Low Frequency Control Options in Surround Sound Critical Listening Rooms
Peter D’AntonioRPG Diffusor Systems, Inc.RPG Diffusor Systems, Inc.
Upper Marlboro, MD
Design Variables
• Variables:– Room dimension and geometryoo d e s o a d geo e y– Number and configuration of speakers– Listening positionsListening positions– Dedicated low frequency surface treatment– Equalization– Equalization
Design Process• Using the maximum and minimum room dimensions
to determine optimal dimensional ratios, using Room SizerRoom Sizer
• Using allowable speaker and listener locations, optimize locations for speakers and listener, using Room OptimizerRoom Optimizer– Minimize SBIR and maximally excite modes: optimally
placed multiple in-phase subsMi i i SBIR d i i ll it d ti ll– Minimize SBIR and minimally excite modes: optimally placed multiple in-phase subs
• Apply low frequency passive absorption at optimal pp y q y p p ppositions in desired frequency bands
• Use parametric digital equalization as needed
Dimensional Ratios:Room Modes
• Reflected waves combine causing both constructive and destructive interference leading to nulls and peaks. These are often called standing waves or room modes g– The resonant frequency and distribution of room
modes is determined by the room’s dimensionsy– The degree of excitation depends on the
positions of the loudspeakers– The degree of audibility depends on the
positions of the listeners
Dimensioning ComparisonCharacteristic Rigid Rectangle Room Sizer
Metric Evenly spaced modes Flattest modal spectrum
AlgorithmAccounts for absorption
222
2 ⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟
⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛=
z
z
y
y
x
x
Ln
Ln
Lncf }),,({
,,∑∑∑∑
∞ ∞ ∞
x y zn n n i inin d
RrrtEFFT2
1=2
20
1=
Absorption Ignores absorptionshifting and broadening modes
Ignores weighting of axial, Impulse response properly and inherently weights
Modal Weightingg g gtangential and oblique modes
y gmodes
Modal OverlapIgnores and groups modes into 1/3 octave bins Accounts for modal overlap
Room Volume Ignores room volume Accounts for room volumeRoom Volume Ignores room volume Accounts for room volume
PerceptionModal spacing several steps removed from modal spectrum
Modal spectrum more closely related to perceptionIncludes minimum and
Constraints Ignores
Includes minimum and maximum room dimensions
Rectangular DescriptionsTh l i i l h h• The rectangular room is a special case where the image model is an exact solution to the wave equation and can be used for all frequencies in aequation and can be used for all frequencies in a perfectly reflecting room
4
5
∑∑∑∞ ∞ ∞ rrA ),()( 0
Modal SummationModal Summation
3
4 ∑∑∑ −−=
x y zn n n nnn
n
jrrArp
)2(),(),( 22
0
ωδωωωω ω
2
Image ModelImage Model
}),,({ ∑∑∑∑∞ ∞ ∞
iRrrtEFFT2
22
0
1=
1
}),,({,
,∑∑∑∑x y zn n n i in
in dRrrtEFFT
1=20
00.01 0.02 0.03 0.04
Time (s)
Room Sizer Flow Chart Start
Choose room dimensions randomlyrandomly
Calculate modal
More Accurate More Accurate ModalModal response
Calculate Change
Modal Modal CalculatorCalculator
Calculate figure of
merit
Change room
dimensions Intelligent Search Intelligent Search EngineEngine
Minimum in figure of merit? No
Standard Standard Deviation of the Deviation of the Modal ResponseModal Response
Yes
End
Performance Index∑N
100
∑=
+−=n
nnp cmfL1
2, )(ε
90
100
Best fit line
70
80
el (
dB)
60
70
Leve (Lp,n - fn)
40
50
0 40 80 120 160 200
f (Hz)
Bolt Comparison
100
110
90
100
(dB)
80Leve
l (
60
70
600 50 100 150 200
Frequency (Hz)
Worst found Optimised Bolt 2:3:5
SSSS
Variation of room quality for 100mVariation of room quality for 100m33 (3531 ft(3531 ft33 )) room. S indicates room. S indicates standard room size of 7 x 5.3 x 2.7m (23 x 17.4 x 8.9 ft)standard room size of 7 x 5.3 x 2.7m (23 x 17.4 x 8.9 ft)
Room Sizer
Non-rectangular Study
15’ 24’19’
Rectangular room Skew room
14’
d
Effect on Standard DeviationR l ti I it t h / 2 f t
9
10
Relative Immunity to change +/- 2 feet
7
8
9
tion
4
5
6
ndar
d D
evia
t
Immunity to change
1
2
3Stan
0
1
15'0"
15'5"
15'10
"16
'3"16
'8"17
'1"17
'6"17
'11"
18'4"
18'9"
19'2"
19'7"
20'0"
20'5"
20'10
"21
'3"21
'8"22
'1"22
'6"22
'11"
23'4"
23'9"
1 1 15 1 1 1 1 17 1 1 1 1 2 2 20 2 2 2 2 22 2 2
Figure of merit
standard deviation 20-200Hz standard deviation 20-100Hz
Nice Start!
• This is a nice start. We now know all of the modes that the room can support.
• However the speakers will unfortunately not be in one• However, the speakers will unfortunately not be in one corner and the listener in the opposite diagonal corner!
• The speaker positions will determine which modes are excited and the listening position will determine whichexcited and the listening position will determine which modes are heard.
• We now have to take into consideration the following:– The positions of the sub-woofers– The position of the listeners
• We have two choices:e a e o c o ces– Optimally activate the modes with the subs (Room Optimizer) for a
given listening position– Nullify all modes with the subs and listener placement for wide area y p
uniformity (Null-mode placement) as suggested by Todd Welti and Floyd Toole
Axial Standing WavesRemember:Remember:
Speaker placementSpeaker placementd t i hi hd t i hi hdetermines which determines which modes are energizedmodes are energized
Listener placementListener placementdetermines whichdetermines whichdetermines which determines which modes are heardmodes are heard
AbscissaAbscissa identifies L, identifies L, W and H mode null W and H mode null positions in the room positions in the room and their frequencyand their frequency
Speaker Placement
• When a speaker is placed 2 ½’ into the room, the f th d d i tfourth order mode is not energized
• When a speaker is placed• When a speaker is placed 3 ½’ from the side wall, the second order mode at 81second order mode at 81 Hz is not energized
• When a subwoofer is placed 5’ above the floor the first order mode at 57 Hz is not energized
Listener PlacementWh li t i l d 7• When a listener is placed 7 ¼’ or 12’ into the room the fourth order mode at 119 Hz is not heardHz is not heard
• When a listener sits in the middle of room width, the odd order modes areodd order modes are inaudible
• When a listener is placed near the mid heightnear the mid height position, the odd order modes are inaudible
• When the listener is at theWhen the listener is at the room’s centroid, only even order modes are heard!
Optimal Sub and Listen Positions
• Optimally activate the modes with the subs (Room Optimizer) for a given listening ( p ) g gposition
• Optimally cancel all modes up to roughly 80Optimally cancel all modes up to roughly 80 Hz
• Must simultaneously minimize the short term• Must simultaneously minimize the short term speaker boundary response and the modal responseresponse
Speaker Boundary Interference20
(3,3,14)VIRTUAL IMAGE
5
10
15 1 Boundary X=4'
2 Boundaries X=4', Y=4'
3 Boundaries X=4', Y=4', Z=4'
3 Boundaries X=1', Y=1', Z=1'
CEILING
-10
-5
0
0
100
200
300
400
500
600
700
800
900
1000
Ene
rgy,
dB
ORIGIN OF SOUND SOURCE(3,3,3)
( )VIRTUAL IMAGE -25
-20
-15
(3,-3,3)(-3,3,3)VIRTUAL IMAGE
WALL
Frequency, Hz
(3 3 3)VIRTUAL IMAGE
FLOOR
(3,3,-3)
Buy one get 4 free!Buy one get 4 free!
Room Optimizer
CURRENT LOCATIONS SIMPLEX SEARCHENGINE FOR NEW
Ener
gy
ENGINE FOR NEWTRIAL LOCATIONS
IMPULSE RESPONSEE
Time
IF ERRORIS LESS THAN
TOLERANCE THEN END,ELSE TRY NEW
LOCATION
Leve
l (dB
)
F
Leve
l (dB
)
F
SPEAKER BOUNDARYINTERFERENCE
MODAL RESPONSE
Frequency Frequency
CALCULATE COMBINED STANDARD
DEVIATION ERROR
Image Source Method
li
5
listener
source3
4
One image source2
listener
0
1
0.01 0.02 0.03 0.04
Time (s)listener
source
Combined Standard Deviation
L Lp nf pN
−∑ ( ), 280
90
100
)
Best fit line
σ i Nnf=
−=1
1
( )150
60
70
Leve
l (dB
)
(Lp,n - fn)
σ σ σ= −+w ws l( )1
100 90
400 40 80 120 160 200
f (Hz)
80
90
Leve
l (dB
70
80
Leve
l (dB
50
60
70
0 50 100 150 200 250 300
L
Best caseWorst case
50
60
0 50 100 150 200 250 300
L
Best caseWorst case
Frequency (Hz) Frequency (Hz)
Short Term Transient Spectra (64 ms time window)
Long Term Spectra
Room/Speaker Interface• To optimize the room/speaker interface you need to
simultaneously optimize the following– L, W, H (rectangular room +/- 2 feet)– Sn(x,y,z) location of each speaker– Ln(x,y,z) location of each listener
P di ti Al ith I d l i f t l ti f th• Prediction Algorithm: Image model is a perfect solution of the wave equation for a elastically reflecting rectangular room
• Metric: Simultaneously minimize the modal frequency d th k b d i t fresponse and the speaker boundary interference response
• Optimization Algorithm: Downhill Simplex or Genetic AlgorithmW f d i i l di id hi i h• We found it practical to divide this program into the room dimensioning optimization and speaker/listener location optimization
Room Pressure Response
p r r QL L L
ik k
n xL
n yL
n zL
n xL
n yL
n zL
s
x y z x y z nnnn
x
x
y
y
z
z
x
x
y
y
z
zzyx
( | ) cos cos cos cos cos cosr r
r0 2 20 0 01=
−
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜⎜
⎞
⎠⎟⎟
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜⎜
⎞
⎠⎟⎟
⎛
⎝⎜
⎞
⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥
=−∞
∞
=−∞
∞
=−∞
∞
∑∑∑ε ε εωρ π π π π π π
n n ny22 2 2
⎛⎜
⎞⎟
⎛⎜
⎞⎟
⎛⎜
⎞⎟
π π πk nL L
nLn
x
x
y
y
z
z
r2 =
⎛⎝⎜
⎞⎠⎟ +
⎝⎜⎜ ⎠
⎟⎟ +⎛⎝⎜
⎞⎠⎟
π π
Low Frequency OptimizationD hill
S IM P L E X S E A R C H
Downhill Simplex
or C U R R E N T L O C AT IO N S
gy
S IM P L E X S E A R C HE N G IN E F O R N E WT R IA L L O C A T IO N S Genetic
AlgorithmSearch Engine
IM P U L S E R E S P O N S E
Ener
g
T im e
IF E R R O RIS L E S S T H A N
T O L E R A N C E T H E N E N D ,E L S E T R Y N EW
L O C A T IO N
Leve
l (dB
)
Leve
l (dB
)
80
90
100
Best fit line
S P E A K E R B O U N D AR YIN T E R F E R E N C E
M O D A L R ES P O N S E
F re que n cy F re que n cy
60
70
80
Leve
l (dB
)
(Lp,n - fn)
Modal ResponseSBIR
C A L C U L A T E C O M B IN E D S T A N D A R D
D E V IA T IO N E R R O R
40
50
0 40 80 120 160 200
f (Hz)
Fitness Metric
Genetic AlgorithmA ti l ith i i th• A genetic algorithm mimics the process of evolution that occurs in biology, wherein the variables, namely th di t f th kthe coordinates of the speakers, listeners and room dimensions comprise the genes
• The genes are simply a set of numbers which describe the room
• A population of individuals (surroundA population of individuals (surround configurations) is randomly formed, and the traits of each room are determined by their genes
Gene 1= Length1, Width1, Height1, Sn1(x), Sn1(y), Sn1(z), Ln1(x), Ln1(y), Ln1(z) etcdetermined by their genes
• Offspring are produces with traits of their parent rooms and mutation is introduced to allow features not present
Ln1(z), etc.
Gene 2 = Length2, Width2, Height2, Sn2(x), Sn2(y) Sn2(z) Ln2(x)introduced to allow features not present
in the initial room populationSn2(y), Sn2(z), Ln2(x), Ln2(y), Ln2(z), etc.
Last Gene
Survival of the Fittest• In biological evolution the fittest• In biological evolution, the fittest
are most likely to breed and pass on their genes, and the least fit the most likely to die, this is also true in an artificial genetic algorithm used in g gnumerical optimisation
• By these principles, the fitness f i l tiof successive populations
should improve. • This process is continued untilThis process is continued until
the population becomes sufficiently fit so that the best room produced can be classifiedroom produced can be classified as optimum
Room Optimizer
• Automatically optimizes the locations of the loudspeakers, listener and acoustical surface p ,treatment
Multichannel SBIR
Multichannel Modal
Nullify Modes– Nullify all modes with the subs and listener
placement for wide area uniformity (Null-mode placement) as suggested by Todd Welti and Floyd Toole
In Phase Subs Cancel Odd Orders R bR b
++++
Remember:Remember:
Speaker Speaker placementplacementdetermines determines which modes which modes are energizedare energized
Listener Listener placementplacementdetermines determines
-- -- which modes which modes are heardare heard
1st and 3rd order modes are cancelled by placement at positive and negative parts f th ti d Th d d d i t i d b thof the respective modes. The second order mode is not energized, because the
sub is positioned at a null.
4 Subs at ¼ Positions
____ ________
L1 & L3 cancelled
L2 not energized ++ --++
-- -- ++--
Uniform LF F/B++++
++--
W1 & W3 cancelled
++++
W2 not energized
Uniform LF across console++ ++
H1 not heard
++
Optimal In-Phase Sub Locations
Should result in cancellation of all odd order axial modesof all odd order axial modes and cancellation of first even mode (subs are at nulls)
Floor/ceiling axial modes areFloor/ceiling axial modes are not cancelled, however, these modes do not vary over a large seating area, assuming
h i ht d ’t hear height doesn’t change.
However, these locations are not very favorable in practical applications, so let’s examine other locations that may not be intuitive and are more practical.
(4) at ¼ of Room Dimensions
No Modal Excitation100(4) Speakers at:
( )
95
(0,0,1)(1/4L, 1/4W, 0.75')(1/4L, 3/4W, 0.75')(3/4L, 1/4W, 0.75')(3/4L, 3/4W, 0.75')Only 4th length mode
(4,0,0)
85
90
B
y gremains and first-order height mode
75
80
Leve
l, dB Moving Listener to
center of the room (L/2, W/2, H/2), removes the first order Floor/Ceiling
6
70
gmode
By moving the Listener to the 5L/8, W/2, H/2 location, the fourth-order length mode (4,0,0)
60
65
0 20 40 60 80 100 120
g ( )is no longer a problem.
Frequency, Hz
4 Speakers @ 1/4 4 Speakers @ 1/4, Listener Centered
4 Speakers @ 1/4, Listener @5L/8, W/2, H/2 All Modes
What Are Practical Sub Locations?
• ¼, ¼, ¼ placement is not very practical• Todd Welti expanded on the Room OptimizerTodd Welti expanded on the Room Optimizer
approach for a listening area and evaluated the most effective number and position of 4the most effective number and position of 4 in-phase subs
Courtesy Todd Welti, Harman International www.harman.com/wp/pdf/multsubs.pdf -
Response of 1-4 Subs
Summary
Courtesy Todd Welti, Harman International www.harman.com/wp/pdf/multsubs.pdf -
Equalization
Low Frequency Absorbers
• We have examined the effect of the room dimensions on modal densityy
• We have examined the optimal placement of subs and listener for optimal excitation orsubs and listener for optimal excitation or optimal nullifying of the modes
• Now we examine possible dedicated low• Now we examine possible dedicated low frequency absorbers
Proof of Performance Testing• The international acoustics community relies on• The international acoustics community relies on
proof-of-performance testing standards set by the International Organization for Standardization (ISO)(ISO).
• The ISO standards level the playing field They• The ISO standards level the playing field. They make transparent the requirements that products must meet in world markets, as well as the conformity assessment mechanisms for checkingconformity assessment mechanisms for checking that those products measure up to standards.
• This protects end users of these products and allows manufacturers to compete on an equal basisbasis.
Absorption Measurements• Random Incidence Rev Room Test: ISO 354
– 20 eigenfrequencies in 1/3-octave band: sample on floor as per ISO. For 200 m3 lower freq limit 100-125 Hz 1/3- octave5 20 i f i i 1/3 t b d l i– 5-20 eigenfrequencies in 1/3-octave band: sample in corner
– <5 eigenfrequencies in 1/3-octave band: • Sine wave excitation of each eigenfrequency separately• T-Room (Nocke) 3x4x5 m room with low frequency limit of roughly 30 HzT Room (Nocke) 3x4x5 m room with low frequency limit of roughly 30 Hz
• Normal Incidence Impedance Tube Test: ISO 10534– Lower frequency limit is based on the wavelength equal to 20 times theLower frequency limit is based on the wavelength equal to 20 times the
microphone spacing. 24’ long tube valid between 20-250 Hz.
• In-Situ: Near Field Mommertz Method: ISO 13472-1
• Free Field: 2 or more Microphone Method
Rev Room Method to Measure αRoom impulse response Integrated impulse response
V
4[i]
Room impulse response Integrated impulse responsedB
-10 [i]ba
0
-4
-8
[ii]
-20
-30[ii]
DiffusorsDiffusors
50 100 150 ms 50 100 150 ms-40
MicrophonesMicrophones
Material Sample [ii]Material Sample [ii]
LoudspeakersLoudspeakersMicrophonesMicrophones
No Sample [i]No Sample [i]
Rev Room With E mount Sample
• Measurements(100 – 5,000 Hz)
Binary Modex
0.900
1.000
0.500
0.600
0.700
0.800
on C
oeff
icie
nt
0.100
0.200
0.300
0.400
Abs
orpt
io
0.000100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000
Frequency, Hz
Rev Room Lower Limit
300Typical room volume of 200 m3, the lower frequency limit is between 100 and 125 Hz
200
250
y, H
z
and 125 Hz.
In critical listening rooms we need additional testing methods below 100
150
Freq
uenc
y additional testing methods below 100 Hz, in the modal frequency range
50
100
010 100 1000 10000
Volume m3
Rev Room- Fraunhofer Institute
Volume: 392 m3
T-Room 3 x 4 x 5mMicrophone Mode Frequency(Hz)
1,0,00,1,0110
Microphone Position
Mode (X,Y,Z)
Frequency (Hz)
Measured Calculated112
3442
541
33.641.6537
Measures down to 34 Hz!Measures down to 34 Hz!
1,1,00,0,11,0,12,0,00,1,1111
234541 784
66
54.156.966.167.670.8
67.270.5781
53.756.8
8844
33
1,1,12,1,00,2,02,0,18
1 78.479.96
7 8488.5
83.788
78.179.2 1144
7766
55
22
Effective Absorption Coefficient
⎞⎛⎞⎛ 11⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟
⎠⎞
⎜⎝⎛=
113.55TTcS
Veffα ⎟
⎠⎜⎝⎠⎝ 12 TTcSff
T-Room- Plate Resonator
Low Frequency Impedance Tube
• Measurements (20-285 Hz)
ik ik
S p xp x
ee
ikx ikx
ikx ikx
( )( )
ReRe
1
2
1 1
2 2
21
ikik
ikxikx SeeR −=
−−
12 ikxikx eSe −21 R=α 1 R−=α
Modex Study
Walk-In Impedance Tube
Length: 8 m (26.2’)
Opening: 1.6 x 1.2 m (5.2’ x 3.93’).
Frequency Range:
20 – 200 Hz with one mic
20 – 400 Hz d/4 mics
Extended Frequency Range
0.5ucfd
For d= 200 mm (7 87”) th
d
(7.87”) the upper frequency is 850 Hz.
When mics are at d/4, h fi d hi dthe first and third modes cancel when summed and the second mode has a
++++
second mode has a null.
Therefore, we can quadruple the upper
-- --quadruple the upper frequency from 850 Hz to 3400 Hz
Complex Impedance of a Membrane
4
5
2
3
Characteristic Impedance of Air
Maximum Absorption when Real Part Equals the Characteristic Impedance of Air (Normalized to 1)
1
0
1
100 120 140 160 180 200 220 240 260 280 300
Impe
danc
e
Characteristic Impedance of Air
-3
-2
-1I
146 Hz Resonance
-5
-4 Resonance occurs when Imaginary Part Equals Zero
Frequency, Hz
real(impedance) imaginary(impedance)
Absorption Coefficient
0.9
1
0 6
0.7
0.8
cien
t
0.4
0.5
0.6
orpt
ion
Coe
ffi
0.2
0.3Abs
0
0.1
0 50 100 150 200 250 300
Frequency, Hz
Membrane 2" Cavity Depth
In-Situ Absorption Measurement• Measure normal incidence impulse responseMeasure normal incidence impulse response• Point mic plus speaker away from wall to measure the transfer function of the
mic/speaker• Gate direct and scattering sound• Deconvolve each with the mic/speaker transfer functionp• Calculate the reflection factor• Determine the absorption coefficient
Acoustic Absorber Design
Acoustic Absorbers• Low FrequencyLow Frequency
– Anechoic WedgesCorner Bass Traps– Corner Bass Traps
– Helmholtz ResonatorsMi f t d/ l tt d R t– Microperforated/slotted Resonators
– Membrane ResonatorsPl t R t– Plate Resonators
– Active Absorbers
Anechoic Wedges
Wedge vs ASA_BCA_CPA
Corner Bass Trap• This is actually a misnomer,
because it actually absorbs at all frequencies, and only
t d t l fextends to lower frequency because of its increased thickness.For a porous absorber• For a porous absorber, maximum absorption occurs when the particle velocity is a maximum i evelocity is a maximum, i.e. at a quarter wavelength.
• In the corner there is zero particle velocity!particle velocity!
Optimal Placement• Porous absorbers are most efficient when
placed at the maximum particle velocity position for a given frequency, namely ¼ wavelength
M i ffi i hi d d f– Maximum efficiency achieved spaced from a boundary
• Resonant absorbers are most efficient when• Resonant absorbers are most efficient when placed at maximum pressure locations, namely at a monohedral dihedral or trihedralnamely at a monohedral, dihedral or trihedral boundary– Maximum efficiency achieved at wall-wall, wall-Maximum efficiency achieved at wall wall, wall
floor or wall-wall-ceiling/floor intersections
Acoustic Absorbers
Helmholtz Resonators
D ∅=2a
Porous absorbent Perforated sheet t
d
Rigid backing
Common types of perforation
S0
S b
ld
Cylindrical holes Slits (”slotted panel”)Cylindrical holes Slits ( slotted panel )
Simple practical solutions
PPorous material
Panel
A)
Fabric(resistance)B)
Panel
Microperf.l
C)
panel
Surface Impedance
[ ][ ])cot(1 kdcmjrz m ρω −+=
The resistance or real term, which is associated
The acoustic mass or imaginary term is associated with phase change or resonant frequencywith energy loss change or resonant frequency
k 2 /λ is the wavenumber in air;k=2π/λ is the wavenumber in air;d the cavity depth;
m the acoustic mass per unit area of the panel;the angular frequency = 2 fω the angular frequency = 2πf ρ the density of air, and
c the speed of sound in air
Resonant Frequency
At resonance, the imaginary term goes to zero
w p rm fm c kd= =2 cot( )
The cavity size is much smaller than the acoustic wavelength, i.e. kd<<1, so that cot(kd)→1/kd
f c= r
This is the basic design equation for resonant absorbers, i.e. Helmholtz Membrane and Plate resonators
fdm
=2p
Helmholtz, Membrane and Plate resonators
Helmholtz Acoustic Mass/Unit Area
m D t a t D t= + + +ÊÁ
ˆ˜
ÈÍ
˘˙ =r d n r2 2
2 8 1’
ma
t aa a
= + + +ÊËÁ
ˆ¯̃Î
ÍÍ ˚
˙˙
=p
dw p2 22 1
2
The last term in the equation is due to the boundary layer effect, and ν is the kinematic viscosity of air. This last term is often not significant unless the hole size is small, say sub-millimetre in diameter.
δ is the end correction factor (not allowing for mutual interaction), which to a first approximation is usually taken as 0.85 and derived by considering the radiation impedance of a baffled piston Other moreconsidering the radiation impedance of a baffled piston. Other more accurate formulations exist.
Helmholtz Resonant Frequency
'2 '2 2 2c c c Sf
md VtD t
2
2 2 2md VtD t da
• t′ is the thickness of the perforated sheet with the end corrections (end corrections allow for the radiation impedance of theallow for the radiation impedance of the orifices)
• t′ and a are assumed to be much 2asmaller than wavelength of sound in air.
• S=πa2 is the area of the holes, and• V the volume=D2d of each unit cell
D
• V the volume=D2d of each unit cell.
Percent Open Area
2aπ2D
ε =2a
D
cf εdt
f'2π
=dt2π
The World of Blox
Acoustical Properties
Absorption CoefficientUnslotted/SealedUnslotted/SealedSlotted/SealedSlotted/SealedSlotted/UnsealedSlotted/Unsealed Unslotted/UnsealedUnslotted/Unsealed
Transmission LossAbsorption Coefficient Transmission Loss
Hybrid LF Diffsorber
• The Helmholtz resonator slots provide low frequency absorption and the reflection phase grating provides p p g g pmid-high frequency diffusion
Empty Tube1
0.8
0.6
ficie
nt
0.4
tion
Coe
ff
Empty Tub
0.2
Abs
orp
00 50 100 150 200 250 300
-0.2
Frequency, Hz
Helmholtz Study
0 8
0.9
1
0.6
0.7
0.8
effic
ient
0.4
0.5
orpt
ion
Coe
0.2
0.3Abs
o
0
0.1
0 50 100 150 200 250 300
Frequency, Hz
Flat Panel 12" Cavity A Topperfo 4" Cavity A Topperfo 12" Cavity Topperfo 12" Cavity Filled R19
Absorption MechanismWhen surface perforations are the same size as a boundary l f i
Viscous Losses
layer of air.
Reflected Sound
avity
Incident Sound
Reflected Sound
Air
Ca
Microperforated Panel Glassp
0.5 mm diameter holesGlass
Microperforated Absorbers
È ˘Ê ˆ2
m Da
t a ta
= + +È
ÎÍÍ
˘
˚˙˙
+ÊËÁ
ˆ¯̃
rp
d nw
2
2 2 8 12
The last term in the equation is due to the boundary layer effect and
a aÎÍ ˚̇Ë ¯p w 2
The last term in the equation is due to the boundary layer effect, and ν is the kinematic viscosity of air (1.8 x E-5 Kg/ms). This last term is often not significant unless the hole size is small, say sub-millimetre in diameterin diameter.
The end correction δ is increased by the boundary layer effect and resonant frequency is reduced due to an increase in acoustic mass .
Losses
z j kd j a+ +2 1 71wrh wrt( ) .z j c kd j
h = + - +2
1rhe e
r re
cot( )
• Generally the resistive term in Helmholtz absorbers is very small and to get good absorption it is necessary to add porous material to the cavity.po ous ate a to t e ca ty
• However, when the holes are sub-millimeter the resistive term (in red above) is very large
• Consequently, no porous material is needed in the cavity
Microperforated OptionsF il 0 1F il 0 1 Sh t 1Sh t 1Foil: 0.1 mm Foil: 0.1 mm Sheet: 1 mm Sheet: 1 mm
Honeycomb: 19 mmHoneycomb: 19 mmPanel: 2 mm Panel: 2 mm –– 15 mm15 mm
Effect of Layers/Backing
Deamp Microslit
Theory
tz
ytρ ω
For an infinitely long slit:
bx
0j = jtan( )
21
tZ t k bρ ωρω′ = ′
1
2k b− ′ where 0
jk ωρ
μ′ =
Low frequency approximation:2 2 2
012 1 6jt btZ tρ ωμ ωρ′ ≈ + + 02 j700 5
Z tb
ωρμ
≈ + +
T.E. Vigrana and O.K.Ø. Pettersenb, a Acoustic Group, NTNU – Dept. Electronics and Telecommunications;b SINTEF-ICT, Trondheim, Forum Acusticum 2005
Theory II
bt
dB
[ ]0 00
1 j (2 ) j cotiZ Z t Z dcωρ ω
ε⎛ ⎞
′= + Δ − ⎜ ⎟⎝ ⎠0cε ⎝ ⎠
T.E. Vigrana and O.K.Ø. Pettersenb
a Acoustic Group, NTNU – Dept. Electronics and Telecommunications;b SINTEF-ICT, Trondheim
Absorption Data
Limp Membrane Resonators
P b b t
Membrane
t Porous absorbent
d
ta
Rigid backingg g
31.21 /kg mf 60cf ρ
mdf 60=
mdf ρ
π2=
340 /c m s
LF Band Cut AbsorbersM b i ll• Membranes- are essentially pressure transducers. They operate where the pressure is high and the particle velocity is low I e near ais high and the particle velocity is low- I.e. near a boundary. They convert pressure fluctuations into air movement in a frequency range to a o e e t a eque cy a gedetermined by the mass and compliance of the membrane and the air cavity depth.
Low Frequency AbsorptionI d T b M t
0.9
1
2" Cavity4"6"
Impedance Tube MeasurementsAbsorption efficiency
0.7
0.8
ent
6"+Damp8"10"
decreases with frequency, because the impedance of
0 4
0.5
0.6
sorp
tion
Coe
ffici
e impedance of the porous material moves further from the
0.2
0.3
0.4
Abs
characteristic impedance of air at low frequencies
0
0.1
40 60 80 100 120 140 160 180
frequencies.
40 60 80 100 120 140 160 180
Frequency, Hz
Plate Resonators
BroadbandHigh Pass
Plate Resonators
Steel Plate Pistonic ResonancePistonic Resonance
MechanismsMechanisms
P f M t lPerf Metal
Damp Bending ModesDamp Bending ModesPolyester
Diffraction Diffraction Above these frequencies absorption occurs Above these frequencies absorption occurs
High Pass Broadbandfrom diffraction of the sound around the plate from diffraction of the sound around the plate into the porous absorberinto the porous absorber
Plate Parameters
E steel, Pasteel density Kg/m3 Poissons ratio
melamine density Kg/m3 E melamine, Pa
c in m/s melamine L, m W, m T, m n m
2.06E+11 7850 0.3 9.5 1.00E+06 324.44284 1 1.5 0.001 1 10 0025 2 20.0025 2 2
3 34 4
fnm bending 1mm, Hz
fnm bending 2.5, Hz fR piston 1mm, Hz fR piston 2.5mm, Hz
3.52 8.79 179.63 113.6114.07 35.1714.07 35.1731.66 79.1456.28 140.69
Performance1 6
1.4
1.6t
1
1.2
oeffi
cien Broadband
0 6
0.8
ptio
n C
o
0.4
0.6
Abs
or
Plate
50 160 500 1600 50000
0.2
50 160 500 1600 5000Frequency, Hz
Plate & Broadband Installation
In-wall installation
A/V Conference Room
1,2
0 8
1
me
[s]
0,6
0,8
erbe
ratio
n tim
0,2
0,4
Rev
e
0
32 63 125 250 500 1000 2000 4000 8000
Frequenzcy [Hz]
no Absorber with Absorber
Active Bass Trap
Conclusion• Much time has been devoted to dimensional ratios,
however, however this is less important that the optimal position of the low frequency speakers and the listener (s).U if l f t 80 H b• Uniform low frequency response up to 80 Hz can be achieved by using multiple in-phase subs Th t ff ti l f b b• The most effective low frequency absorbers are metal plate resonators and membrane absorbers
• Diligent use of parametric equalization of low• Diligent use of parametric equalization of low frequency peaks is effective in fine tuning the room responseresponse
Ray Tracing
Image Model��
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White- poor response
SS
Gray- good response
Black- excellent responseSS
Variation of room quality for 100mVariation of room quality for 100m33 (3531 ft(3531 ft33 )) room. S indicates room. S indicates standard room size of 7 x 5.3 x 2.7m (23 x 17.4 x 8.9 ft)standard room size of 7 x 5.3 x 2.7m (23 x 17.4 x 8.9 ft)
Variation of room quality for 50mVariation of room quality for 50m33 (1765 ft(1765 ft33 )) room. room. B1 and B2 location of two ratios attributed to Bolt; LB1 and B2 location of two ratios attributed to Bolt; LB1 and B2 location of two ratios attributed to Bolt; L B1 and B2 location of two ratios attributed to Bolt; L location of best ratio of Louden. The triangular location of best ratio of Louden. The triangular regions are mapped out by standards equations.regions are mapped out by standards equations.
Variation of room quality for 200 mVariation of room quality for 200 m33 (7063 ft(7063 ft33 )) room room
Diffractal1
0.8
0.9
0.6
0.7
Coe
ffici
ent
0.4
0.5
bsor
ptio
n C
0 1
0.2
0.3Ab
0
0.1
0 50 100 150 200 250 300
Frequency, Hz
Diffractal 12" Cavity
Table of Contents• How to optimize rectangular room dimensions and
speaker/listener positions• Low Frequency Surface Treatments• Low Frequency Surface Treatments
– Proof of Performance Testing• Rev Room
Impedance Tube• Impedance Tube• T-Room• In-situ
Designs– Designs• Wedges• Helmholtz Resonators• Tuned Damped MembranesTuned Damped Membranes• Broadband Metal Resonators• Microperforated/slotted panels
Room Modes
3 x 4 x 5 m room, SPL at 1.3 m
Potential Acoustical Problems
• Modal Response• Speaker Boundary InterferenceSpeaker Boundary Interference
Ch ll• Challenge:– They must be minimized simultaneously, as they
i d d t i blare independent variables
Time/Frequency Equivalence
90
100
80
90
B)
60
70
Leve
l (dB
50
60
400 40 80 120
f (Hz)f (Hz)
Modal decomposition Image source Measured
BEM Predictions
Helmholtz-Kirchhoff prediction not restricted to rectangular rooms
( ) ( )G R P∂ ∂( , ) ( )( ) ( , ) ( ( ) ( , ) )( ) ( )s q
q
G R q P qP R P Q R P q G R q Sn q n q
∂ ∂α∂ ∂
= + − Δ∑
4
QRikr
sQR
ePrπ
−
= ( , )4
Rqikr
Rq
eG R qrπ
−
=(1)0
1( , ) ( )4 RqG R q H kri
=QR
Non-Rectangular Rooms
• We begin by comparing the Boundary Element Method calculation with the Modal Decomposition approach used in Room Optimizer
120
130
110
120
90
100
Leve
l, dB Lam's model
BEM
70
80
600 20 40 60 80 100 120 140 160 180 200
Frequency, Hz
Effect of One Inch Increments
Little effect at low frequency- Modal shifting at high
20
30
10
20
-10
0
Leve
l
-30
-20
-50
-40
0 50 100 150 200 2500 50 100 150 200 250Frequency, Hz
19'0" 19'1" 19'2" 19'3" 19'4" 19'5"
Effect of One Foot IncrementsLow frequencies shifted, modal pattern complex
30
10
20
-10
0
Leve
l, dB
-30
-20
L
-50
-40
0 50 100 150 200 250Frequency, Hz
19'0" 20'0" 21'0" 22'0" 23'0" 24'0"