Alexis Baskind
Room Acoustics
Alexis Baskind, https://alexisbaskind.net

Alexis Baskind
Room Acoustics
Course series
Fundamentals of acoustics for sound engineers and music producers
Level
undergraduate (Bachelor)
Language
English
Revision
January 2020
To cite this course
Alexis Baskind, Room Acoustics, course material, license: Creative Commons BY-NC-
SA.
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Room Acoustics

Alexis Baskind
Outline
1. Time-Space perspective: Sound propagation in a
room
2. Frequency-Space perspective: Room modes
3. Time-Frequency perspective
4. Room acoustics design
5. Room acoustics of listening rooms
6. Spatial hearing in a room
Room Acoustics

Alexis Baskind
Sound propagation in a room
• The time evolution of the sound propagation in a
room can be considered from the point of view of
sound rays, reflection, absorption and diffusion
surfaces
• Most of room acoustics simulation softwares uses
indeed among others raytracing algorithms
(similar to 3D image rendering algorithms)
• For this, let’s first consider a simple rectangular
room, with a sound source and one listener
Room Acoustics

Alexis Baskind
Sound propagation in a room
• The sound sources only emits a short impulse, for
example a hand clapping, or a gunshot (gunshots were
used a lot in the early ages to measure room acoustics)
Room Acoustics
Source: Charles Feilding

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Direct Sound
• The first information that reaches the listener is the direct sound
• Without any further reflections, this would correspond to the so-
called free-field (in an anechoic chamber)
Room Acoustics
Temporal
representation
Spatial
representation
Source: Charles Feilding

Alexis Baskind
Early reflections
• After a moment (called initial time-delay gap), the first reflected
waves reach the listener, with less level because of absorption and
the distance (inverse-square law)
Room Acoustics
Temporal
representation
Spatial
representation
In red: the initial
time delay gap
Source: Charles Feilding

Alexis Baskind
Early reflections
• The temporal density of reflections increases drastically with time
Room Acoustics
=> =>Direct sound
First-order reflections
(i.e. reflected once)
Second-order reflections
(i.e. reflected twice)
Source: Geoff Martin

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Late Reverberation
• After 20-100ms (depending on the room dimensions and on the
diffusion – see below), the reflections become dense and come
from every direction: the sound field becomes more and more
diffuse => late reverberation
Room Acoustics
Temporal
representation
Spatial
representation
Source: Charles Feilding

Alexis Baskind
Late Reverberation
Without flutter echoes or other late reflections, the sound pressure
decays on average exponentially with time during the late
reverberation process
Room Acoustics
Soundpressure(linear)
Room impulse response (schematic), linear representation

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Late Reverberation
Without flutter echoes or other late reflections, the sound pressure
decays on average exponentially with respect to time during the late
reverberation process
Room Acoustics
Sound
pressure
(Pa)
Time (ms)
in red: envelope of late
reverberation decay
Room impulse response (measured), linear representation

Alexis Baskind
Late Reverberation
Thus the sound pressure level (on a logarithmic scale) decays on
average linearly with respect to time
Same room impulse response (measured), logarithmic representationSound
pressure
level
(dB SPL)
time (ms)
in red: envelope of late reverberation decay
in blue: measurement noise
Room Acoustics

Alexis Baskind
Sound
pressure
level
(dB SPL)
Time (ms)
Reverberation Time
• The Reverberation Time (T60) is the time the sound pressure level
needs for a 60 dB decrease
• The reverberation time is the most well known measure to
characterize a given reverberation
60 dB
T60 = time
corresponding to a
60 dB decrease
Room Acoustics

Alexis Baskind
Sound
pressure
level
(dB SPL)
Time (ms)
Reverberation Time
• In practice, the reverberation time is measured thanks to an
estimation of the envelope (called „Schroeder-curve“), which is
much smoother as the impulse response.
In black: Schroeder-curve
60 dB
T60 = time
corresponding to a
60 dB decrease
Room Acoustics

Alexis Baskind
Sound
pressure
level
(dB SPL)
Time (ms)
Reverberation Time
• Since a dynamic range of 60 dB is almost impossible to achieve, the
reverberation time is calculated based on a decay of 30 dB or 20 dB, and
then doubled (for 20dB) or tripled (for 60dB), in order to stay coherent
with T60 => Those estimations are called T20 and T30.
• T30 is measured between -5 dB and -35 dB, and T20 between -5 dB and
-25 dB with regards to the maximum of the curve
T30 / 2
Max – 5dB
Max – 35dB
Room Acoustics

Alexis Baskind
Sound
pressure
level
(dB SPL)
Time (ms)
Reverberation Time
• Since a dynamic range of 60 dB is almost impossible to achieve, the
reverberation time is calculated based on a decay of 30 dB or 20 dB, and
then doubled (for 20dB) or tripled (for 60dB), in order to stay coherent
with T60 => Those estimations are called T20 and T30.
• T30 is measured between -5 dB and -35 dB, and T20 between -5 dB and
-25 dB with regards to the maximum of the curve
T20 / 3
Max – 5dB
Max – 25dB
Room Acoustics

Alexis Baskind
Free field / diffuse field
• The time evolution of the sound propagation in a room can
be considered as the evolution from a free field to a diffuse
field
– Direct sound = free field: the signals that reach the
microphones/ears are highly correlated
– Early reflections = the correlation between recorded signals drops
more and more down as new reflections reach the microphones
– Late reverberation = diffuse field:
1. The sound is coming from all directions with the same level
2. The correlation between sound pressures at different positions is close to
zero
3. The diffuse field has the same characteristics at all positions of the room
Room Acoustics

Alexis Baskind
Critical Distance
• The critical distance (or Room Radius) is defined as the distance to
the source where the energy of the direct sound equals the energy
of the reverberated sound
Room Acoustics
Distance from source
• Below this distance, the
energy mainly follows
the inverse square law
• Above this distance, the
energy is roughly always
constant whatever the
position is, and
corresponds to the level
of the reverberant field

Alexis Baskind
Diffusion
• Late reflections, even attenuated by absorption, are often
disturbing, since they may lead to audible echoes
• The worst case is flutter echoes between parallel surfaces
• Therefore, diffusive surfaces are often used as an
alternative to reflective surfaces: they help to reduce late
reflections without making the room dryer
• The more diffusive surfaces, the earlier the transition to
diffuse reverberation
Room Acoustics

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Diffusion
Room Acoustics
Without diffusion With diffusion
Source: Takatoshi Yokota, Shinichi Sakamoto and Hideki Tachibana

Alexis Baskind
Diffusion
Room Acoustics
Source: Takatoshi Yokota, Shinichi Sakamoto and Hideki Tachibana

Alexis Baskind
The effect of Distance
• How is the reverberation changed when the source gets
farther ?
Room Acoustics
timetime
The source is farThe source is close

Alexis Baskind
Effect of Distance
With increasing distance:
1. The direct sound and the early reflections come later
2. The initial time delay gap is smaller
3. The early reflections come less from the sides and more
from the front. According to the cocktail-party effect, they
are preceptually less easy to distinguish from the direct
sound => Coloration
4. The level of the direct sound decreases, but the level of
the diffuse reverberation remains more or less identical
=> the relative part of reverberation increases
Room Acoustics

Alexis Baskind
The effect of Room Size
• How does the reverberation depend on the size of the
room ?
Room Acoustics
The room is bigThe room is small
timetime

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The effect of Room Size
If the room is bigger:
1. The overall sound level decreases
2. The early reflections come later
3. The reverberation time is longer
This means that a relatively long reverberation time can be
achieved:
– In a small room which walls, ceiling and floor are not good
absorbers (like small echo chambers used in studios)
– In a very large room which walls, ceiling and floor are good
absorbers
=> the main difference between those two cases is that
early reflections come earlier in a small room (which is used
by perception to recognize if a room is small or big)
Room Acoustics

Alexis Baskind
Limits of the geometrical model
• The geometrical model makes only sense if the
wavelengths are short enough, so that reflections can
occur.
• This is a requirement in order to consider the reverberant
field as diffuse
• At low frequencies, surfaces and distances between them
are too small compared to the wavelength: the geometrical
model does not work any more, and must be replaced with
a modal model (i.e. standing waves)
Room Acoustics

Alexis Baskind
Outline
1. Time-Space perspective: Sound propagation in a
room
2. Frequency-Space perspective: Room modes
3. Time-Frequency perspective
4. Room acoustics design
5. Room acoustics of listening rooms
6. Spatial hearing in a room
Room Acoustics

Alexis Baskind
Room resonances
• Reminder: monodimensional standing waves between two walls
Room Acoustics
Wall 1 Wall 2
distance between walls
wavelength

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Axial modes only depend on 1 dimension Tangential modes depend on 2 dimensions
Room resonances
• In 3 dimensions, more complex combinations are possible:
Room Acoustics
Oblique modes (also
called diagonal)
depend on 3
dimensions
Image sources: mcsquared.com

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Room resonances
• In 3 dimensions, more complex combinations are possible:
Room Acoustics
Image source: gikacoustics.com

Alexis Baskind
Frequency distribution of modes
• Because modes are 3-dimensional, their frequencies
(called eigenfrequencies) are not distributed regularly (on
a harmonic series), contrary to the 1-D case
Room Acoustics
Example: simulated eigenfrequencies for a rectangular room with
dimensions: 4.6m x 3.75m x 2.34m
Hz
frequency

Alexis Baskind
Frequency distribution of modes
• The frequency distribution depends on the size of the
room: the bigger the room, the bigger the modal density
(i.e. the number of modes per frequency)
• The higher the frequency, the bigger the modal density
Room Acoustics
Example: simulated eigenfrequencies for a rectangular room with
dimensions: 9.2mx 7.5m x 4m
Hz
frequency

Alexis Baskind
Modes: Duration and Bandwidth
• The duration and the bandwidth of single modes, like for
every resonances (or like band-pass filters), are inversely
proportional with each other: the longer it lasts, the
narrower it is in the frequency spectrum
• Therefore:
– Modes in a room without any absorbing material are long, thus
very narrow in the frequency spectrum (= a high quality factor)
=> very clear resonances, holes between two modes
– Modes in a room with a proper acoustic treatment (i.e. enough
absorption at low frequencies) are short, thus wider in the
frequency spectrum (= a low quality factor) => the spectrum is
more flat, less obvious resonances
Room Acoustics

Alexis Baskind
Modes: Duration and Bandwidth
-0.10
0.00
0.10
Volts/Volts
0 100 200 300 400 500
Time (ms)
Impulse Response
-0.10
0.00
0.10
Volts/Volts
0 100 200 300 400 500
Time (ms)
Impulse Response
-0.10
0.00
0.10
Volts/Volts
0 100 200 300 400 500
Time (ms)
Impulse Response
Frequency Response Impulse Response (time)
lessresonant
(=lowQ-Factor)
moreresonant
(=highQ-Factor)
Room Acoustics
Behavior of a single mode with respect to frequency and time, depending on damping

Alexis Baskind
Modes: Duration and Bandwidth
Example: empty room (no treatment)
Source : Ethan Winer
Time
Frequency
Level
Room Acoustics

Alexis Baskind
Modes: Duration and Bandwidth
... With 12 thin absorbers: 703-FRK from Owens Corning
Source : Ethan Winer
Time
Frequency
Level
Room Acoustics

Alexis Baskind
Modes: Duration and Bandwidth
... With 12 thin absorbers: 705-FRK from Owens Corning
Source: Ethan Winer
Time
Frequency
Level
Room Acoustics

Alexis Baskind
Modes and frequency response
The overall frequency spectrum at low frequencies consists in the
overlapping of all modes.
Example: calculated modes and frequency response in a rectangular room
(left: single modes, right overlapping = estimated frequency response)
Room Acoustics
Image sources: BBC Research Department Report, Low-Frequency Room Responses

Alexis Baskind
Modes and frequency response
Room Acoustics
Caution: the overlapping of modes leads not only to constructive
interferences, but also sometimes destructive
Holes in the frequency spectrum
Example (Simulation of room modes in the
Software “Room EQ Wizard”):
• The eigenfrequencies of the room modes
are shown als colored lines
• There are holes at ca. 44Hz and 52 Hz,
that result from the big frequency
distance between the closest modes as
well as from destructive interferences
between them.
• There is also a hole at 62 Hz although the
closest mode (63 Hz) is quite strong at
this position. This hole can only be
explained with destructive interferences

Alexis Baskind
Example of the frequency response of real room
Room Acoustics

Alexis Baskind
Example of the frequency response of real room
Room Acoustics
Low-frequency Modes

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The problem with room modes
When the modal density is too small at low frequencies
(i.e. for small rooms), the sound pressure level present
strong variations as a function of the position of the
source and of the listener.
Room Acoustics
Source: Thomas Görne, “Tontechnik”
Simulated position-dependent sound field in a rectangular room 3m x 3.40m x 2.40m
(Reverberation time ca. 0.5 s); sound pressure on the horizontal plane 1,2m above the floor at
80 Hz, 93 Hz, 109 Hz, 127 Hz; the level varies up to 40 dB as a fonction of position

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Modes and Modal Density: Summary
• Modes can also interfere in a destructive way
• The position of the loudspeakers and the listening position are
extremely important for the linearity of reproduction at low
frequency
So there are 3 possible causes for amplitude dips at low
frequencies:
1. The loudspeaker or the listening point is at a node of a room
mode
2. The frequency lies between 2 modes with a big frequency
distance between their eigenfrequencies
3. The frequency lies between 2 modes with a small
distancebetween their eigenfrequencies, but the two modes
interfere in a destructive way at the listening position
Room Acoustics

Alexis Baskind
Modes and Modal Density: Summary
• If the modal density is too small:
1. There will be amplitude dips between the eigenfrequencies
2. The amplitude varies a lot for a given position with respect to
position
• If the modal density is big enough:
1. The distance between the modes is smaller
2. The amplitude for a given frequency depends on several
modes => less influence of position, less destructive
interferences, the room sound field is more diffuse
The bigger the modal density, the better
• Room modes are especially problematic in small rooms,
for which the modal density is often too small at low
frequencies
Room Acoustics

Alexis Baskind
Schroeder-Frequency
• The Schroeder-Frequency provides an order of magnitude
of the frequency region above which the modal density is
big enough (>=3) to consider the room sound field as
diffuse
• It can be calculated as follows:
• This means:
– The bigger the room, the smaller the Schroeder-Frequency
– The drier the room , the smaller the Schroeder-Frequency
Small listening rooms must be dry in order to minimize linear
distortions at low frequencies
Room Acoustics
Fs» 2000
T60
V
(T60 is the reverberation time in this frequency region, V
is the room volume)

Alexis Baskind
Acoustics of Listening Rooms
The ITU-R BS.1116-1 recommendation suggests that:
• The average reverberation time, measured over
the frequency range 200 Hz to 4 kHz, should be:
… where V is the volume of the room in m3
RTm = 0.25
V
100
3 (s)
Room Acoustics

Alexis Baskind
Acoustics of Listening Rooms
The ITU-R BS.1116-1 recommendation suggests that:
• The reverberation time stays in the given limits:
RTm
Room Acoustics

Alexis Baskind
Outline
1. Time-Space perspective: Sound propagation in a
room
2. Frequency-Space perspective: Room modes
3. Time-Frequency perspective
4. Room acoustics design
5. Room acoustics of listening rooms
6. Spatial hearing in a room
Room Acoustics

Alexis Baskind
Time-frequency model of a reverberation
• Time and frequency approaches can be grouped in a single model:
Room Acoustics
Frequency (Hz)
Time (s)
Modes
Early reflections
Diffuse reverberation

Alexis Baskind
Waterfall View
• The Waterfall view is a time-frequency representation of a measured
room response:
Room Acoustics
Frequency (Hz)
Time (ms)
Level (dB)

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Waterfall View
• The Waterfall view shows very well the frequency
dependence of the late decay (see later)
• On small rooms, the low-frequency modes are also
quite visible
• It gives in general more information as the
frequency response (since it also shows thetime
evolution of the spectrum)
• But: the time resolution is very low. Among others,
it does not reveal the early reflections
Room Acoustics

Alexis Baskind
Outline
1. Time-Space perspective: Sound propagation in a
room
2. Frequency-Space perspective: Room modes
3. Time-Frequency perspective
4. Room acoustics design
5. Room acoustics of listening rooms
6. Spatial hearing in a room
Room Acoustics

Alexis Baskind
Room acoustics design
• The first step and requirement for the acoustic design of a
room is the stipulation of the desired reverberation time
• The required reverberation time depends on the usage of
the room (recording room, listening room, concert hall,
teaching room etc.). There are specific recommandation for
each kind of room: for instance, a listening room is
designed to be typically drier as a recording room
• Based on the reverberation time, the room dimensions and
the construction materials (concrete, dry wall, wood...), a
selection of absorbing, diffusive and reflective surfaces is
being made in order to reach the required reverberation
time and optimize the acoustics
Room Acoustics

Alexis Baskind
Prediction of the Reverberation Time
• Several (partly empirical) formulas provide an estimation of the
reverberation time. The most well known are from Sabine (1898)
and Eyring (1920)
=> Sabine Formula (for low absorptions coefficients): the surfaces
are categorized by their material, thus their absorption properties:
… with: V = Room volume in m3
αi is the absorption coefficient for the surface Si
The product αi.Si is called equivalent absorption area (unit =
Sabins).
• Since the absorption coefficient depends on frequency, the
reverberation time also depends on frequency
Room Acoustics
𝑇60 ≈ 0.161
𝑉
𝛼𝑖 𝑆𝑖𝑖

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Absorption Coefficient of various materials
Room Acoustics

Alexis Baskind
Frequency-dependent absorption
• Reverberation time is typically bigger at low frequencies, since
most absorbers are not efficient for big wavelengths:
Room Acoustics
Example: Reverberation time as a function of frequency for 3 concert halls

Alexis Baskind
Sound Absorbers
• Absorbers are usually classified in 3 categories
Room Acoustics
. Porous absorber
(=velocity-based
absorber)
=> Used as wideband
absorbers if they are
thick enough
1/ Resonant absorbers (=pressure-based absorbers)
. Membrane absorbers
. Helmholtz-Absorber: with holes or slots
2/ „Tube traps“
(3/ active bass traps)
Absorptioncoefficient
High-frequency absorber mid-frequency absorber low-frequency absorber
Frequency

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Porous Absorbers
• Porous Absorber are velocity-based absorbers: they reach
a maximum of efficiency at positions where the sound
velocity is maximum
• The sound velocity is maximum at zeros of the sound
pressure (=nodes)
Room Acoustics
• This means for standing waves, that the
maximum of efficiency is reached for a
distance to the wall of λ/4, 3λ/4, 5λ/4,
etc.
blue: sound pressure
red: sound velocity

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Porous Absorbers
This means: the lower cutoff frequency of absorption
depends on the thickness of the absorber
Room Acoustics
red: sound velocity for standing waves with various wavelengths
gray: porous absorber
high frequencies: several maxima of the sound velocity in
the absorber => maximum efficiency
Lower cutoff frequency: the first maximum of sound
velocity is at the limit between absorber and air
Low frequencies: maxima of the sound velocity are
outside the absorber => lower efficiency

Alexis Baskind
Porous Absorbers
This means: the lower cutoff frequency of absorption
depends on the thickness of the absorber
Room Acoustics
Example: simulated absorption coefficient for two different thicknesses
(source: www.acousticmodelling.com)

Alexis Baskind
Porous Absorbers
Room Acoustics
High-frequency
absorber
High-frequency absorber with increased
absorption surface
Corner absorbers: often sold as als „bass traps“, but
typically efficient above 100-200 Hz and almost useless
at lowest frequencies

Alexis Baskind
Porous Absorbers
A possibility to increase the efficiency at low frequencies is to
place the absorber at a certain distance with the reflecting
surface => for instance usefull for ceiling absorbers
Room Acoustics
red: sound velocity for standing waves with various wavelengths
gray: porous absorber
High frequency Frequenzen: several maxima of the sound
velocity in the absorber => maximum efficiency (although
bigger dependence on the wavelength)
smaller (but not zero-) efficiency
Again good efficiency, since the first maximum of the
sound velocity is within the absorbing material
Air gap

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Porous Absorbers
Room Acoustics
Example: simulated absorption coefficient with and without air gap
(source: www.acousticmodelling.com)
Porous Absorber with air gap with reflecting surface

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Resonant Absorbers
• Resonant absorber are pressure-based absorbers: they
reach a maximum of efficiency at positions where the
sound pressure is maximum: this means against the walls
and room corners
• Resonant absorbers are harmonic oscillators and work like
spring-mass systems. This means:
– The absorption is achieved thanks to friction. Without friction,
the energy may actually be amplified instead of absorbed
– The resonance frequency:
• Increases with the spring constant (stiffness)
• Decreases with increasing mass
• Decreases with increasing friction
– The bandwidth increases with friction
Room Acoustics

Alexis Baskind
Membrane absorbers
Room Acoustics
Source: Heinrich Kuttruff,
“Room Acoustics”
• Membrane absorbers consist in a thin
oscillating rigid or soft membrane (typically
wooden) clamped with a spacing to the
ceiling or wall. The enclosure is airtight and
partly filled with absorbing (porous) material
• The mass is the masse of the membrane
• The stiffness depends on the volume of air
and absorbing material in the enclosure, and
partly also on the elasticity of the membrane
and clamping
• Friction takes place partly in the wood but
mostly in the absorbing material

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Perforated plates, slat absorbers
Room Acoustics
Source: Heinrich
Kuttruff, “Room
Acoustics”
• Perforated plates and slit absorbers work
as Helmholtz resonators: the panel does
not vibrate, but the air in the openings
(holes or slots)
• The resonance frequency depends on the
geometry (thickness and width of the
openings), width of the air volume.
Source: topakustik.ch

Alexis Baskind
Perforated plates, slat absorbers
Room Acoustics
Perforated Panel with Porous Absorber
Properties of panel Display options
Panel thickness (tp) 6,0 mm 0,236 in Start graph at 62,5 Hz Eq 6.8
Repeat distance (D) 25,0 mm 0,984 in To see the graph in the standard
Hole radius (a) 10,0 mm 0,394 in analysis frequencies, select
Open Area ( ) 50,27% Show subdivisions of "Whole Octaves" and set the
Properties of cavity starting frequency to 62.5Hz
Cavity depth (d) 100,0 mm 3,937 in
Absorber thickness (ta) 10,0 mm 0,394 in
Air space in cavity (d - ta) 90,0 mm 3,543 in This is ignored for the "No Air Gap" plot. Cavity assumed to be filled with absorber.
Absorber flow resisitivity 10 000 rayls/m
This plot is a simplification of reality because it is only calculated for normal incident sound.
2 f
2 /
Eq 5.19
Eq 5.20
Eq 5.11
Eq 5.9
Eq 5.10
Eq 5.26
Eq 5.27
Eq 6.15
Eq 6.26
Eq 1.22
Eq 1.25
Eq 6.22
Eq 6.23
Eq 6.24
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
62,5
70
79
88
99
111
125
140
157
177
198
223
250
281
315
354
397
445
500
561
630
707
794
891
1000
1122
1260
1414
1587
1782
2000
2245
2520
2828
3175
3564
4000
4490
5040
5657
6350
7127
8000
8980
10079
11314
12699
14254
16000
Absorption
Frequency (Hz)
Normal incidence absorption Absorber against panel Absorber against backing No Air Gap
a/
b/
c/
• The absorption properties depend also on the
position and thickness of the material

Alexis Baskind
Outline
1. Time-Space perspective: Sound propagation in a
room
2. Frequency-Space perspective: Room modes
3. Time-Frequency perspective
4. Room acoustics design
5. Room acoustics of listening rooms
6. Spatial hearing in a room
Room Acoustics

Alexis Baskind
Acoustics of Listening Rooms
Room dimensions
• Most important: a listening room (and the position
of the loudspeakers) should have a symmetry
axis!
• It should be big
– Room modes are lower in frequency and the modal
density is bigger
– Reflections do not arrive too early (to avoid a “boxy”
sound)
100 m3 (it would correspond for example to 6m x 6m x
3m if it were rectangular) is the reference volume in
the ITU-R BS.1116-1 recommendation
Room Acoustics

Alexis Baskind
Acoustics of Listening Rooms
• A listening room should not be too dry
– Unnatural sound
– Tendency to add too much artificial reverberation in
the mix
– Need for a certain amount of short reverberation
(typically 0.25 – 0.3 s)
– Need for envelopment => late reflections
• But it should not be too live as well
– Lack of precision
– Spectral effects (because of early reflections)
Room Acoustics

Alexis Baskind
Acoustics of Listening Rooms
The ITU-R BS.1116-1 recommendation suggests that:
• The reverberation time stays in the given limits:
Room Acoustics
RTm

Alexis Baskind
Acoustics of Listening Rooms
For mid and high frequencies (> 200 Hz)
• There should not be flutter echoes => no parallel
walls (otherwise put absorbers or diffusors)
• The ceiling and the floor as well can create flutter
echoes => ceiling should not be horizontal
(otherwise put absorbers or diffusors)
Room Acoustics

Alexis Baskind
Acoustics of Listening Rooms
• Too loud early reflections (< 15ms) entail comb-
filtering and alteration of the stereo image
• The ITU-R BS.1116-1 recommendation suggests
that:
“Early reflections caused by the boundary surfaces of
the listening room, which reach the listening area
during a time interval up to 15 ms after the direct
sound, should be attenuated in the range 1-8 kHz by
at least 10 dB relative to the direct sound.”
Room Acoustics

Alexis Baskind
Acoustics of Listening Rooms
The fluctuations of the frequency responses are mostly
determined by the early reflections (comb-filtering)
Room Acoustics
Influence of the early reflections
Example:
measurement of a
listening room,
frequency response
for the direct sound
only

Alexis Baskind
Acoustics of Listening Rooms
The fluctuations of the frequency responses are mostly
determined by the early reflections (comb-filtering)
Room Acoustics
Influence of the early reflections
Example:
measurement of a
listening room,
frequency response
for the first 1.3 ms

Alexis Baskind
Acoustics of Listening Rooms
The fluctuations of the frequency responses are mostly
determined by the early reflections (comb-filtering)
Room Acoustics
Influence of the early reflections
Example:
measurement of a
listening room,
frequency response of
the whole room
response

Alexis Baskind
Acoustics of Listening Rooms
The ITU-R BS.1116-1 recommendation suggests that the
frequency response stays in the given limits:
Room Acoustics
Frequency response

Alexis Baskind
Example 1: LEDE
• LEDE-design (“Live-End-Dead-End”), proposed in
1979, aims at reducing the early reflections while
keeping enough late diffusion (for the
envelopment)
Room Acoustics
(Source: F.
Rumsey, Spatial
Audio)

Alexis Baskind
Example 2: RFZ
• With RFZ-design („Reflection-free zone“), proposed in 1984,
early reflections are not any more strongly absorbed but
deviated from the zone around the sweet spot
• Like with LEDE, the back wall is diffusive (and not
absorbing), so that the room does not become to dry
Room Acoustics

Alexis Baskind
Outline
1. Time-Space perspective: Sound propagation in a
room
2. Frequency-Space perspective: Room modes
3. Time-Frequency perspective
4. Room acoustics design
5. Room acoustics of listening rooms
6. Spatial hearing in a room
Room Acoustics

Alexis Baskind
Perception of distance
• As explained above, the perceived distance to the
sound source depends on:
– The direct-to-reverberant ratio: the softer the direct
sound with respect to reverberation, the farther the
source is localized
– The initial time delay gap: the smaller the ITDG, the
farther the source is localized
– The lateralness of the early reflections: the source is
localized farther if the early reflections come from the
front as if they come from the sides
Room Acoustics

Alexis Baskind
Perception of the room size
• Human Hearing uses two cues to judge the size of a
room:
– The reverberation time is the major parameter
– The time distribution of the early reflections are
considered to provide extra cues, but only in extreme cases
Room Acoustics
A reverberant chamber is a small
but very reverberant room. It’s
meant to simulate big halls, and it
works somehow well, even if the
early reflections are “too” early

Alexis Baskind
Clarity
• The Clarity of a room for a given seat is the ability to
understand the message (usually speech) driven by
the source
• Clarity is known to depend on three factors:
– The quantity of early reflections after the echo threshold
(typically 20-30 ms for percussions, 50-60 ms for speech,
80-100 ms for signals without clear transients): early
echoes can heavily damage the clarity of the sound !
– The direct-to-reverberant ratio: reverberation can partly
mask the direct sound and reduce clarity
– Reflections in the direction of the source damage the clarity
more than lateral reflections (see cocktail-party effect and
comb filtering)
Room Acoustics

Alexis Baskind
Clarity
• Examples (from David Griesinger)
Room Acoustics
• Dry speech
– Note the sound is uncomfortably close
• Mix of dry with early reflections at -5dB.
– The mix has distance (depth), and is not muddy!
– Note there is no apparent reverberation, just depth.
• Same but with the reflections delayed 20ms at -5dB.
– Note also that with the additional delay the reflections begin to be heard as discrete
echos.
• But the apparent distance remains the same.
• Same but with the reflections delayed 50ms at -3dB
– Now the sound is becoming garbled. These reflections are undesirable!
– If the speech were faster it would be difficult to understand.
• Same but with reflections delayed 150ms at -12dB
– I also added a few reflections between 20 and 80ms at a level of -8dB to
smooth the decay.
– Note the strong hall sense, and the lack of muddiness.

Alexis Baskind
Apparent Source Width
• The Apparent Source width corresponds to the
perceived size of the source
• A point source in a non reverberant room will be
perceived as very narrow (equivalent of a
monophonic pan-potted sound)
• The presence of early lateral reflections (before 80-
120ms) blurs the time and intensity cues and creates
a (often pleasant) widening of the perceived source
• The reflections have to be lateral to create this effect.
Frontal reflections only modify the tone color
Room Acoustics

Alexis Baskind
Envelopment
• Envelopment is the sensation of being surrounded by the
diffuse field
• This sensation corresponds to the proportion of late lateral
reflections (after 100-150ms)
Room Acoustics
until ca. 100 ms:
widening
ca. 100-200
ms:
Envelopment
Perception of the room
Time
Perception of the source
Soundpressure
Direct sound
Early reflections
Late reverberation

Alexis Baskind
Reverberation Timbre
• The timbre of the reverberation („dark hall“,
„warm room“, „bright stage“, etc.) depends on the
ratio between reverberation times at low, mid and
high frequencies:
– For a „dark“ room, the reverberation time is relatively
longer at low frequencies
– For a „warm“ room, the reverberation time is relatively
longer at low-mids than at low and high frequencies
– A „bright“ room has similar reverberation times at low
and high frequencies
Room Acoustics