Room Acoustics An Approach Based on Waves and Particles

Transcription

1 5// Roo Acoustics An Approach Based on Waves and Particles Jens Holger Rindel Odeon A/S, Denark Outline Introduction Waves and noral odes in roos Diffuse and non-diffuse sound fields Particles and reflections in roos Diffraction scattering curved surfaces Coputer odelling Speech in roos Music in roos Conclusion

2 5// Introduction Wallace C. Sabine (868 99) Setup for easureent of reverberation tie using four sets of organ pipes 3 Measured decay ties 4

3 5// Measureent results with and 4 organ pipes: Decay ties t 8,69 s t 4 9,55 s Level differences L log, db L 4 log 4 6, db The reverberation tie is the tie for a 6 db decay; thus: T 6 ( t ) 4 t (9,55 8,69) 8,6 s 6, 5 Waves and noral odes Ripple tank odel of an auditoriu (around 99) The wave length is visible 6 3

4 5// 4 7 Modes in a rectangular roo z z y y x x l z n l y n l x n p p π π π cos cos cos p : Sound pressure in the roo (p is axiu) l x, l y, l z : Roo diensions n x, n y, n z : Natural nubers or Relative sound pressure p/p 8 Transfer function in a roo At low frequencies the roo odes ay be identified by peaks at the natural frequencies + + z z y y x x n l n l n l n c f c : Speed of sound (344 /s)

5 5// Noral odes in a roo Bandwidth of the odes, B r T Modal overlap Nuber of odes within the bandwidth of the odes M B r N f 9 Schroeder s liiting frequency Modal overlap should be iniu M 3 for statistical considerations This is fulfilled above the liiting frequency f st T V T : Reverberation tie (s) V : Volue ( 3 ) 5

6 5// Transfer function above f st Measured sine sweep, 9 Hz, A: Reverberant roo, B: Dead roo Average distance between axia in the transfer function depends on the reverberation tie f ax 4 T Ref.: Lyon (969) A: f ax Hz > T s B: f ax.5 Hz > T.5 s Natural frequencies in 3D Frequency space with the odes of in rectangular roo. Volue of /8 sphere: (4 π f 3 / 3) / 8 π f 3 / 6 Volue of one cell: c 3 / (8 l x l y l z ) c 3 / (8 V) Total nuber of odes below f : N π f 3 8V 4π V c 3 c This is only the 3-diensional odes f 3 6

7 5// Noral odes in a roo Modal density dn df 4π V c f π S' + f c + 3 L' 8c dn df 4π V 3 c f The average odal density increases with f V : Volue S : Total surface area L : Total edge length c : Speed of sound, 343 /s f : Centre frequency of band f 3 Particles and reflections Optical light beas in section of a hall. (Satow, 99) 4 7

8 5// Reflection density A rectangular roo with iage sources N( t) π ( ct V 4 ) 3 3 dn t dt 3 c 4π t V The average reflection density increases with t 5 Early and late reflections 3 Suggested transition tie t st V (s) Section V : Volue ( 3 ) Early reflections can (often) be identified Late reflections erge together with high reflection density Sound energy : Direct sound : Early reflections 3: Late reflections Tie 6 8

9 5// Specular and scattered reflection Specular reflections are not a good representation after typically 3rd -4th order reflections (depends on the actual roo) Later reflections are doinated by scattered energy 7 Building a roo - Direct sound 8 9

10 5// One reflecting wall - Echo st order iage source Tie delay 6 s 9 Three walls st and nd order iage sources shown Several echoes

11 5// Six surfaces Up to 3 rd order iage sources shown A sound wave represented by a ray Mean free path in a 3D diffuse sound field: l 4V/ S V : Volue S : Surface area NB: It is assued that all surfaces have the sae absorption coefficient α Energy of sound wave is reduced by (-α ) after each reflection

12 5// Sound pressure after n reflections n p ( t) p ( α ) p e n ln( α ) Total path: i l i c t n l p ( t) p e c ln( α ) t l t T6 p ( t) p 6 e c l ln( α ) T General equation for reverberation tie 6 T ln() c l ln( α ) T 3.8 l 3.8 l c ln( α ) c α 6 3 Reverberation tie equations General: T l 3.8 l c ln( α ) c α 3D: 4 V l S 55.3 V c S ln( α ) 55.3 V c S α D: l π S U x 43.4 Sx c U ln( α ) 43.4 S x c U α D: l l x 3.8 lx c ln( α ) 3.8 l c α x 4

13 5// Eyring and Sabine equations (3D) Special cases for 3D diffuse field and even distribution of absorption Eyring: T V c S ln( α ) More correct for very high absorption, α Sabine: T V c S α Approxiately the sae as Eyring for α <,3 Better when α is different for different surfaces 5 Non-diffuse roos Exaple: Rectangular roo Direction l () α T 6 (s) 3-di. (Sabine) 3-di. (Eyring) di. (horizontal) di. (length) -di. (width) -di. (height)

14 5// The scattering coefficient, s (-s) s Ratio of reflected energy in non-specular directions 7 Siulation with ray tracing Low scattering: s. T 3,69 khz 8 4

15 5// Siulation with ray tracing s.5 T 3,4 khz 9 Siulation with ray tracing s.5 T 3,7 khz 3 5

16 5// Siulation with ray tracing s. T 3,7 khz 3 Non-diffuse roos The sound decay in a roo is a coplicated ixture of the decay of -, -, and 3-diensional odes With uneven distribution of absorption the degree of scattering is very iportant 3 6

17 5// Finite size single reflectors Reflector S Characteristic distance a * a a a + a 33 Kirchhoff-Fresnel approxiation Coordinate syste has Origo in the point of geoetrical reflection Φ Q j 8πλ A e jk ( r+ s) rs ( cos( n, r) cos( n, s) ) d A Q cosθ Φ j e 4πλ a a A jk ( r+ s) d A Diensions of the surface << a and a 34 7

18 5// 8 35 Transforation of variables η θ λ ξ λ + + cos a a v a a u ( ) jn M a a Q j a a jk + Φ + ( ) e 8π Rectangular aperture d d v v v j u u u j v e u e jn M π π ( ) [ ] ( ) [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( v S v S j v C v C u S u S j u C u C jn M 36 Cornu s spiral Result for an infinite large surface: This is taken as the reference for the attenuation due to size ( ) z z v C v d cos ) ( π ( ) z z v S v d sin ) ( π The Fresnel integrals:

19 5// Rectangular reflector Deviation fro geoetrical acoustics: ( K ) L s log K K K ( C( u ) C( u )) + ( S( u ) S( u ) ) ( C( v ) C( v )) + ( S( v ) S( v ) ) ) ) (Two orthogonal sections) λ a ( e ) cosθ v, i b * v i, e * λ a cosθ (corresponds to left edge of plate) (corresponds to right edge of plate) 37 Rectangular reflector Low freq. High freq. 38 9

20 5// Reflection fro finite size surface Angle of incidence 3, a 3., a 3. easureent theory Attenuation below a liiting frequency due to diffraction Frequency, Hz 39 Attenuation due to size siplified odel Design frequency: f g c a * S cosθ Frequency c 344 /s is speed of sound a* is characteristic distance S is area of reflector θ is angle of incidence 4

21 5// Measured directivity of reflection Scattering due to finite size Plane surface Diffusing surface Ref.: M. Kleiner (996) 4 Scattering due to finite size Incident sound Reflected sound Reflected sound intensity in the considered direction I I r sin X siny X ka ( cosα cosα ) r,ax X Y Y kb ( cos β cos β ) 4

22 5// Directivity for angle of incidence α 9,9,8,7 ka /4 ka / ka 3,6,5,4,3,, ka ka 4 ka 8 ka 6 ka 3 Labert 6 9 Angle of radiation 5 8 / octave band 43 Directivity for angle of incidence α 3,9,8,7,6,5 ka /4 ka / ka ka ka 4 3 6,4 ka 8,3,, ka 6 ka 3 Labert 9 Angle of radiation 5 8 / octave band Ref.: Rindel, BNAM (4) 44

23 5// Exaples of diensions and ka Panel size Frequency in Hz a ka /4 ka / ka ka ka 4 ka 8 ka 6 ka 3, , , , , Specular and diffuse reflections Scattering coefficient s: The ratio between the acoustic energy reflected in non-specular directions and the totally reflected acoustic energy Defined in ISO 7497-:

24 5// Typical results of scattering coefficients Ref.: CSTB, France 47 Reflection based scattering coefficient Energy which is not scattered due to diffraction Energy which is not scattered due to roughness S r ( Sd ) ( Ss ) Resulting specular fraction i.e. not scattered due to roughness or diffraction 48 4

25 5// Scattering coefficient due to diffraction, s d Scattered energy Attenuated specular reflection Two cutoff frequencies defined fro length and width of panel, and distance fro source. 49 Reflection based scattering Scattering depends on: size of reflecting surface distance fro the source 5 5

26 5// Roo Geoetry and scattering In a detailed odel the scattering coes autoatically fro the geoetry Odeon Licensed to: Odeon A/S In a siplified odel the scattering coefficients ust be set by the user 55 Siple odel without scattering 5 5 6

27 5// Siple odel with scattering Detailed odel

28 5// Curved reflectors plane convex concave 55 Geoetrical analysis Iage source Iage Receiver Receiver Source R dϕ a d β / cosθ a d β / cosθ L k ( a + a ) d β log ( a + a ) d β 56 8

29 5// Attenuation due to curvature R < (concave) R < (concave) R > (convex) * a L k log + R cosθ a * a a a + a 57 Coputer odelling Schroeder (97) 58 9

30 5// Sound reflection and iage sources One surface Two surfaces st and nd order iage sourcs Potential, but not valid iage source 59 Iage source odel 6 3

31 5// Particle Tracing Model Schroeder (97) 6 Particle tracing 6 3

32 5// Ray Tracing Method P Ray tracing highlighted one ray fro source point Odeon Ray Tracing Method P Ray tracing highlighted one ray fro source point Odeon

33 5// Ray Tracing Method cobined with Visibility Check P Secondary sources created at all reflection points. Each source has tie delay and frequency dependent strength according to Ray Tracing history 65 Ray Tracing Method cobined with Visibility Check P Receiver point collects contributions fro all visible secondary sources 66 33

34 5// Iage Source Method First order reflection - Specular part of reflection: (-α)(-s) receiver 3 Iage source P source α : absorption coefficient s : scattering coefficient 67 Iage Source Method First order reflection - Diffuse part of reflection : (-α)s Many secondary sources distributed over the reflecting surface P source α : absorption coefficient s : scattering coefficient receiver

35 5// Reflection paths including 3 rd order reflections Arrival tie: 6.74 s (. s rel. direct) Level of: -6.6 db (. db rel. direct) Aziuth angle: 9.6, elevation angle:. Reflection:. order,. reflection of 3, source: Reflectogra Elevation Aziuth SPL (db) P , Odeon 985-5,,3,4,5,6,7,8 tie (seconds rel. direct sound),9,,, 63 5 Frequency (Hz) Odeon Head Related Transfer Function (HRTF) Frequency Tie Exaple: Sound incident fro the left Ref.: D. Haershøj (993) 7 35

36 5// Auralisation Anechoic recording, e.g. a trupet Binaural roo ipulse response fro siulation p (%) 5-5 -,,4,6 Left ear,8,,4,6,8 tie (seconds incl. filter delay) Right ear 5 Result of the convolution p (%) -5 -,,4,6,8,,4,6,8 tie (seconds incl. filter delay) Odeon Licensed to: Odeon A/S 7 Auralisation Anechoic recording, e.g. a trupet Binaural roo ipulse response fro siulation p (%) 5-5 -,,4,6 Left ear,8,,4,6,8 tie (seconds incl. filter delay) Right ear 5 Result of the convolution p (%) -5 -,,4,6,8,,4,6,8 tie (seconds incl. filter delay) Odeon Licensed to: Odeon A/S 7 36

37 5// Auralisation Anechoic recording, e.g. a trupet Binaural roo ipulse response fro siulation p (%) 5-5 -,,4,6 Left ear,8,,4,6,8 tie (seconds incl. filter delay) Right ear 5 Result of the convolution p (%) -5 -,,4,6,8,,4,6,8 tie (seconds incl. filter delay) Odeon Licensed to: Odeon A/S 73 Auralisation Anechoic recording, e.g. a trupet Binaural roo ipulse response fro siulation p (%) 5-5 -,,4,6 Left ear,8,,4,6,8 tie (seconds incl. filter delay) Right ear 5 Result of the convolution p (%) -5 -,,4,6,8,,4,6,8 tie (seconds incl. filter delay) Odeon Licensed to: Odeon A/S 74 37

38 5// Speech in roos Vocal counication and abient noise 75 The Lobard effect Vocal effort, ISO 99:3 Speech level ( ) db(a) Relaxed Noral Raised Loud Very loud Shouting Abient noise level, db(a) 76 38

39 5// Theoretical odel Abient noise level fro speech, assuing a diffuse sound field, equivalent absorption area A, and nuber of persons speaking at the sae tie N S : log, A L N A c c N S (db) Where c is the Lobard slope. With c.5 db/db we get: A 93 log, L N A NS (db) NB: Double A > - 6 db. Double N S > + 6 db. 77 Food court, V 333 3, T.9 s 85 8 Noise level, db(a) 75 7 Calculated Measured 65 g 3 persons per speaking person Nuber of people Measureents: Navarro & Pientel (7), Applied Acoustics 68, pp Calculations: Rindel, accepted for Applied Acoustics () 78 39

40 5// Noise level and speech level 9 8 db(a) 7 6 Paraeter c,5 db/db Noise level Speech level, Absorption area () / Nuber of speaking persons 79 Open plan office new paraeters ISO/DIS Acoustics Measureent of roo acoustic paraeters Part 3: Open plan spaces Spatial sound distribution of STI (Speech Transission Index) Distraction distance: r D (distance fro a speaker where STI falls below,5) Privacy distance: r P (distance fro a speaker where STI falls below,) 8 4

41 5// Open plan office new paraeters With background noise 35 dba Distraction distance: r D 9.9 Privacy distance: r P.8 Ref.: Vironen et al. (9) 8 Music in roos 8 4

42 5// Roo acoustic paraeters Measureent ethod: ISO 338-:9 Subjective listener aspect Subjective level of sound Perceived reverberance Perceived clarity of sound Apparent Source Width, ASW Acoustic quantity Sound Strength, G, in db Early Decay Tie, EDT, in s Clarity, C 8, in db Definition, D Centre Tie, T S, in s Early Lateral Energy Fraction, LF Listener Envelopent, LEV Late Lateral Sound Level, LG, in db Inter Aural Cross Correlation, IACC 83 DR Concert Hall, Copenhagen Architect: Jean Nouvel Acoustics: Toyota, Nagata Acoustics 8 seats, 8. 3 RT, khz (with audience) Opened Jan

43 5// Musical instruents for Mahler s st Syphony Instruent Nuber of sources Nuber of Recordings Directional characteristic st violin 6 Violin nd violin 4 Violin Viola Violin Cello Oni Double bass 8 Oni Flute 4 Oni Oboe 4 4 B-Clarinet Clarinet 5 4 B-Clarinet Bassoon 3 3 B-Clarinet French horn 7 7 French horn Trupet 4 4 Trupet Trobone 3 3 Trupet Tuba Oni Percussion 4 4 Oni Total Coputer odel Odeon Licensed to: Odeon A/S Orchestra setup with 95 sources 86 43

44 5// Tutti Position R Odeon Licensed to: Odeon A/S 8787 Brass only Position R

45 5// Acknowledgeents to orchestra siulation The anechoic recordings of the Mahler Syphony were ade by Jukka Pätynen, Ville Pulkki, and Tapio Lokki fro Helsinki University of Technology with usicians fro various Finnish orchestras The directional characteristics were easured by Felipe Otondo (DOREMI project) The Odeon odel of the concert hall was delivered by Dr. A.C. Gade 89 Conclusion Particle tracing and ray tracing are very efficient for roo acoustic siulations, if cobined with wave-based odels for scattering and diffraction There is a need for good wave-based siulation odels for sall roos and low frequencies (proising results have appeared with the finite difference tie doain ethod, FDTD) 9 45