Acoustics and electroacoustics

Transcription

1 coustics and lctoacoustics Chapt : Sound soucs and adiation ELEN78 - Chapt - 3

2 Quantitis units and smbols: f Hz : fqunc of an acoustical wav pu ton T s : piod = /f m : wavlngth= c/f Sound pssu a : pzt o aticl vlocit m/s : p t v z t v t kg/m³ : mdium dnsit ai : ~=. kg/m³ c m/s : spd of sound in a mdium ai : c ~= 34 m/s ELEN78 - Chapt - 3

3 coustic wav quations c t p p v z t p gad p t ELEN78 - Chapt - 3 3

4 ELEN78 - Chapt Hamonic pu ton solution: th Hlmholtz quation Sinusoidal solution: t j z al t z p t z p z t p t c z t j z c t j =- k c k z k z

5 3D sphical wavs I Conditions: - Isotopic point souc in = isotopic mdium - Sphical coodinats q and f. - Th solution of th Hlmholtz quation dos not dpnd on q and f. jk p t al B jk jt B cos t k cos t k B ogssiv wav along + Rgssiv wav along - ELEN78 - Chapt - 3 5

6 3D sphical wavs II ogssiv wav solution : jk p t cos t k 8 L = logp ms /p f / 6 4 Lpm - log Th sound pssu lvl dcass b 6 db at ach doubling of th distanc to th souc.. m ELEN78 - Chapt - 3 6

7 ELEN78 - Chapt D sphical wavs III Radial paticl vlocit pogssiv solution onl jk. j c V V gad V j z V al v p gad p t t z v jk t j In-phas componnt with pssu 9 out of phas componnt

8 3D sphical wavs IV Sound intnsit I pogssiv solution onl i t p v t... cos c cos t k t k sint k k *... In-phas componnt: i inph t c cos Tim avag : I t k pms c I pms c al V * ELEN78 - Chapt - 3 8

9 3D sphical wavs V Rlation btwn th souc pow and th SL at th civ pogssiv solution onl I pms c al V * W 4 ² I 4 ² pms c jk c pms W ² But w hav also: p SL log 4. ms WL c log log 6 db Th sound pssu lvl dcass b 6 db at ach doubling of th distanc to th souc. ELEN78 - Chapt - 3 9

10 Sound souc adiation : th pulsating sph o monopol I Rcpto =a V =V Constant RDIL paticl vlocit V at th sph s bounda. jk a jk c V Low fqunc pssion: ka: j c V k a a jk q jka jk 4 q = at of mass injction p scond = 4 a tv q dq dt t ELEN78 - Chapt - 3

11 Sound souc adiation : th pulsating sph o monopol II Rcpto V =V If ka<< th adiatd pow is popotionnal to ² and V². I al V * p c ms 4 a V c ka =a RDITION IMEDNCE of th pulsating sph: Z V j ka c jka ad a ka<< : imagina and pop. to ka>> : al and = c nalog with lctic pow: I al * V alz a ad V ELEN78 - Chapt - 3

12 ELEN78 - Chapt - 3 R d<< q 4 4 q jk jk R R jk d q jkr q 4 cos t gat distanc fom th dipol R>>: th pssu distibution dpnds on th angl q!! Sound souc adiation : th point dipol

13 Sound souc adiation : th piston in an infinit igid baffl I ssumptions: - th piston sufac is highl flctiv - th piston is instd into th hol of an infinit igid baffl - «v» is th spd of th piston. ds vds Monopol souc on a flctiv sufac : q jk 4 j v ds m³/ s² kg / s² jk 4 Q j v Q S jk ds S S ds' ds' vag pssu on th piston Radiation impdanc: Z ad v j S S ds S ' jk ' ds' : distanc btwn ds and ds ELEN78 - Chapt - 3 3

14 Sound souc adiation : th piston in an infinit igid baffl II Sound fild adiatd b a cicula piston in th fa fild: jkr J kasinq R q j v a² R kasinq v a: piston adius J Bssl function q R Q!!! R = piston adius in th figus ELEN78 - Chapt - 3 4

15 Sound souc adiation : th piston in an infinit igid baffl III Sound fild adiatd b a cicula piston in th fa fild:!!! R = piston adius in th figus ELEN78 - Chapt - 3 5

16 Sound souc adiation : th piston in an infinit igid baffl IV Radiation impdanc of th cicula piston v J ka Hka Z ad c j ka ka a: piston adius J Bssl function H Stuv function q R Q If ka <<: Z ad c ka 8ka j 3 a² ² c 8 a j 3 - th al pat sistanc is popotional to ² - th adiatd intnsit is popotional to a² - th imagina pat is positiv adiation «mass». ELEN78 - Chapt - 3 6

17 Sound souc adiation : th piston in an infinit igid baffl V Z ad J ka Hka j c ka ka v q R Q ka <<: Z ad imagina al and imagina pats ka >>: Z ad = c ELEN78 - Chapt - 3 7

18 D plan wavs I Conditions: - opagation of th sound wavs in on diction guidd wavs. - p and v constant in ach plan ppndicula to. - Catsian coodinats and z. - Th solution of th Hlmholtz quation dos not dpnd on and z. jk p t al B jk jt cos t k B cos t k B ogssiv wav along + Rgssiv wav along - ELEN78 - Chapt - 3 8

19 D plan wavs II aticl vlocit: v z t t j V p gad p gad V V. jk jk B c Sound intnsit fo pogssiv wavs: V V. * I al V c pms c and V a in-phas ELEN78 - Chapt - 3 9