 59,37 63,88 55,60 60,87 59,49 50,97 56,86 53,34 57,36
31,5 61,70 57,79 62,68 69,11 69,38 65,33 73,04 65,74 60,78 67,05 58,20 64,53 71,01 64,40 67,71 63,06 66,70
35,5 70,19 68,49 61,11 73,04 71,84 67,64 73,61 67,47 66,16 68,31 66,62 57,53 77,90 71,94 72,26 70,57 74,70
40,0 74,16 67,65 60,80 68,27 67,40 70,35 74,49 76,30 67,89 64,16 71,56 69,68 78,80 73,62 70,20 69,05 73,34
45,0 76,99 77,27 77,92 70,23 72,45 73,11 76,85 74,19 70,80 58,46 71,26 74,03 73,28 76,32 68,91 75,71 69,12
50,0 77,44 71,87 70,26 75,52 68,73 80,85 81,51 78,81 70,49 63,38 70,55 74,82 77,02 77,33 70,47 73,11 71,09
56,0 71,85 69,72 73,39 79,79 77,09 78,37 74,09 80,44 78,01 68,04 78,66 77,21 74,14 72,84 78,64 79,73 67,01
63,0 76,71 78,71 67,41 81,36 78,18 79,12 70,65 81,45 78,95 71,87 77,45 74,65 77,73 77,40 80,28 78,80 71,32
71,0 70,49 75,30 63,00 77,07 79,39 76,17 72,51 79,00 70,06 75,48 73,12 65,38 73,72 78,26 74,98 72,52 76,02
80,0 67,67 74,60 69,62 70,16 74,12 74,77 67,79 78,22 72,52 76,24 73,75 66,25 73,07 74,27 77,25 71,22 76,34
90,0 66,80 74,60 71,23 69,62 69,53 65,47 71,27 73,47 75,34 68,17 74,63 67,95 68,49 75,87 75,62 69,94 72,91
100,0 64,79 67,56 69,29 73,08 68,81 70,35 69,02 68,56 71,69 69,65 73,36 75,14 72,06 75,46 73,03 72,44 73,92
112,0 70,00 66,21 67,83 73,82 68,74 67,32 71,26 68,60 72,68 68,07 72,11 70,04 69,77 71,00 73,91 71,90 71,89
125,0 61,74 70,36 64,95 70,28 66,92 65,39 67,63 60,61 67,93 69,11 71,08 70,16 68,19 66,97 73,36 73,56 69,92
140,0 60,65 61,96 64,30 67,75 62,10 61,11 66,13 56,90 70,79 63,56 64,71 67,21 65,33 66,62 68,31 62,97 66,57
160,0 67,15 65,47 60,85 66,44 62,95 69,05 64,39 66,00 66,94 63,53 63,75 69,07 69,44 70,17 68,22 66,35 64,49
175,0 62,82 63,02 61,90 64,88 61,66 67,85 65,68 60,57 63,36 65,14 67,04 64,90 70,08 66,94 67,93 62,49 65,24
200,0 61,48 58,22 58,07 62,94 59,84 66,40 68,91 56,30 67,76 62,89 60,21 62,95 67,55 69,61 69,27 63,24 63,05
46
Four Unit Cluster measurement positions [dBSPL]
FREQ[Hz] X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
20,0 59,03 54,99 61,98 55,74 59,12 63,00 65,23 63,73 57,66 58,80 55,47 57,55 50,68 56,60 41,48 47,76 53,72
22,4 61,74 59,04 65,25 58,42 56,85 65,78 63,72 56,91 63,59 58,63 58,71 61,83 59,36 60,69 50,53 51,75 60,72
25,0 68,54 59,48 67,56 57,10 57,58 70,67 69,16 66,52 62,30 71,64 62,22 64,26 68,20 61,83 55,53 56,81 57,74
28,0 62,59 57,49 63,28 65,57 60,24 70,76 66,28 68,29 68,47 65,43 61,59 66,44 67,46 59,71 59,30 50,21 64,41
31,5 70,95 65,20 70,38 71,02 68,75 73,48 66,32 73,63 74,33 72,96 73,90 67,60 74,33 58,36 69,23 67,07 66,54
35,5 70,58 70,00 68,53 69,69 65,19 72,94 71,90 70,27 77,68 72,79 73,79 65,64 62,03 60,85 63,43 64,91 69,02
40,0 69,88 68,46 63,68 74,29 70,76 78,65 78,92 74,39 78,77 71,46 75,99 71,58 68,86 66,23 61,08 69,25 75,59
45,0 66,87 71,49 76,33 71,00 61,31 78,68 70,75 76,56 80,25 72,22 75,96 79,39 73,14 68,99 72,68 69,89 67,56
50,0 69,50 65,44 73,09 62,87 65,45 76,27 71,18 69,86 77,66 68,22 71,25 75,07 73,45 67,20 65,24 70,74 64,39
56,0 71,68 60,65 62,47 60,85 71,61 69,46 69,00 73,34 80,77 73,48 74,93 81,17 70,00 73,53 63,55 75,45 66,64
63,0 61,98 65,89 68,28 73,78 78,67 66,01 69,29 70,39 83,21 77,21 76,20 77,90 63,66 77,15 70,88 72,64 70,64
71,0 64,57 63,24 77,22 77,27 76,58 68,52 74,13 72,65 84,42 80,59 79,54 78,16 62,31 78,18 75,83 71,32 71,68
80,0 68,39 67,76 71,31 79,21 79,90 70,02 81,40 71,31 82,31 76,95 79,46 72,57 72,25 74,18 73,20 71,44 75,96
90,0 74,24 71,53 72,35 75,43 77,25 74,27 83,22 75,08 83,79 84,52 78,13 78,42 71,75 71,12 77,27 75,53 77,98
100,0 72,83 78,39 72,58 77,10 77,64 71,89 83,03 75,44 85,71 81,41 81,72 80,76 73,29 70,71 72,41 71,37 79,70
112,0 69,69 76,08 76,33 74,99 73,82 71,11 82,66 74,28 81,05 79,28 78,46 78,48 73,74 71,08 77,91 75,34 78,64
125,0 71,09 74,67 74,47 80,75 77,52 72,14 79,50 74,42 81,69 77,02 78,62 78,44 70,71 70,27 71,23 77,76 78,82
140,0 69,87 68,96 74,98 74,25 74,50 68,33 71,21 58,77 80,59 70,91 74,54 70,30 67,22 64,18 66,60 73,49 69,65
160,0 68,37 65,32 69,42 75,21 76,24 69,78 70,26 64,12 80,39 68,22 79,42 76,67 66,14 68,85 72,43 69,16 74,85
175,0 66,01 65,54 70,76 71,05 64,02 69,41 66,52 64,48 74,96 72,95 77,07 69,76 63,15 64,63 63,27 69,34 70,66
200,0 59,79 63,42 66,20 68,83 67,44 69,78 65,81 63,43 70,81 75,74 75,87 70,20 65,13 66,04 64,00 63,30 63,29
47
The Vortex measurement positions [dBSPL]
FREQ[Hz] X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
20,0 62,14 59,66 65,77 59,35 62,74 64,78 66,30 64,72 60,25 61,24 58,30 59,90 49,85 58,70 40,89 49,14 55,04
22,4 64,40 64,33 70,56 63,96 60,17 70,83 68,59 59,58 70,15 66,93 63,51 65,63 63,29 63,79 58,23 58,13 65,15
25,0 70,49 61,14 70,02 62,37 62,95 72,00 70,71 68,38 66,12 74,52 63,98 67,44 70,11 63,34 56,41 58,69 58,51
28,0 64,98 61,78 68,39 69,43 66,60 74,47 70,49 71,42 72,38 70,78 66,87 69,53 71,14 63,86 64,65 57,16 68,95
31,5 75,36 70,86 74,13 75,18 70,46 78,45 73,76 77,91 78,38 75,81 78,07 70,57 78,10 62,86 75,00 72,47 71,57
35,5 75,46 73,98 72,99 73,75 69,02 77,85 76,44 75,69 81,96 76,02 77,57 68,81 66,89 64,32 67,06 68,63 71,87
40,0 71,47 70,74 67,26 76,72 74,40 79,67 80,98 76,46 81,54 74,59 79,26 74,41 73,77 70,29 60,36 71,72 78,14
45,0 67,27 71,87 75,99 72,71 64,16 78,80 73,02 76,18 81,29 72,21 76,19 79,30 73,50 68,41 74,03 70,29 69,86
50,0 69,23 64,87 73,22 61,25 65,99 75,37 70,77 70,04 78,00 68,02 71,51 74,79 73,08 66,73 65,49 70,77 64,15
56,0 72,02 60,48 61,24 61,07 69,79 64,21 67,00 73,44 79,51 73,52 74,08 79,98 67,19 73,20 64,95 74,25 65,42
63,0 72,33 67,24 64,12 73,64 76,33 69,57 66,65 70,57 80,70 75,04 72,54 73,93 71,76 74,81 72,76 71,79 65,14
71,0 68,73 72,35 73,80 73,85 73,08 69,64 73,29 78,26 81,99 81,20 76,95 75,57 70,41 72,89 77,90 68,03 70,95
80,0 65,56 70,90 63,75 72,72 76,78 61,72 75,38 77,06 73,83 79,20 71,17 71,76 67,78 75,86 75,53 73,69 73,87
90,0 70,81 72,05 73,59 80,12 71,38 75,07 78,01 74,56 69,95 81,61 79,12 73,34 72,28 73,27 73,85 75,19 71,19
100,0 69,48 77,83 78,62 81,57 76,61 69,96 84,09 76,39 74,32 84,85 84,28 80,80 72,44 76,05 78,36 75,68 81,53
112,0 69,36 76,98 79,10 79,25 69,76 69,77 81,78 74,99 73,51 80,71 79,23 70,78 73,20 71,61 77,38 71,59 76,69
125,0 69,34 78,20 77,85 82,35 73,51 75,35 81,95 74,91 79,47 80,51 81,83 75,55 73,05 65,98 71,88 78,66 77,64
140,0 69,07 72,45 74,58 75,60 74,25 70,93 71,65 59,20 79,51 71,75 76,57 68,91 68,45 64,26 67,18 73,55 69,71
160,0 66,30 65,74 67,11 73,72 76,94 71,52 70,06 64,79 80,40 65,27 77,39 77,79 70,31 68,70 72,18 67,44 75,02
175,0 63,42 64,45 67,99 67,48 69,25 74,33 68,50 62,23 75,67 69,33 74,44 76,15 68,82 66,48 67,05 66,65 70,54
200,0 63,30 67,72 66,04 69,34 69,99 75,93 68,19 58,57 74,05 69,08 68,15 74,55 70,20 67,27 63,84 64,14 62,65
48
Rear Wall Cancellation measurement positions [dBSPL]
FREQ[Hz] X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
20,0 57,89 54,54 57,28 56,01 57,43 55,54 52,79 61,93 57,26 57,04 52,85 56,05 55,65 53,41 51,88 56,42 55,45
22,4 67,47 62,78 60,32 60,99 64,65 64,43 63,16 69,04 60,27 64,51 58,84 59,91 66,42 63,30 54,90 57,94 61,48
25,0 64,80 63,21 62,57 58,94 64,02 66,84 66,88 68,57 61,11 62,70 62,10 60,82 65,09 59,27 54,79 55,84 55,32
28,0 60,45 57,47 60,07 55,48 59,99 66,48 70,91 65,27 61,05 64,05 61,17 60,00 66,97 52,77 58,50 52,28 57,30
31,5 74,84 71,01 72,09 73,51 71,24 73,20 73,77 74,30 72,48 73,53 73,76 70,12 77,93 67,24 73,67 69,93 68,87
35,5 73,31 73,84 69,34 73,99 72,40 75,20 76,03 75,14 74,44 67,61 73,98 66,37 81,60 75,53 73,39 71,73 75,28
40,0 74,78 72,67 63,34 74,55 69,66 74,75 75,26 79,13 72,74 68,67 71,55 70,81 79,55 78,77 76,66 71,56 77,82
45,0 78,71 75,20 76,73 81,80 71,50 74,17 75,66 81,28 72,95 69,28 61,79 69,69 81,65 76,84 83,26 69,68 77,57
50,0 76,21 74,34 69,69 75,83 69,13 78,01 81,88 82,87 67,04 66,14 66,79 67,18 76,68 77,80 73,86 72,02 70,22
56,0 79,73 75,59 69,54 79,51 70,04 81,15 81,46 84,21 70,04 68,74 73,92 64,80 80,86 77,84 77,25 75,99 65,64
63,0 85,00 80,60 73,33 74,08 77,77 84,45 84,17 84,85 74,11 70,23 74,15 75,51 86,71 80,09 76,38 73,31 72,72
71,0 79,42 74,93 71,72 74,35 71,50 82,72 78,74 80,16 74,37 66,44 77,82 73,78 85,79 78,94 75,72 70,78 69,24
80,0 76,95 70,64 66,81 68,24 64,55 80,25 78,32 76,01 74,78 68,87 68,12 71,15 81,88 67,31 76,11 65,58 67,42
90,0 68,94 69,52 63,78 68,65 58,17 72,63 78,86 74,04 66,72 64,31 66,97 62,14 77,01 68,60 72,27 66,28 60,70
100,0 74,42 70,86 69,00 69,72 68,61 73,78 72,61 77,07 66,52 70,74 71,03 71,04 76,72 73,42 72,25 63,44 70,38
112,0 69,70 68,47 66,09 72,71 67,35 71,15 72,20 75,77 72,49 63,24 70,99 71,97 71,36 71,90 71,28 66,70 67,51
125,0 66,17 67,47 66,54 69,58 67,41 68,11 69,18 69,48 68,02 63,26 68,95 67,47 71,19 68,28 72,42 67,78 65,57
140,0 64,20 67,42 67,04 64,14 65,66 62,56 65,71 63,50 67,27 63,07 60,86 65,73 69,09 66,00 67,23 64,62 58,37
160,0 63,85 67,03 64,03 69,44 66,00 67,32 66,13 68,74 67,96 64,71 69,32 67,20 72,78 68,62 69,69 68,02 63,97
175,0 64,51 63,23 63,25 64,06 64,04 66,39 62,51 66,73 66,72 64,15 61,36 60,14 68,76 66,90 69,69 61,67 66,49
200,0 56,30 59,45 56,31 65,15 58,39 62,47 61,15 62,38 62,08 59,72 61,14 62,89 71,12 68,52 65,12 60,97 58,06
49
Surrounding the Audience measurement positions [dBSPL]
FREQ[Hz] X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17
20,0 60,22 60,45 59,92 61,16 62,13 55,58 56,89 59,10 61,56 61,12 59,93 58,33 57,63 56,82 57,00 61,86 61,59
22,4 62,33 58,68 57,28 59,47 59,52 61,37 56,52 63,03 58,24 56,00 59,79 56,29 62,97 54,72 53,58 58,13 59,03
25,0 62,52 58,73 61,71 61,06 64,03 68,38 66,01 64,79 64,00 62,69 62,92 57,55 66,23 54,31 49,86 52,57 58,91
28,0 63,34 60,34 66,63 68,00 67,95 64,85 68,65 62,38 65,85 65,92 62,42 57,46 68,68 52,98 56,56 53,64 67,01
31,5 72,51 69,62 74,17 75,88 74,71 69,43 76,77 72,32 71,90 74,76 73,00 72,74 76,74 67,51 73,77 68,54 72,28
35,5 75,03 77,78 79,60 78,14 73,12 82,70 82,13 83,34 84,24 81,45 83,37 74,30 71,16 73,46 78,46 73,66 75,78
40,0 76,48 74,40 74,62 79,13 73,93 85,08 80,29 80,52 75,51 81,70 75,79 73,46 74,36 74,97 81,01 76,78 71,12
45,0 79,68 76,08 76,22 78,12 72,38 80,77 80,68 73,50 72,50 78,98 77,91 73,22 78,34 77,97 82,03 77,32 74,74
50,0 79,51 78,72 80,01 81,34 73,53 81,35 81,85 75,17 77,09 78,51 83,32 75,39 80,59 79,30 82,07 84,30 75,07
56,0 79,88 79,87 80,64 80,32 80,13 80,47 77,35 79,94 75,99 75,52 79,04 77,80 82,41 78,64 77,65 80,00 70,83
63,0 79,09 84,33 78,10 81,56 82,36 82,46 82,80 82,41 85,10 80,81 78,45 81,71 85,13 79,69 82,03 78,58 69,87
71,0 75,76 78,60 75,79 79,24 83,73 79,60 80,99 84,55 81,59 77,31 77,41 81,54 82,70 81,29 80,65 80,31 77,11
80,0 74,93 75,95 69,07 72,48 75,70 78,23 76,09 79,68 79,83 75,34 77,66 74,18 74,72 77,49 74,90 74,58 75,50
90,0 70,64 77,58 72,83 75,13 71,73 78,64 77,25 76,93 73,52 76,36 80,88 70,13 73,17 75,09 74,44 77,09 77,39
100,0 72,67 73,57 75,26 75,90 72,51 72,31 73,62 79,85 71,42 78,44 75,80 69,49 72,11 67,43 77,38 76,74 75,25
112,0 69,00 71,47 73,99 73,70 69,14 72,62 71,07 71,37 74,71 74,48 76,26 67,57 71,15 71,86 73,72 73,97 76,89
125,0 69,20 69,28 67,43 74,14 66,20 65,86 73,43 70,85 67,59 73,78 71,10 66,61 74,08 66,58 73,24 73,74 66,08
140,0 64,48 70,97 66,81 69,16 67,00 65,50 71,67 65,48 68,78 75,26 69,98 73,53 65,87 65,47 71,90 69,33 62,56
160,0 66,10 69,67 65,60 70,27 66,95 71,82 71,33 72,04 72,07 68,98 73,91 76,50 72,68 70,45 69,90 73,99 72,03
175,0 67,76 68,88 61,95 69,14 65,71 67,81 70,16 68,02 60,52 69,52 66,58 70,69 69,34 66,83 64,07 73,96 69,17
200,0 67,46 69,82 63,97 65,73 59,28 65,90 68,70 66,23 67,67 70,98 64,71 66,38 64,82 67,79 68,60 67,74 71,45