Auditorium & Room Acoustics

Transcription

1 UIUC Phyic 406 Acoutical Phyic of Muic Auditoriu & Roo Acoutic Sound out in the open, ditance r away fro ound ource: Free Field r Sound Intenity I () r = Power 4pr ound ource: r Intenity, I in Watt/ (ince SI unit of Power are Watt) Sound propagation direction Sound intenity I(r) decreae a 1 r, pread out radially in all direction fro ound ource * Sound Intenity Level, LI (r) = 10log10(I(r)/Io) decreae by 6 db for every doubling of r. * Ground (gra, weed, buhe, etc.) aborb ound ound level LI (r) fall off fater than 1 r (LI (r) fall off ore teeply than 6 db) * Put a reflecting urface behind uician for focuing ound to audience * Confined ound in an encloure (e.g. a roo): Get ound reflection off of all wall (jut like light bouncing off of irror) Angle of incidence = Angle of reflection Law of reflection (light and/or ound) arie fro energy/oentu conervation at wall/irror!) Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

2 UIUC Phyic 406 Acoutical Phyic of Muic Reverberation/Reverberant Sound: Totality of ound = direct ound, ultiple echoe and clutter Reverberation Tie, T = tie for ound to decay to 10 6 (one illionth) of it original intenity, I. 6 L10log I I 10log db. Correponding change in Loudne Level/SPL: Hence, reverberation tie T i alo known a T60. Reverberation Tie, T µ (= proportional to) roo volue, V - ie.. T µ V Reverberation Tie, T µ 1 Area of hole() in roo, A T µ 1 A Sabine Equation: V A T = K where K = contant of proportionality= T A V If we know V and A and then eaure T, we find K=0.049 ec/ft (= univeral nuber!!!) - - Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

3 UIUC Phyic 406 Acoutical Phyic of Muic Sabine Equation V = Roo volue in ft 3 ( 3 ) V T = K (econd) A A = hole area in ft ( ) K = in ec/ft (= ec/) ( ) ( ) æ 3 3 V ft ö æ V ö Reverberation Tie, T = T60 = = econd A( ft ) A( ) çè ø çè ø = tie for ound to decay to 10-6 of it original intenity. If the roo ha NO hole in it, the area A phyically repreent the effective area of the roo that behave a if it were a hole, due to ound aborption. 1 ft =1 aborption unit Suppoe a roo with volue V ha a urface area S ade up of ae aterial on all 6 ide: Stop S3 S S4 S1 Sbotto Total urface area of roo S: area of ide area of top and botto S = S1 + S + S3 + S4 + Stop + Sbotto A = as A a º S a aborption coefficient, 0 a 1 a = 0 no ound aborption (no hole, i.e. A = 0) a = 1 total ound aborption ( hole = roo area, i.e. A = S!!!) Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

4 UIUC Phyic 406 Acoutical Phyic of Muic For a ore coplicated/realitic roo: N = N = å n n= 1 N = N N = å n= 1 A A A A A A A as a S as a S a S a S n n for N object (urface) in roo. The Optiu Reverberation Tie: * If reverberation tie i too hort, roo ound dead * If reverberation tie i too long, roo ound uddled/obcured Max Intenity Iax = PA, where P (Watt) = acoutic power of ound ource and A = total aborption (eaured in quare eter). Suppoe e.g. we input P = 1 Watt of acoutic power into a roo, allow tie for the ound to build up to a teady level, and then ue an SPL eter, i.e. a device to eaure the ax SPL (in db) in the roo. Suppoe we find (i.e. we eaure) ax db = We then invert the db forula: ax db = 10log10(Iax/Io) to obtain: Iax = Io = W/. Thu: A P = = Iax 1 Watt W = 110 quare eter 100 quare ft (= 100 aborption unit) Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

5 UIUC Phyic 406 Acoutical Phyic of Muic The Optiu Reverberation Tie: Optiu reverberation tie i ubjective! tepo dependent ound level dependent coplexity dependent frequency dependent Calculation of Reverberation Tie Note frequency the dependence of aborption coefficient for variou building aterial! Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

6 UIUC Phyic 406 Acoutical Phyic of Muic Exaple Calculation of Reverberation Tie, T=T60: Fro exaple calculation of T in John Backu book The Acoutical Foundation of Muic T = =.7 ec Too long! 4300 If T 1.5 ec, then: V A³ = = 7800 ft ( = Ab. unit) T 1.5 If 4300 aborption unit already preent, Then need to add = 3500 aborption unit 1 thick perforated tile have aborption coefficient, a = 0.70 (@ 500 Hz) A = as =3500 ft \ A 3500 ft S = = = 5000 ft a 0.70 Need 5000 ft of 1 thick perforated tile. * Need to be careful here: eat, people, etc. are ound aborbing too!!! * Acoutical propertie of an epty auditoriu are not the ae a when full!!! Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

7 UIUC Phyic 406 Acoutical Phyic of Muic n.b. Air aborb ound oewhat too i.e. air teperature & relative huidity alo atter! Taking into account air aborption, the Sabine Equation i odified a: T 3 3 V ft V A ft V ft A V where i a teperature, huidity and frequency-dependent paraeter, varying fro ~ 0.01/ at KHz to ~ 0.1/ at 8 KHz for ~ NTP condition with RH ~ 30-50%. Nowaday, all of thi i done uing acoutical coputer iulation progra (e.g. EASE, LARA), all tuned fro real eaureent. Input all of the gory detail of hape, ize, and volue of roo, exact hape, ize, and location of all ound aborbing eleent, etc. (alo frequency dependence ee figure below)! Again, Recoended => ubjective deciion were ade about thi Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

8 UIUC Phyic 406 Acoutical Phyic of Muic Auditoriu Background Noie: Abient/background noie level in auditoriu/concert hall e.g. fro noie ource uch a ventilation yte, nearby traffic, etc. need to be controlled uch that it doe not detract (or ditract) fro the audience enjoyent of the uic perforance. Poorly deigned ventilation yte often generate ~ 1/f type noie (or even reonance!) a well a broad-band noie fro air flow in duct and through grille. Inadequate iolation fro corridor noie, noiy and/or queaky door, etc. can alo contribute unwanted ound. Over the year, Noie Criteria (NC) curve have been developed that pecify axiu periible noie level in octave frequency band for a particular noie rating. A pecification for NC-0 (or below) require octave-band ound preure level SPL (in db) at or below the NC-0 curve hown in the figure below (n.b. which cloely follow the Fletcher-Munon apparent loudne level curve): Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

9 UIUC Phyic 406 Acoutical Phyic of Muic A good concert hall hould at leat eet the NC-0 curve, and preferably the NC-15 curve. For lecture hall and claroo, the noie level hould be at (or below) the NC-30 curve, or better yet, the NC-5 curve. T60 reverberation tie hould alo be < 0.5 econd in lecture hall and/or claroo, in order to avoid peech interference proble, particularly in the peech intelligibility range of Hz. A teacher uing a noral voice will produce a ound preure level of ~ 46 db at the ear of a tudent 30 ft away; the NC-30 curve correpond to an average background noie level of ~ 36 db in thi frequency range, thu a 10 db difference in peech v. noie level, a required for peech intelligibility. Today, audio/acoutic engineer can harne the power of the coputer and ue ophiticated coputer progra to create accurate 3-D iulation of the acoutical environent/acoutical propertie of an arbitrarily-haped roo be it a concert hall, a theatrical tage, a church, etc. Ray-tracing technique are ued to iulate 3-D ound propagation fro accurately-odeled ound ource, or even actual recorded ound, reflecting off of the 3-D urface of the roo, including frequency-dependent aborption and diffuivity coefficient of thee urface. The ot coon eaure of the reverberation tie for thee progra i T30, (the tie for the ound intenity to decay to 1/1000 th of it teady-tate value noting that T60 = T30) which i calculated fro the lope of the curve fit through the iulated ray-tracing generated reverberation tie data for the ound intenity level v. tie a the ound intenity level decay fro 5 db to 35 db. The T30 reverberation tie obtained in thi anner i a ore enitive indicator of the true reverberation propertie of a roo than that obtained fro the Sabine equation, becaue it take into account both the aborption and the diffuivity of the roo urface, a well a the detailed pecific of the geoetry of the roo (liited only by the accuracy input to the 3-D odel of the roo). In uch acoutic ray-tracing progra, one can alo invetigate T30 e.g. in different octave band (i.e. a a function of frequency) uch ore eaily than T60, which require ignificantly ore coputation tie. Ray-tracing acoutical iulation oftware progra can alo obtain accurate etiate of the ound preure level everywhere in the iulated roo (and a a function of frequency) to enable the {a unifor a poible}ound preure level independent of the location of a peron in the roo, thu eliinating and/or iniizing dead pot or hot pot in the roo. Pleae ee/read the P406 Lecture Note hand-out on EASE Exaple for ore detail. Speech intelligibility i another iportant acoutical attribute of a litening roo, particularly for lecture hall, theater- and church-goer i.e. any roo or acoutical environent where public peeche are iportant. One tatitic for peech intelligibility i Definition D50, defined a the ratio of the integral of the quare of the overpreure within the firt 50 ec of the initiation of ound aociated with e.g. a very hort ound ipule (< 50 ec duration) to that integrated over all tie for that ae ound, expreed a a percentage: D 50 t50 p () t dt t % t p () t dt t0-9 - Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

10 UIUC Phyic 406 Acoutical Phyic of Muic Thu, D 50 i a eaure of the per-cent total ound energy arriving within 50 ec after an initial pule of ound. If ot of the energy of the ound ipule i within thi 50 ec window, then it will be {uch} eaier for people in thi roo to undertand peech than if e.g. there are any echoe over a longer tie for people to try to coprehend. Thi ound paraeter can only be deterined (reaonably eaily) with ray-tracing acoutical iulation oftware, for a realitic roo. A good litening roo fro a peech-intelligibility perpective ha D50 50%. A related tatitic i peech Clarity, C 50 defined a: C 10log t50 p () t dt p () t dt p () t dt t t t50 t0 t0 db For > 80% yllable intelligibility, a clarity of C50 dbi required, and i conidered the iniu adiible liit for good peech intelligibility. Muic Clarity, C 80 defined a: C 10log t80 p () t dt p () t dt p () t dt t t t80 t0 t0 db Another tatitic i the Center Tie ipule, defined a: t t, the ean/average tie aociated with a ound t t0 t t0 t p () t dt p () tdt The {ubjective} ean/average yllable intelligibility V i related to the center tie t by: V 5 t % n.b. t in ec tie unit, here. For ean/average yllable intelligibility V 80%, a center tie of t 130 ec i required. If the center tie i eaured v. octave band center frequencie, then for peech one want t f ec for the 4 octave band center at 500 Hz, 1000 Hz, 000 Hz & 4000 Hz ctr In the reverberant portion of the ound field of a large litening roo/auditoriu (i.e. far enough away fro a ound ource, e.g. located at the front of the large roo/auditoriu pleae ee/read UIUC Phyic 406 Lecture Note 10 p. 1-3 for ore detail), the center tie t aociated with hort ipulive ound i related to the reverberation tie T 60 by t 13.8 T Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

11 UIUC Phyic 406 Acoutical Phyic of Muic Two other tatitic are the Echo Criterion for peech, Echo Criterion for uic EK where 14 ec T t0 t t0 tt n t p( t) dt n tt n p( t) dt EK t where 9 ec and the. Defining the tie-dependent tatitic: where n = /3 (1) for peech (uic) Then the Echo Criterion for Speech EK t, and the Echo Criterion for Muic, repectively defined a:, 9 T t T t T t T t ec T t EKt, 9 ec 9 ec, 14 T t T t T t T t ec T t EKt, 14 ec 14 ec An echo occur when ax EKt, 1.0 and/or EK t are ax EK t, 1.8, repectively. A flutter echo can exit (e.g. due to an ipulive-type ound bouncing rapidly back and forth ax EK t, 1.0 and/or between two parallel reflecting urface i.e. axial ode), when ax, 1.8 EK t occur periodically, e.g. at interval of ~ 50 ec for peech, and at interval of ~ ec for uic. The clarity aociated with the direct ound level in a large litening roo/auditoriu can be characterized by the C 7 tatitic, defined a: C 10log t7 p () t dt p () t dt p () t dt t t t7 t0 t0 db The direct ound level clarity tatitic C 7 hould be well-correlated with the ound ourcelitener eparation ditance, and hence hould not fall below a range of C7 ~ 10 db to 15 db. Nuerou other, often ore coplicated, frequency-dependent roo acoutic eaureent tatitic have alo been developed over the year by ound engineer, uch a the Speech Traniion Index (STI), Roo Acoutic Speech Traniion Index (RaSTI), Clarity for uic C80, Inter-Aural Cro Correlation (IACC), Strength Meaure (G), Early Decay Tie (EDT), Reverberance (R) a eaure of the acoutic liveline of a reverberant roo, an Echo Criterion for uic ( EK ), Lateral Efficiency (LE) and Lateral Fraction (LF), Ba Ratio (BR), Warth (W), Brilliance (B), The peech intelligibility tatitic, %ALCON per cent Articulation Lo of Cononant in Phyic 406 Lecture Note 10, p. 4-6, will be dicued after firt dicuing variou apect of the nature of a ound field in a litening roo Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.

12 UIUC Phyic 406 Acoutical Phyic of Muic Legal Diclaier and Copyright Notice: Legal Diclaier: The author pecifically diclai legal reponibility for any lo of profit, or any conequential, incidental, and/or other daage reulting fro the i-ue of inforation contained in thi docuent. The author ha ade every effort poible to enure that the inforation contained in thi docuent i factually and technically accurate and correct. Copyright Notice: The content of thi docuent are protected under both United State of Aerica and International Copyright Law. No portion of thi docuent ay be reproduced in any anner for coercial ue without prior written periion fro the author of thi docuent. The author grant periion for the ue of inforation contained in thi docuent for private, non-coercial purpoe only Profeor Steven Errede, Departent of Phyic, Univerity of Illinoi at Urbana-Chapaign, Illinoi All right reerved.