Download PDF - 1.84 Mo

C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
The decibel (1/2)
dB
9 The sensitivity of human ear depends
on the frequency
9 The auditive sense is proportional to
the logarithm of the acoustical
intensity I of the wave
with I s = 10
W.m
120
100
80
60
40
−2
20
ULTRASOUNDS
INFRASOUNDS
Chapter 2
( )
L = 10 log 10 I I s
−12
Threshold of pain
140
Audible area
Speech
Threshold of audibility
0
1 Hz
20 Hz
1 kHz 2 kHz
20 kHz
frequency
The unit for the sound level is the decibel (dB) (one tenth
of a bel), named like this in honour of the physicist
Alexandre Graham Bell. This unit has the advantage of
being based very well on the differential sensitivity of
human ear, since 1 dB gap between two sound levels
substantially corresponds to the smallest difference (in
sound level) detectable by the human ear.
Physiological acoustics,
decibel
Alexandre Graham Bell
(1847-1922, american inventor)
http://en.wikipedia.org/wiki/Alexandre_Graham_Bell
Sound levels (1/2)
Sound levels (2/2)
z Sound level which results from two non-correlated sources
dB
9 The sensitivity of human ear depends
on the frequency
9 The auditive sense is proportional to
the logarithm of the acoustical
intensity I of the wave
( )
L = 10 log 10 I I s
INFRASOUNDS
140
120
100
80
60
40
20
with I s = 10
−12
W.m
(
r
p r m s (r ) =
20 Hz
(
⎛ I1 + I 2 ⎞
⎟ = 10 log 10 10 L 1 10 + 10 L 2
L res = 10 log 10 ⎜
⎜ Is ⎟
⎝
⎠
)
[p(rr ; t )] 2
20 kHz
[p(rr ; t )] 2
PE
)
3
2.5
frequency
p s = ρ 0 c 0 I s = 400 ⋅10 −12 = 2 ⋅10 −5 Pa
with
10
Lres-L1 (dB)
1 kHz 2 kHz
averages over time, over an acoustic period T:
r
r
r
r r r
∀r
p (r ) = 0
v (r ) = 0 ρ (r ) = 0
p
T
Speech
0
L = 20 log 10 p r m s p s
Ptot
Audible area
Threshold of audibility
−2
1 Hz
I ∝ p 2rms
ULTRASOUNDS
Threshold of pain
1⌠
⎮
T →∞ T ⎮
⌡
1.5
1
+T 2
[p(rr ; t )] 2 d t
= lim
2
−T 2
0.5
L2-L1 (dB)
[p(rr ; t )] 2 ≠ [p(rr ; t )]
time (s)
2
Acoustic pressure level
dB
140 threshold of pain
100 000 000
130
rjet engine
(distance: 25 m)
10 000 000
110
100
pop band
take-off
(distance: 100 m)
120
1 000 000
pneumatic drill
90
80
truck
100 000
road traffic
-10
(
-9
-8
)
L res = L res − L 1 + L 1
The decibel
Acoustic pressure
µPa
0
-7
-6
with
-5
-4
-3
(
-2
-1
L res − L 1 = 10 log 10 1 + 10
(L 2 −L 1 ) 10
)
0
Equal loudness contours
Pa
pressure level Lp (dB)
dB
200
20
2
0,2
0,02
0,002
0,0002
0,00002
threshold of pain
140
120
100
80
60
40
20
0
70
speech
60
10 000
office
50
40
1 000
living room
= 2 X
43 dB
30
library
threshold of audibility
20
100
10
mountain
bedroom
+
40 dB and 40 dB =
20
0 threshold of audibility
noise
bruit
=
+
40 dB and
140 dB
=
frequency (Hz)
loudness: subjective intensity of a sound; unit: the phon
140 dB
Example: A 70 phons sound provokes the same auditive perception than a 1000
Hz sound, the physical level of which is 70 dB
1
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
A weighting curves: dB(A)
Structure of human ear
high pitch and low pitch sounds
malleus
temporal lobe
of brain
incus
semi-circular
canals
oval window
auditory nerve
are less perceived
cochlea
pinna
temporal
bone
auditory canal
eardrum
eustachian
tube
stapes
circular
window
Outer ear
Middle ear
Inner ear
Ossicles
The tympanic membrane (eardrum)
incus
stapes
malleus
From Robier
Transfer of acoustic pressures (sonic waves) from air medium to fluid
media and to inner ear structures (cochlea)
incus
malleus
"small" displacement (not very compressible liquid)
strength "higher" and S smaller
==> higher pressure
Transfer of acoustic pressures (sonic waves) from air medium to fluid
media and to inner ear structures (cochlea) - animation
The sound wave moves the eardrum and attached ossicular chain. The stapes footplate, in the
oval window, transfers the vibrations to the perilymphatic compartment (scala vestibuli) and to
the inner ear structures. Depending on the frequency, the vibration has a maximum effect
(resonance) at a different point along the basilar membrane, accounting for passive tonotopy.
stapes
stapes
pivot
ossicles
eardrum
eardrum
"large" displacement (compressible gas)
"less large" strength and greater S
==> smaller pressure
a high frequency sound affects a
basal portion of the cochlea
a low frequency sound affects a more apical
part of the cochlea
Text and images from website "Promenade 'round the cochlea" (http://www.cochlee.info)
by R Pujol et al., Université Montpellier 1 et INSERM - France
http://www.iurc.montp.inserm.fr/cric51/audition/fran%E7ais/ear/fear.htm
2
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
Schematic functioning of the eardrum
Cochlea - Organ of Corti - Hair cells
scala vestibuli
ear
cochlear
tunnel
eardrum
outer hair
cells
organ of
Corti
scala tympani
inner hair
cells
nose
healthy cells
equilibrium of pressures
damaged cells
nerve fibers
of the
auditory
nerve
http://ile-de-france.sante.gouv.fr/santenv/bruit/notions/celcil.htm
http://ile-de-france.sante.gouv.fr/santenv/bruit/notions/corti.htm
Hair cells
Audiograms
Hearing loss (dB)
Hearing frequency (Hz)
Too much silence?
z Danger
9 at work (wearing of hard hat)
9 in the streets (noiseless vehicles)
z Deprivation of sound information
9 noise of an engine
9 functioning of a machine
9 lack of pleasantness (the good noise!)
normal hearing
hearing loss reaches 2000 Hz
hearing loss at 4000 Hz
important or irreversible
deafness
Sound levels - Noise annoyance
The audible sounds range from 0 dB (threshold of
hearing) and 140 dB. The threshold of pain is
around 120 dB. Annoyance, which is a subjective
concept, is felt with a great variability from one
person to another.
Consequently, no objective noise level can give
an absolute indication of the annoyance.
z Discomfort
9 public transports (train)
9 open-plan offices
http://www.acnusa.fr/bruit_et_mesure/bruit_et_mes_echelle.asp
3
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
Terrestrian transports
Noise contour maps (Paris - France)
Exposure of population to roadway noise:
number of road black points
Leq ≥ 70 dB(A) between 8 h -20 h
Nord
Pas-de-Calais
Picardie
Haute
Normandie
Lorraine
Ile
de-France
Basse
Normandie
Bretagne
Champagne
Ardenne
Alsace
Pays-de-Loire
Centre
Bourgogne
Franche
Comté
Poitou
Charentes
Limousin
Rhône-Alpes
Auvergne
100
From data bank of LRPC Strasbourg
- France (results 1998)
Aquitaine
Provence
Alpes
Côte d'Azur
1st district
Midi-Pyrénées
Languedoc
Roussillon
16th district
www.paris.fr/FR/Environnement/bruit/carto_bruit/default.ASP
French noise annoying plan
(plan de gène sonore - PGS in french)
French noise annoying plan
(plan de gène sonore - PGS in french)
Document provided by French law 92-1444 of 31
December 1992 (Article 19) which permits to define the
areas in which residents are eligible for assistance for
soundproofing.
Roissy CDG Airport (1999)
http://www.adp.fr/labo/web/surenv/bruit/index.html
French noise exposure plan
(plan d'exposition au bruit - PEB in french)
French noise exposure plan
(plan d'exposition au bruit - PEB in french)
Orly
Orly- France
Document provided by the French law 85-696 of 11th
July 1985 which regulates urbanism near airports so as
not to expose new populations to noise annoyance.
Specific measures can take into account the specificities
of the pre-existing context.
Orly airport
Precautionary principle
http://www.adp.fr/labo/web/surenv/bruit/index.html
4
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
Example of solution: traffic management
(noise mitigation)
PEB - PGS: merger?
z Maximum number aircrafts movements
(Orly airport : 200.000 per year)
z Time of day restrictions (Orly airport : 7 am to 11 pm)
z Choice of air lanes
z Departure flight path and slope
An french interministerial working group studied the
question of bringing together the procedures relating to
the noise exposure and noise annoying plans in France.
A report released in December 2007 weighs the
advantages and disavantages of a merger of the two
zonings, and makes proposals.
or
Report of the working group « Rapprochement des procédures PEB et PGS » - report
n°004577-01 - june 2007 (format pdf - 784,9 Ko) - Authors : Gilles Rouques (CGPC) and
Annick Helias (IGE)
http://publications.ecologie.gouv.fr/publications/IMG/pdf/Rapport_GT_Rapprochement_PE
B_et_PGS.pdf
Perception and room acoustics (1/10)
Perception and room acoustics (2/10)
z Sounds
z Perception
3 Location: comparison by the brain of
• intensities
• times of arrival
3 noise (annoyance, alert function)
3 speech (intelligibility)
3 music (esthetic)
organization of sounds
• time (rythm, melody)
• spatial (fill the space)
- visually
space
- auditively
to the two ears
3 Attributes:
perceived
• monaural hearing
• binaural hearing
loundness, pitch, timbre
(timbre), soundscape
∆L d B
∆t ms
0dB
0 ms
3 spectrum
3 intensity
3 duration
3 Continuous: formants for the voice
3 Transient: consonants, musical attack
Perception and room acoustics (3/10)
z The sound space
3 Location of one source
• binaural
• pinna
• scattering
0dB
0 ms
3 Location of two sources
• coherent sources: impossible
• non coherent sources: distinct
Perception and room acoustics (4/10)
∆L d B
∆t ms
z Soundscape: intelligibility and noise
3 Noise masking speech
• Example: pernicious effect of reverberation
3 Reverberation which permits to the speaker to hear himself
3 Too high reverberation: tiredness
| h(t) |
3 Delay between two coherent sources
• summation effect (~ 1ms)
• precedence effect (loudness + space effect)
• space effect (3D)
3 These three effects can be simultaneously perceived
(reflections in a room)
3 Large number of reflections, late effects: reverberation
≈ 100 ms
straightforward
sound
1st (geometrical)
reflections
time
reverberation
(statistics)
5
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
Perception and room acoustics (5/10)
z Soundscape, room acoustics (2/6)
z Soundscape, room acoustics (1/6)
¾ Expectation of the listener
¾ Expectation of the performer
Perception and room acoustics (6/10)
¾ Listeners
blooming, esthetic pleasure
interpretation of music
Sonorous sound
Orchestra: 10 to 100 W (in facts < 110 dB)
9 good distribution of sound energy
9 increase the number of reflections
The listener try to:
9 benefit from a sonorous sound (avoid tiredness)
9 make the most of his two ears (space effect)
9 well understand music (but small "fuzziness")
9 have a good adjustment of tones (instrumental
equilibrium, tonal equilibrium, …)
increase the volume of the room (6 to 11 m3 per listener)
Use of the two ears
9 initial side reflections (close to the listener)
improve the clarity
Good understanding
9 limited reverberation (compromise with sonorousness)
Moreover, the musician try to:
9 well listen what he is playing
9 have a good contact with other musicians
favor the small "fuzziness"
Good adjustement of tones (delicate)
9 avoid front reflectors (above and behind the
orchestra),
coloration
if the reflector are present, split them
Perception and room acoustics (7/10)
z Soundscape, room acoustics (3/6)
Perception and room acoustics (8/10)
z Soundscape, room acoustics (4/6)
¾ Impulse response
¾ Musicians
p r (t ) = h (t )* p anechoic (t )
listen what they are playing
9 return of sound towards stage
9 good coupling stage / room
good contact between them
9 reflectors above the orchestra
| h(t) |
¾ The room
Room acoustics ≡ question of geometry
9 arrangement of volumes
9 arrangement of walls
• contact listeners / musicians
• coupling stage / room
≈ 100 ms
straightforward
sound
1st (geometrical)
reflections
time
reverberation
(statistics)
Absorbant acoustical treatment does not improve anything
9 (permits eventually to remove some echoes)
Perception and room acoustics (9/10)
z Soundscape, room acoustics (5/6)
¾ Subjective characterization
9
9
9
9
9
9
9
9
Reverberation
Clarity
Loudness
Intimacy
Uniformity
Diffusion
Envelopment
Performer's satisfaction
¾ Questionnaire
¾ Binaural hearing
9 numerical simulation, scale model
Perception and room acoustics (10/10)
z Soundscape, room acoustics (6/6)
¾ Objective characterization (examples)
9 sound amplitude
9 reverberation duration at -60 dB
9 early decay time (1st reflections)
9 timbre
⎛
⎜ ⌠ 80 ms
10 log10 ⎜ ⎮ p 2 (t ) d t
⎜⎜ ⌡ 0
⎝
⎡ ⎛ 5000 Hz
⎢ ⎜⌠
10 log10 ⎢ ⎜ ⎮
M(f ) d f
⎢ ⎜⎜ ⌡ 500 Hz
⎣⎝
⎞
⎟
4500 ⎟
⎟⎟
⎠
⎛
⎜
10 log10 ⎜
⎜⎜
⎝
∞
⌠ 2
2
⎮ p (t ) d t p ref
⎮
⌡0
⎞
⎟
⎟
⎟⎟
⎠
⎞
∞
⎟
⌠
2
⎮ p (t ) d t ⎟
⎟⎟
⌡ 80
⎠
⎛ 500 Hz
⎜⌠
⎜⎮
M(f ) d f
⎜⎜ ⌡ 50 Hz
⎝
⎞
⎟
450 ⎟
⎟⎟
⎠
⎤
⎥
⎥
⎥
⎦
¾ Numerical simulation
¾ Scale model
6
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
Example of mistakes (1/2)
large movie projection screen on
a perfectly reflecting wall
McKinnon Theater, Kettering University, Flint, MI
Example of mistakes (2/2)
z flutter echo
succesive echoes
large movie projection screen on
a perfectly reflecting wall
400 seats
http://www.kettering.edu/acad/scimath/physics/acoustics/McKinnon/McKinnon.html
McKinnon Theater, Kettering University, Flint, MI
http://www.kettering.edu/acad/scimath/physics/acoustics/McKinnon/McKinnon.html
Animation courtesy of Dr. Dan Russell, Kettering University
7
C. Potel, M. Bruneau, "Acoustique générale (...)", Ed. Ellipse, collection Technosup, ISBN 2-7298-2805-2, 2006
Slides based upon
C. POTEL, M. BRUNEAU, Acoustique Générale - équations
différentielles et intégrales, solutions en milieux fluide et solide,
applications, Ed. Ellipse collection Technosup, 352 pages,
ISBN 2-7298-2805-2, 2006
8