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��

�

�

��

��

���

���

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"