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Damping of The Room LF Acoustics
Reza Kashani, Ph.D.Professor of Mechanical Engineering
The University of Dayton
Jim WischmeyerPresident
Modular Sound
November 6th, 2010129th AES Convention
San Francisco, CA
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Outline: LF Room Acoustics• Rooms excessively amplify sound at certain
frequencies– Dictated by room size and geometry
• Standing waves (acoustic resonances/modes) – Waves whose oscillation is continuously reinforced by their
own reflections
• Rooms have many resonances– The LF resonances are
» discrete
» distinct
– Typically, the first resonant mode accommodates most of the acoustic energy build up in the room
– In a typical listening room the resonant frequencies of standing waves fall in the bass frequency region
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Outline: Solutions
• Dissipative remedies, using sound absorbing material, are ineffective at low frequencies
• Reactive devices (bass traps) are commonly used for absorbing LF acoustic energy – Different passive and active bass trapping techniques
will be talked about • Their advantages/disadvantages discussed
• Damping measurement/quantification– Different techniques for low and high frequencies
• The tutorial will conclude by comparing/contrasting damping with equalizing
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Wave Propagation• Acoustic waves
– Pressure (and particle velocity) distribution that propagates through any medium
• Particles moving back and forth creating regions of compression and refraction
• Produces the sensation of sound
• 3-dimensional wave motion– Spherical
» Planar
• Spatial and time dependant– Wave equation:
» In Cartesian coordinates
2
2
2
2
2
22
2
2
22
2
2
z
p
y
p
x
pc
t
p
pct
p
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Standing Waves• With no obstacle/boundaries impeding the propagation of
acoustic waves, they moves in one direction only– Free field propagation
• In presence of boundaries, i.e., impedance change, a percentage of the wave energy gets reflected back – Percentage: between 0 to 100%
• Depending on how much absorption occurs at the boundary
– Common in enclosed spaces
• At certain discrete frequencies, the reflected wave overlaps the original wave, exactly, creating a standing wave/acoustic resonance– Occurs at all frequencies, low, mid and high– The wavelength of the standing waves between two parallel
walls• l1=2L, l2=L, l3=.66L, ….• f= c/l
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• For a rectangular shoe-box room, with rigid walls the natural frequencies and the shape of the modes can readily be evaluated
– Excel, Matlab,…
• For more irregular rooms numerical toolsare used to find the frequencies and mode shapes
Mode Shapes and Frequencies
,...2,1,0,,
, ,
))(cos)(cos(cos
zyx
z
zz
y
y
y
x
xx
zyx
nnnwhere
l
nk
l
nk
l
nk
zkykxkshapes
2
1
222
2
z
z
y
y
x
x
l
n
l
n
l
ncfreq
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– FEA tools can be used in analyzing the modal response of a room with • Any geometry
• Any boundary condition
• Any obstacle/equipment in the room
–Prior to having the room built• Such analyses will aid in
– Proper dimensioning of the room
– Placement of LF acoustic treatments
– Placement of audio equipment
Finite Element Analysis
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–Model the space geometry
–Mesh the model
• Discretize it to many small pieces (finite elements)
– Apply boundary conditions
– Solve • Modal analysis
• Frequency response analysis
– Post-process the results
Analysis Steps
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• Irregularities in a room change the shapes and frequencies of the standing waves/modes
Mode 134 Hz 35.2 Hz
Irregular Rooms
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Mode 4 of a
room
without and
with
furniture/
equipment
Leather
sofa
Audio
equipment
Obstacles/Equipment in a Room
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• A resonating wall can affect the modal character of the room
– With no damping built into the resonating wall, it can split an acoustic mode into 2 modes
• 34 Hz mode is split into 27 and 40 Hz modes
– Incorporating some damping into the resonating wall, turns the wall into a tuned absorber
• This is the principle behind panel absorption
27 Hz
40 Hz34 Hz
Resonating Walls
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The Effects of Standing Waves• Standing waves (acoustic modes) make a room to
accommodate the excessive reverberation of sound at certain frequencies. – This results in the reinforcing and lingering of certain
tones, long after they should have ceased – This is because the original oscillations of standing waves
are continuously reinforced by their own reflections– standing waves are discrete at low frequencies
• Lower modes normally carry most of the energy• The wavelength of these modes match the
dimensions of smaller rooms • Resonant frequencies: 20 to 80 Hz
• Lower modes alter the natural sound at these frequencies dramatically making the sound boomy and tonal
0 50 100 150 200 250 300 350 400 450 500-3
-2
-1
0
1
2
3
Am
plit
ude
Time increment; 1.6 msec steps
sound measurement with Etrap off and on
Etrap on
Etrap off
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Frequency Response Function (FRF)
• Most commonly used tool in identifying room modes• Definition: output/input over various frequencies in any
linear system is called frequency response function– Also called transfer function by practitioners– Measured at steady state
• A complex quantity– Magnitude– Phase
– In acoustics • Output: pressure or particle velocity
– Measured by a microphone or hot wire• Input: rate of change of volume velocity
– Normally created by a loudspeaker
– Commonly used in low-frequency acoustics• Peaks in FRF indicate resonances
LF HF
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FRF Evaluation Techniques• Analytical
– Used when an analytical model (partial differential equation) for the system is available
• Numerical– Used when a numerical (e.g., finite element) model
for the system is available
• Experimental– Most commonly used technique
• Requires the measurement of the output and input
– Fast Fourier Transform (FFT) algorithm is used in evaluation of experimental FRFs
)FFT(
)FFT()FRF(
I
O
)(
),()FRF(
IP
IOP
ii
oi
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Dealing with LF Resonance• Note that resonance is caused by reflection of
a wave upon itself
Pi+ Pr =Pi+R*Pi, where R is the reflection coefficient
• R=0 eliminates the resonance
– Walls need to be removed!
• This is why resonance exists in enclosed, not open, spaces
• Next best solution is making R small
– Reflection=1-|Absorption|2
• Increasing absorption abates the resonance– Dissipating acoustic energy
» Acoustic damping
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Frequency Response and Damping• Peaks in a frequency response is an indication of
acoustic resonances (standing waves)
– The sharpness of a peak indicates lack of dampingin that standing wave (mode)
– Normally the first mode is the one in need of most damping• Absorbing the energy of the
first mode lowers the boominess and lingering of sound associated with that mode
– Addition of damping to that mode is exhibited by flattening it in the frequency response
20 30 40 50 60 70 80-60
-50
-40
-30
-20
-10
0
10
Scale
d M
agnitude (
dB
)
Frequency (Hz)
Sub at:[0.1 0.935 0.25] mListener at:[4.752 0.935 1.2] m
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Sound Absorption/Damping• Acoustic energy
– Kinetic energy, KE• Particle velocity
– Potential energy, PE
• Acoustic pressure
– Total Energy• KE+PE
– Where one is maximum the other one is zero
– Sound absorbing material absorb KE energy• Their fibrous nature entangles
the sound, dissipating its KE
– To be effective they need to be placed in the region of high particle velocity
• Edge effect also contributes to absorption
a>1low at low
frequencies
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Sound Absorbing Material Effectiveness
• Facts:
– Acoustic modes have zero velocity at the walls
• Their velocity is maximum ¼ wavelength away from the walls
– Sound absorbing material, the main element n dissipative absorbers, are normally installed on the walls
• To have space left in the room, the thickness of sound absorbing material should be reasonable
• Although very effective at high frequencies, dissipative absorbers are not good dampening the LF standing waves of a room Note that the wavelength of a 25 Hz
resonance is around 50 ft
Middle of the room for the first mode
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Reactive Absorbers
• Absorbers of any kind are commonly placed close to or on the walls/surfaces
– That is where velocity is zero/small but pressure is maximum/large
• Reactive absorbers are damping mechanism that
– Convert PE energy (pressure) to KE (velocity)
– Dissipate KE
• Commonly used reactive absorbers
– Helmholtz resonators
– Quarter wave tubes
– Panel absorbers
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Helmholtz Resonator• Cavity
– acting as spring
• Neck/throat
– acting as mass
• Dissipation
– Turbulence in the neck and neck to cavity transition
– Sound absorbing material
• Placed next to the neck in the cavity
• HR is similar to a spring mass dashpot system
– Resonate at single frequency; a tuned device
• Whistle caused by blowing in a bottle is a tone at this frequency
Sound absorbing
material
Neck
Cavity
ICn
1 I =(air density)*(neck length)/(neck area)
C=(cavity volume)/[(air density)(speed of sound)^2]
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Cavity Backed Perforated Panels• A number of Helmholtz resonators with individual necks and
common cavity
• The backing volume acts as the cavity
• The perforations act as necks
• A tuned device– Similar to a Helmholtz resonator,
perforated panels can be viewed as a single resonance device
• Acceptable assumption up to a certain frequency
– Commonly used in aircraft engines
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Panel Absorbers • Panels/plates have many structural
resonances
– Sheet metal, plywood, etc.
– Backed by a cavity, to add stiffness• Cavity houses sound absorbing material
• The first structural resonance of the panel is tuned to a target acoustic mode of a room
– The acoustic pressure pulsation causes the panel to vibrate at resonance• The panel convert the acoustic PE into
acoustic KE – KE is dissipated in the sound absorbing
material
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Issues with Reactive Absorbers• The tuning of such devices is half the story
• The other half is the size of such devices– A tiny Helmholtz resonator and a very large one can have the same
resonant frequency
• This does not mean that they both have the same effectiveness
– The low frequency resonance of standing waves requires large reactive devices
• Bulky when tuned to low frequencies
– Once designed and tuned to a room, can not be used in another room with different geometry
– The higher order resonant frequencies of these devices might introduce undesirable effects
• Mode splitting
– With not enough damping in the reactiveabsorber, the target mode gets splitted
• Energy is not dissipated, just re-distributed
100 150 200 250 300 350 400 450 500-70
-60
-50
-40
-30
-20
-10
0
10
Frequency, Hz
Mag
nitu
de, d
BFRF Magnitude Corrugated PR 2nd Mode
PR Off
PR On
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Impedance of an Absorber• Acoustic impedance of a surface
– Specific acoustic Impedance
• Complex
• Frequency dependant
• Semi-empirical impedance models
• Measured impedance
- Pressure-Velocity measurement
– PU probe
– In-situ measurement
– Pressure-Pressure measurement
– 2 microphone technique
• Impedance can be used as the– Measure of sound absorption
– Boundary condition in finite element model of the room
uA
p
q
pZ
ZAu
pz
100 200 300 400 500 600 700 800 900-10
-5
0
5
10
15
20
Freq, Hz
Magnitude,
dB
U=2.5 m/s
U=5 m/s
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Absorption Measurement
• Random incidence (reverberant field) measurement
– Measurement is done in a reverberant room with non-parallel walls in which diffused sound field is generated• Standards such as ASTM C423 are used
– Suitable for characterizing mid to high frequencies absorbers
• Normal incidence measurement
– Measured by placing the face of the absorber at one end of an impedance tube with planar, 1D wave propagation
• Standards: ISO 10534-2, ASTM E-1050 and JIS 1405-2
– Hardware and software for measuring the frequency-dependent absorption coefficient , reflection coefficient, and acoustic impedance
– Suitable for characterizing low-frequency absorbers
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Active Acoustic Absorbers• Reactive tuned absorbers are
commonly used to add damping to LF modes• Large in size• Not re-tunable
• Active reactive absorbers• A powered subwoofer radiating in
response to the measured pressure• Nearly-collocated feedback control• A small microphone as sensor• Targets one (or two) LF mode(s)
• Size of a small, subwoofer• Low power demand• Robust, low-order, tunable and re-
tunable• Placement
– Where it couples effectively with the target mode(s)• At a high pressure location of the target
mode
• A true damping solution – Not equalization
Sound
pressure
room
Controller
1
Controller
2
Amplifier Control
speaker
Controller
Figure 3. Electronic feedback using two controllers, tuned to the 35 Hz structural
mode and the 1 st acoustic mode (55 Hz in the simulation).
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Simulation of a Small Room
• At low frequencies the modes are discrete– The modal density increases with frequency
20 40 60 80 100 120 140 160 180 200-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
Frequency (Hz)
Scale
d M
agnitude (
dB
)
Sub at:[0.1 0.7366 0.25] m
Listener at:[2.5603 0.3683 1.2] m
Resonant Frequencies
Mode index Frequency
L W H Hz
1 0 0
2 0 0
0 1 0
1 1 0
0 0 1
1 0 1
2 1 0
3 0 0
2 0 1
0 1 1
54
107
116
128
141
151
158
161
177
183
2 modes in
20 to 110 Hz range
8 modes in
110 to 184 Hz range
Uncontrolled
controlled
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A Test Room
noise source at wall 1,4electronic bass trap at wall 2,3room dims 18 x 9.7 x 13.6 feetcalculated modes 31, 39, 50, and58 Hz
164
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FE Modal Analysis
Resonant
frequencies
1 31 Hz
2 39
3 50
4 58.3
21
3 4
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Corner 3
BLACK - CONTROLLER OFFBLUE - CONTROLLER ON OPTIMIZED
RED - CONTROLLER ON OPTIMIZED FOR CORNER 2
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Time Domain Data
BLUE - CONTROLLER OFF
RED - CONTROLLER ON
MIC AT LISTENING POSITION
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More MeasurementsBlue: off Red: on
H1_2,1(f)
H1_2,1(f)_c0
80 15 20 30 40 50 60 70
58.0000
31.0000
32.0000
34.0000
36.0000
38.0000
40.0000
42.0000
44.0000
46.0000
48.0000
50.0000
52.0000
54.0000
56.0000
Frequency (Hz)
dB (V/V)
H1_2,1(f): 62.9883, 38.7717
H1_2,1(f)
H1_2,1(f)_c1
80 15 20 30 40 50 60 70
60.0000
42.0000
43.5000
45.0000
46.5000
48.0000
49.5000
51.0000
52.5000
54.0000
55.5000
57.0000
58.5000
Frequency (Hz)
dB (V/V)
H1_2,1(f): 62.9883, 52.2342
H1_2,1(f)
H1_2,1(f)_c2
H1_2,1(f)_c1
H1_2,1(f)_c2
80 15 20 30 40 50 60 70
58.0000
12.0000
15.0000
18.0000
21.0000
24.0000
27.0000
30.0000
33.0000
36.0000
39.0000
42.0000
45.0000
48.0000
51.0000
54.0000
Frequency (Hz)
dB (V/V)
H1_2,1(f): 62.9883, 34.2340
H1_2,1(f)
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
H1_2,1(f)_c1
80 15 20 30 40 50 60 70
59.0000
14.000015.0000
18.0000
21.0000
24.0000
27.0000
30.0000
33.0000
36.0000
39.0000
42.0000
45.0000
48.0000
51.0000
54.0000
57.0000
Frequency (Hz)
dB (V/V)
H1_2,1(f): 62.9883, 38.7009
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Software Tool
• Dynamic signal analysis
– Uses the sound card• Plays the
excitation noise thru the speaker output
• Acquires the measured sound thru the mic input
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Other Applications• Vehicular
applications– Can be used both
as a bass trap inside large vehicles (SUVs and minivans) to• Abate boom noise
• Enhance the listening experience
• Passive absorbers for addressing LF modes in a vehicle would be too large
0 50 100 150-60
-50
-40
-30
-20
Freq, Hz
Shroyer at 35 mph
0 50 100 150-60
-50
-40
-30
-20Shroyer at 30 mph
0 50 100 150-60
-50
-40
-30
-20
Scale
d M
ag,
dB
Shroyer at 20 mph
UC
C
0 50 100 150-60
-50
-40
-30
-20I-675 at 65 mph
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Other Applications
• Industrial application
– Acoustic resonance in an enclosed industrial combustor
20 30 40 50 60 70 80 90 100 110 12040
60
80
100
120
MagsplR
MS
, dB
(a) Pwr spectrum of sound outside the model
20 30 40 50 60 70 80 90 100 110 12080
90
100
110
120
MagsplR
MS
, dB
(b) Pwr spectrum of sound at the fan mouth
20 30 40 50 60 70 80 90 100 110 12060
80
100
120
140
MagsplR
MS
, dB
(c) Pwr spectrum of sound inside the model
Freq, Hz
uncontrolled
controlled
no instability and no control
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Damping vs. Equalizing• Damping dissipates
energy
– Flattening a peak in the frequency response is because energy is being removed from the system at that resonance• Lowers ringing/lingering of
sound at the target mode
– Damping is a parameter of the system
• Energy removal affects all the locations the same way
• EQ is a narrow-band volume control
– Flattening a peak in the frequency response is not because energy is being removed from the system at that resonance• Does not affect the
ringing/lingering of sound at the target mode
• Not effective in room with live music
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Summary
• Rooms excessively amplify sound at certain frequencies– Dictated by room size and geometry
• Standing waves (acoustic resonances/modes)• Tonal lingering of sound
• Passive tuned acoustic damping• Helmholtz resonator, panel absorbers, quarter wave tube, etc.
• Active tuned acoustic damping– Small, and effective way of adding tuned damping to a room
• Abates severe bass coloration – Tunable and re-tunable – Occasional and low power demand– One (or two) controllers can be tuned to add damping to one (or two) acoustic
mode(s) of the room• Multiple controllers (circuits) are cascaded in parallel and share resources
– Other applications• Vehicular and industrial
• Quantifying the absorption of LF dampers– Impedance tube measurement