The sound field of moving sources

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1 Nose Engneeng / Aoss -- ong Soes The son el o mong soes ong pon soes The pesse el geneae by pon soe o geneal me an The pess T poson I he soe s onenae a he sngle mong pon, soe may I he soe s I be wen as So, he pesse el o mong pon soe s Q q s, q p y y y y,, Q p s s,

2 The son el o mong soes Fo he eae me, τ, he pesse el s p Q, whee, e, s elae mah nmbe an s s The soe s mong wh a onsan eloy. U poson o soe a emsson me Soe s mong pah aken by mong soe obsee / U Nose Engneeng / Aoss --

3 The son el o mong soes I he soe s nea he ogn n a emsson me an he obsee s a away y Uτ, he eqaon may be ewen as U / os The eqeny o he son hea by an obsee an be eemne by ompang p, p / p Q os p p Q os Q Nose Engneeng / Aoss --

4 The son el o mong soes The son aae by a mong soe o eqeny ω s hea a a he Dopple she eqeny os Appoahng θ Poeeng θ os os Obsee Nose Engneeng / Aoss --

5 The son el o mong soes The Dopple ao o a mong soe. Soe has aelle a sane T beween es emsson Ces A eme a me O s s o age T+τ Ces B eme a me T s o age τ / U To Obsee Nose Engneeng / Aoss -5-

6 The son el o mong soes To oban he τ, eplly o any obsee poson Sbson soe eloy Speson soe eloy U sgn only Only one ale o τ lple solons o τ Obsee Nose Engneeng / Aoss -6-

7 The son el o mong soes To one o he eepon me oonae, wo aables ae noe. U / U/ The eae me, τ, ewen n eepon oonaes The pesse n emsson me oonaes s ewng no he eepon oonaes Q, p os sn os U sn os Nose Engneeng / Aoss -7-

8 The son el o mong soes An so p, Q sn os sn eepon oonaes ae s oonaes n eeene ame ha moes wh he soes. I s smla o he obseaon o wn nnel. U obsee Nose Engneeng / Aoss -8-

9 The son el o speson mong soes ong soes In speson mong soe, he son s hea whn he ah one egon X X U Sn - / U ah one Nose Engneeng / Aoss -9-

10 Nose Engneeng / Aoss -- The son el o speson mong soes The son eme a wo sn mes s hea smlaneos a a A he obsee poson, he son pesse s, U, Q Q p

11 The son el o speson mong soes ong soe wh ne lengh To onse soe lengh, he pesse pebaon o he nal poson ηη,, s p Q Q U Fo he -eonal soe lengh l, he soe an be onsee as a speposon o he mong pon soes, l p, Q Q Nose Engneeng / Aoss --

12 The son el o speson mong soes poson o a soe o - onaes a me I he soe has a ne lengh n he -eon, he son hea s ha e o an negal o he soe elemen, an eae me s a non o soe elemen U Nose Engneeng / Aoss --

13 The son el o speson mong soes Fo eons n whh he eee waelengh s mh longe han he boy menson, he ee o he aaon o eae me along he soe lengh an be neglgble Fo an obsee on he ah one, ~,, eae me aes aply along he soe lengh. A san obsee heas he amlae son eme by he soe ng he ene me. To emonsae lealy, pesse pebaon s allae n he below onons. l U p, Q, appo. s sngla o l Q, Nose Engneeng / Aoss --

14 The son el o speson mong soes Nose Engneeng / Aoss -- Fo a soe wh ne le-span, he pesse pebaon s no eaye by sqae oo o σ n he ase o abaly σ. The ems o n he negan ae o be ealae a eae me. I he soe ems son o a ne me < τ <T,, o an obsee n he ey san a a-el, he negan s zeo oe he mos anges o negaon. Sne he ne me aon me s al hng.

15 The son el o speson mong soes ah wae son anshes nless s =. = an U- = σ ombne o o ge =, he ah wae son s p U T, Q Nose Engneeng / Aoss -5- The ah wae son hea n he ey a-el eays nesely wh sane. All he son ee elease ng he ene hsoy o he soe s hea by he san obsee n one bg bang! T Q,,

16 The son el o speson mong soes Pah aelle by soe whle eme son U Plane on ' ~ X o T l e Wae ons begn o e an eenally eole no a ah wae son el whee ~ o T l The ey san ah one Nose Engneeng / Aoss -6-

17 The son el o speson mong soes Soe a me Soe a me X= σ=sn - / U U sn Tha s, - =-σ σ=u- an The ah wae geomey Nose Engneeng / Aoss -7-

18 The son el o speson mong soes ong soes wh mass nee an oe apple The son el geneae eae when he el o ensyρ ρ s nee e a a ae ρ β an a oe apple a he mong pon =U ass onseaon : Lnea momenm : U p' U Combnng an Solon p' p' U { U p', Nose Engneeng / Aoss -8-

19 The son el o speson mong soes b U Hene p', Ee o soe moon ~ Noe βτ an τ τ ae no nepenen n geneal Nose Engneeng / Aoss -9-

20 The son om he mong oegn boes The oegn boes n he low s senly smooh n on. s. Nose Engneeng / Aoss --

21 The son om he mong oegn boes Dela non δ on = q q s Dene Hease non H s H = o > o < Inse he onol sae, H=, whee < ' H Nose Engneeng / Aoss --

22 Nose Engneeng / Aoss -- The son om he mong oegn boes ass onseaon eqaon omenm eqaon ' ' H H H H H H De o he moon o boy De o he l moon p H Hp H

23 Nose Engneeng / Aoss -- The son om he mong oegn boes Combnng mass & momenm eqaon The solon s ' ' p HT H H o / / /, ' y y y y y y y y p y y y HT H o p T whee,

24 The son om he mong oegn boes To onse he ee o mong sol bonay, s onenen o noe a mong ame wh aeleaon, a, eloy V, a any e pon, η V, V, y, Consan a Consan An, mong sae s saonay elae o he mong ame. The peos monopole ole em o son geneae by he saonay oegn boy s ae mong ee S n S n S V V S a V V Nose Engneeng / Aoss --

25 The son om he mong oegn boes To oban moe genealy, he oegn boy s anslang an oang V, V Ω y, The negaon o olme an sae s nepenen o he eae me. Hene, he soe ems o qapole an pole ae no hange. s Nose Engneeng / Aoss -5-

26 Nose Engneeng / Aoss -6- The son om he mong oegn boes Usng he eny o non n g g g, s ae o o he negaon Usng he eny o non U n g, wh espe o he eae me., a T V V S V e e e g g y g

27 Nose Engneeng / Aoss -7- The son om he mong oegn boes The Fows Wllams ms m - s-hawkngs eqaon s ee. The s em o o FW- W-H H eqaon oespons o he solon ha The s em o T o ases n Lghhll l l W H qaon oespons o he solon ha e W FW F l s heoy. An, he seon em epesens he ases n Lghhll heoy. An, he se h s son geneae by lang oe, se e, e on em epesens he o se, eee by sol bonay. lang oe son geneae by e, eee by sol bonay., An, he emanng wo ems means he son geneae by he wo ems An, he emanng w olme splaemen ees a T e e e e V V S V,

28 The son om he mong oegn boes I he eloy V o any pon o soe egon s speson, he Dopple ao omes os I anshes a he angle, os The eslng snglaes ae he same as hose ha wee assoae wh ah wae emsson. Howee, when sppoe by oegn boes ah waes ae oen able o oalese no he nense shok. When he sae, S, s saonay, a =V=, η=y, FW-H eqaon ees o Cle s eqaon T, y, y Nose Engneeng / Aoss -8- V S y, S

29 Nose Engneeng / Aoss -9- The son om he mong oegn boes Usng mong oonae sysem y = η + s s η η, η,τ,τ Whee J,K ae Jaobans ns, no olme hange, e, J=K= S o S V KS n KS n p JT H, '

30 The son om he mong oegn boes I he sae s mpeneable, e, he nomal sae eloy ms be eqal o ha o he low. n n = n n H', S onk S V p JT n K S S Qapole Dpole onopole Nose Engneeng / Aoss --

31 Nose Engneeng / Aoss -- The son om he mong oegn boes A ompa plsang sphee mong a low mah nmbe << neglgble Lnea & ompa plsaon, ωa/<<, ' s n s n p T H S o S V

32 The son om he mong oegn boes Fo an obsee n he o o-el, eqaon wh he eae me -τ -τ τ η =l -η-uτ Uτ l τ = - ll/ + + n n/ ll /osθ sne he soe s ompa, an << nompessbel el, he el lose o he boy sases he poenal eqaon Φ= On η=l =lηl=a, he nomal eloy o he sphee n φ= φ= τ + U η / η Nose Engneeng / Aoss --

33 Nose Engneeng / Aoss -- The son om he mong oegn boes The solon o eq. q. q wh hs BC. Beomes Veloy Pesse pebaon om nseay Benoll Le s ealae eah em; monopole UA a A } { 5 UA a A y V ' U p S S o S b UA A n S /

34 Nose Engneeng / Aoss -- The son om he mong oegn boes Epan wh τ, Whee, Ealang he negal l o lage e, HOT a UA UA b UA A b UA A os os / os os A a A a n S S o os os U

35 Nose Engneeng / Aoss -5- The son om he mong oegn boes Smlaly y Dpole Qapole In oal, os A a s n p S A a O T V os, ' A a

36 The son om he mong oegn boes Noe moon amples he pesse pebaon by ½ Dopple ao, a moe omplae han he pon soe aselnea ase I s e o he ople momenm la assoae wh a olme l. The son el geneae eae by he oe s only a mah nmbe smalle han he leang em!! Nose Engneeng / Aoss -6-

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