Akustik und Schallforschung - oeaw.ac.at · 2020. 10. 2. · ANSI/ASA S1.1-2013 Standard: (a)...
Transcript of Akustik und Schallforschung - oeaw.ac.at · 2020. 10. 2. · ANSI/ASA S1.1-2013 Standard: (a)...
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Akustik undSchallforschungWolfgang KreuzerOctober 2, 2020
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Ausblick
Was ist Akustik/Schall/Lärm ?GrundbegriffeBeispiele und Modelle aus:
Signalverarbeitung (Fourier, Kurzzeitfourier, Spektrogramm)1D-Schwingung, 1D-Wellengleichung/Helmholtz (Saite,Vokaltraktmodell)Erweiterung auf 2D, 2.5D, 3D, FEM-BEM
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Was ist Akustik?
Duden: Lehre vom Schall
ANSI/ASA S1.1-2013 Standard: (a) Science of sound, including itsproduction, transmission, and effects, including biological andpsychological effects, (b) Those qualities of a room that, together,determine its caracter with respect to auditory effects
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Was umfasst der Begriff’Akustik’?
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Akustik
Die interdisziplinäre Akustik
ARTS
LIFE
SCIENCES
ACOUSTICS
PS
YC
HO
AC
OU
ST
ICS
INSTRUMENTS
ROOM ACOUSTICS
SHOCK
ANDVIBRATION
ELECTRO
ACOUSTICS
CO
MP
UT
AT
ION
AL
AC
OU
ST
ICS
NON-INVASIVE
PHYSIOLOGY
PHOTOA
COUST
IC
IMAGIN
G
SEISMIC WAVES
UNDERWATER
OTHERS
MEDICIN
E
BIOLOGY
PS
YC
HO
LOG
Y
HU
MA
N
CO
MM
UN
ICATIO
N
MUSIC
MULTIMODAL
ARCHITECTURE
ME
CH
AN
ICA
LA
ND
PH
YS
ICA
LE
NG
INE
ER
ING
ELECTRICAL
AND CHEMICAL
ENGINEERING
OTHERS
SOCIAL
SCIENCES
PHYSICSAND
ENGINEERING
EARTHSCIENCES
SPEECH
PRO
DU
CTIO
N
SPEECH
PERCEPTION
MATH
EMATIC
S
AC
OU
STICAL
SIG
NAL
PR
OC
ESS
ING E
NVIRONMENTAL
NOISE
AUDIO
ENGINEERING
CO
MP
UT
ER
SC
IEN
CE
FORMAL
PHYSICS OF
EARTH, OCEAN,
AND ATMOSPHERE
SOUND INATMOSPHERE
SINGING
MUSIC THEORY
BIOACOUSTICS
INVASIVE
PHYSIOLOGY
ULTRASOUNDQ
UANTUM
ACOUSTICS
Vielen Dank an Piotr Majdak
WHEEL OF ARI
Frei nach: Lindsay, J. Acoust. Soc. Am. 37(2), 361, (1965)
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Akustik
Die interdisziplinäre Akustik
ARTS
LIFE
SCIENCES
ACOUSTICS
PS
YC
HO
AC
OU
ST
ICS
INSTRUMENTS
ROOM ACOUSTICS
SHOCK
ANDVIBRATION
ELECTRO
ACOUSTICS
CO
MP
UT
AT
ION
AL
AC
OU
ST
ICS
NON-INVASIVE
PHYSIOLOGY
PHOTOA
COUST
IC
IMAGIN
G
SEISMIC WAVES
UNDERWATER
OTHERS
MEDICIN
E
BIOLOGY
PS
YC
HO
LOG
Y
HU
MA
N
CO
MM
UN
ICATIO
N
MUSIC
MULTIMODAL
ARCHITECTURE
ME
CH
AN
ICA
LA
ND
PH
YS
ICA
LE
NG
INE
ER
ING
ELECTRICAL
AND CHEMICAL
ENGINEERING
OTHERS
SOCIAL
SCIENCES
PHYSICSAND
ENGINEERING
EARTHSCIENCES
SPEECH
PRO
DU
CTIO
N
SPEECH
PERCEPTION
MATH
EMATIC
S
AC
OU
STICAL
SIG
NAL
PR
OC
ESS
ING E
NVIRONMENTAL
NOISE
AUDIO
ENGINEERING
CO
MP
UT
ER
SC
IEN
CE
FORMAL
PHYSICS OF
EARTH, OCEAN,
AND ATMOSPHERE
SOUND INATMOSPHERE
SINGING
MUSIC THEORY
BIOACOUSTICS
INVASIVE
PHYSIOLOGY
ULTRASOUNDQ
UANTUM
ACOUSTICS
Vielen Dank an Piotr Majdak
WHEEL OF ARI
Frei nach: Lindsay, J. Acoust. Soc. Am. 37(2), 361, (1965)
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Akustik
Die interdisziplinäre Akustik
ARTS
LIFE
SCIENCES
ACOUSTICS
PS
YC
HO
AC
OU
ST
ICS
INSTRUMENTS
ROOM ACOUSTICS
SHOCK
ANDVIBRATION
ELECTRO
ACOUSTICS
CO
MP
UT
AT
ION
AL
AC
OU
ST
ICS
NON-INVASIVE
PHYSIOLOGY
PHOTOA
COUST
IC
IMAGIN
G
SEISMIC WAVES
UNDERWATER
OTHERS
MEDICIN
E
BIOLOGY
PS
YC
HO
LOG
Y
HU
MA
N
CO
MM
UN
ICATIO
N
MUSIC
MULTIMODAL
ARCHITECTURE
ME
CH
AN
ICA
LA
ND
PH
YS
ICA
LE
NG
INE
ER
ING
ELECTRICAL
AND CHEMICAL
ENGINEERING
OTHERS
SOCIAL
SCIENCES
PHYSICSAND
ENGINEERING
EARTHSCIENCES
SPEECH
PRO
DU
CTIO
N
SPEECH
PERCEPTION
MATH
EMATIC
S
AC
OU
STICAL
SIG
NAL
PR
OC
ESS
ING E
NVIRONMENTAL
NOISE
AUDIO
ENGINEERING
CO
MP
UT
ER
SC
IEN
CE
FORMAL
PHYSICS OF
EARTH, OCEAN,
AND ATMOSPHERE
SOUND INATMOSPHERE
SINGING
MUSIC THEORY
BIOACOUSTICS
INVASIVE
PHYSIOLOGY
ULTRASOUNDQ
UANTUM
ACOUSTICS
Vielen Dank an Piotr Majdak
WHEEL OF ARI
Frei nach: Lindsay, J. Acoust. Soc. Am. 37(2), 361, (1965)
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Das Institut für Schallforschung
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Geschichte
Pythagoras (um 550 BC): Schwingende SaiteAristoteles (um 350 BC): Schall als Verdichtung andVerdünnung (von Luft)Vitruvius (um 20 BC): Raumakustik und ArchitekturHuygens: Schall als WellenphänomenBernouli, D’Alembert, Euler, Lagrange (um 1750-1800), Eulerpubliziert Wellengleichung, Chladni visualisiert PlattenmodenHelmholtz (um 1850, Über die Tonempfindung), Rayleigh (um1900, Theory of Sound)
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Was ist Schall?
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Was ist Schall?
Schall stellt die Ausbreitung bzw. die hörbaren Schwingungen(Schallwellen) von Druck- und Dichteschwankungen in einemelastischen Medium (Gase, Flüssigkeiten, Festkörper) dar.1
Luftschallwellen setzen sich aus abwechselnden Regionen mithohem und geringen Luftdruck zusammen, die sich mit einerbestimmten Geschwindigkeit ausbreiten
1https://de.wikipedia.org/wiki/SchallKreiza (ÖAW) Acoustics October 2, 2020 9 / 33
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Grundbegriffe
p(t,x) =Asin(kx−ωt+φ)
A: Amplitude/Schalldruck p(x)Einheit: Pascal [Pa]f = ω
2π = ck2π : Frequenz
Einheit: Hertz [Hz], Schwingungenpro Sekundeλ= c
f : WellenlängeEinheit [m]φ: Phase [rad]c: SchallgeschwindigkeitEinheit [m/s]
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Grundbegriffe (Mechanik)
Geschwindigkeitspotential (Velocity potential): u(x, t)
Schalldruck: p(x, t) = ∂u(x,t)∂t
Schallschnelle: v(x, t) =∇u(x, t) ·n(x)
B Schallgeschwindigkeit 6= Schallschnelle B
Schallgeschwindigkeit c: globale Geschwindigkeit derDruckwelle
Ï Schallschnelle v(x): lokale Geschwindigkeit einesTeilchen(pakets)
Ï Impedanz: Z(ω) = p̂(ω)v̂(ω) , wobei f̂ (ω) die Fouriertransformierte
von f (t) bezeichnet
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Amplitude
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Amplitude
from http://www.chartvalley.com/decibel-scale-chart
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Amplitude
Ein kleines Ratespiel
Normale Luftdruck auf Seehöhe: pa = 105 Pa.Kleinste Luftdruckschwankung, die das Ohr registriert?
p0 = 2 ·10−5 Pa = 0 dB SPLAb wann wird es wirklich laut:
p1 = 10 Pa ≈ 113 dB SPL
1dB= 20 log10
(pp0
)
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Amplitude
Ein kleines Ratespiel
Normale Luftdruck auf Seehöhe: pa = 105 Pa.Kleinste Luftdruckschwankung, die das Ohr registriert?
p0 = 2 ·10−5 Pa corresponds to 0 dB SPLAb wann wird es wirklich laut:
p1 = 10 Pa ≈ 113 dB SPL
1dB= 20 log10
(pp0
)
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Amplitude
Ein kleines Ratespiel
Normale Luftdruck auf Seehöhe: pa = 105 Pa.Kleinste Luftdruckschwankung, die das Ohr registriert?
p0 = 2 ·10−5 Pa corresponds to 0 dB SPLAb wann wird es wirklich laut:
p1 = 10 Pa corresponds to ≈ 113 dB SPL
1dB= 20 log10
(pp0
)
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Isophone
Doppelter Schalldruck: ≈ 6dB, aberdoppelt empfundene Lautheit: ≈ 10dB
1 Sone entspricht doppelter LautheitAußerdem werden verschiedene Frequenzen verschieden lautwahrgenommen (Phon)
https://commons.wikimedia.org/wiki/File:Akustik_db2phon.jpg,
https://de.wikipedia.org/wiki/Lautst%C3%A4rke#/media/Datei:Akustik_phon2sone3.jpg
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Frequenz, Tonhöhe
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Frequenz
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Frequenz
Mel/Bark Skala: Abbildung der “akustischen” Frequenz auf diewahrgenommene Frequenz
fMel = 2595 log10(10(1+ f /700)),1 Bark= 100 Mel
Verdoppelung des Bark Werts, verdoppelteTonhöhenwahrnehmung.Kritische Bandbreite: 2 simultan präsentierte Tönen könnennicht als zwei verschiedene Töne wahrgenommen werden
BWcritical = 25+75(1+1.4(f /1000)2
)0.69
Frequenzunterscheidung3.5Hz für ∆f ≤ 500Hz∆f ≈ 0.0007f für f > 500Hz
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Wellenlänge
λ= cf
Wichtig z.B für Schwingung einer Seite oder Schallreflexion anObjekten
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Phase
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Phase
Addition von Sinustönen mit gleicher Frequenz
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Phase
Kombination von Schallquellen
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Phase
Lokalisation von Schallquellen (I):Zeitunterschied zwischen Empfängern
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Zusammenfassend
Schall entsteht durch Druckschwankungen im Medium undbreitet sich mittels eine longitudinal Welle (mitSchallgeschwindigkeit c) ausWichtige Kenngrößen
Schalldruck
Frequenz
Phase
Schnellepotential (velocitypotential)
Schallschnelle
Wellenzahl und Wellenlänge
Impedanz/Admittanz
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Wahrnehmung
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Menschliches Gehör
PinnaMittelohrCochlea
Blausen.com staff (2014). "Medical gallery of Blausen Medical 2014". WikiJournal of Medicine 1 (2).
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Die Menschliche Pinna
Lokalisation von Schallquellen
Quelle oben
Quelle vorne
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HRTFs
Reflexionen von Schall an der Pinna wirkt wie einrichtungsabhängiger FilterKopfbezogene Übertragungsfunktionen (HRTFs)
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Lokalisation von Schallquellen
HorizontalZeitdifferenz zwischen rechtemund linkem Ohr (ITD)Unterschied in derAmplitude/Level (ILD)
VertikalSpektrale Cues also HRTFs
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Die Menschliche Cochlea
Basilarmembran:Frequenzanalyse, nichtlinearInnere Haarzellen:Bewegung wird in neuronaleAntwort umgewandeltÄußere Haarzellen: aktivesElement, nichtlineareVerstärkung von leisemSchall https://commons.wikimedia.org/wiki/File:Cochlea-
crosssection-de.png
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Psychoakustik
Hören wir alle Komponenten im Schall?Zeit/FrequenzmaskierungIrrelevance FiltersDatenkomprimierung (ogg, mp3, ...)
Hören wir etwas, das nicht da ist?Residualton/Missing FundamentalAuditorische Illusionen
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Darstellung
Wie können wir Schall darstellen?
1) Wellenform (Zeitbereich)
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Darstellung
Wie können wir Schall darstellen?
2) Spektrum (Frequenzbereich)
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Darstellung
Wie können wir Schall darstellen?
3) Das gute alte Notenblatt (Zeit-Frequenzebene)
https://www.freejazzlessons.com/wp-content/uploads/2013/04/summertime-chord-chart-lead-sheet.jpg
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Darstellung
Wie können wir Schall darstellen?
4) Spectrogram (Zeit-Frequenzebene)
44
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Verschiedene Instrumente
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Verschiedene Instrumente
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