Investigation of the Inlet and Outlet Location on the Soundproofing Ventilation Unit

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1 Send Orders for Reprints to The Open Acoustics Journl Open Access Investigtion of the Inlet nd Outlet oction on the Soundproofing Ventiltion nit Nsu Tsunetoshi 1 nd Nishimur Tsuyoshi * 1 Fculty of Engineering Kummoto niversity Kurokmi Kummoto Jpn Fculty of Computer Science Sojo niversity 4--1 Iked Kummoto Jpn Astrct: This pper dels with A-type nd B-type rectngulr cuoid SV (soundproofing ventiltion unit) contin n inlet nd outlet in opposite surfces. The difference etween them is whether they re locted in smll or ig cross section re. Following the theoreticl clcultion the shpe nd loction of the inlet nd the outlet re determined y n investigtion of the distriution of higher order mode wves formed inside the SV. Finlly experimentl results of A- type nd B-type sed on the reverertion chmer method re shown to e in resonle greement with our theoreticl predictions. The results of theoreticl clcultion nd experiments conducted led to the conclusion tht A-type is suitle for soundproof ventiltion unit. Keywords: Higher order mode resonnce frequency soundproofing wve eqution. 1. INTRODCTION The uthors re presenting concept of mnufcturing windows clled SPCW (Sound Proofing Csement Windows) which re cple of ventilting regulting sunlight nd reducing trffic noise inside the house of developing countries in tropicl climte zones [1]. The size nd the structure of SPCW re designed to e identicl to the current csement windows in order to void ny costs incurred when replcing those windows. The proposed SPCW comines two sic components nmely the ventiltion soundproofing unit nd the lighting unit s shown in Fig. (1). The lighting unit cn e constructed using one glss lyer mounted etween two soundproofing ventiltion units (SV). Due to the fct tht SV must hve lrge volume to ttenute the low frequency rnge of trffic noise sound propgting through SV is comintion of plne wve nd the higher order mode wve. The higher order mode wve hs een reviewed in numerous experimentl nd nlyticl studies [3-1] prticulrly in the nlysis nd design of silencing systems. It genertes very high levels of sound pressure especilly those t resonnce frequencies. Therefore in order to mximize the soundproof cpility it is necessry to reduce the sound pressure levels or prevent the genertion of higher order mode wves in ny technique. The SV cn consist of squre rectngulr cuoid or more complicted shpes depending on decortive considertions. Needless to sy the unit requires simple internl structure nd lrge input nd output to mximize ventiltion s well s preventing outside noise from entering the house. Actully n input nd output cn e locted t vrious positions on the SV ccording to the design of window. *Address correspondence to this uthor t the 4--1 Iked Nishi-ku Kummoto 86-8 Sojo niversity Jpn; Tel: ; Fx: ; E-mils: nisimur@cis.sojo-u.c.jp nis66@gmil.com igh1ng& unit&&&&&& & trffic& noise&&&&&& & outdoor&&&&&&&&&&&&&&&& indoor& trffic& noise&&&&&& & Fig. (1). A side view of proposed csement windows. Soundproofing& Ven1l1on& unit&&&&&& & This pper dels with the rectngulr cuoid SV which contins n inlet nd outlet in opposite surfces s shown in Figs. ( 3). The difference etween them is whether they re locted in smll or ig cross section re. Herefter we shll refer to them s A-type nd B-type respectively. Following the development of the theoreticl clcultion in section the shpe nd loction of the inlet nd the outlet re determined y n investigtion of the distriution of higher order mode wves formed inside the SV. Finlly experimentl results of A-type nd B-type sed on the reverertion chmer method re shown to e in resonle greement with our theoreticl predictions /14 14 Benthm Open

2 The Open Acoustics Journl 14 Volume 7 Tsunetoshi nd Tsuyoshi () t x = V x = (3) (3) t y = V y = (4) y Fig. (). A-type SV. y Fig. (3). B-type SV.. THEORETICA CACATIONS Theoreticl clcultion of the sound pressure inside the rectngulr cuoid including the effects of higher-order mode wves [] is summrized s follows: Consider the cse of rectngulr cuoid hving crosssectionl re S w = nd depth which hs the inlet nd outlet locted on the opposite fces. The cross-sectionl re of n inlet nd outlet is S = nd S = respectively. z z x x The generl solution of wve eqution in terms of velocity potentil cn e given s: ( ) ( C sinα x Dcosα x ) φ = Ae z Be z ( E sin s α y F cos s α y ) (1) where A B C D E nd F re ritrry constnts determinle from the oundry conditions other symols re constnts. V x = φ / x V y = φ / y nd V z = φ / z re the velocity components in the x y nd z directions respectively. Assuming the wlls of the cvity to e perfectly rigid nd the loss t the wll cn e neglected then oundry conditions my e expressed s: (1) t x = V x = () (4) t y = V y = () () t z = V z = V F (x y) (6) (6) t z = V z = V F (x y) (7) where V nd V re the driving velocity t the inlet nd outlet F (x y) =1 t the inlet nd F (x y) = elsewhere F (x y) =1 t the outlet nd F (x y) = elsewhere. According to the ove oundry conditions the velocity potentil φ(x yz) cn e determined s: φ (x yz) = m= n= ( ) mn sinh mn cosh mn (z ) cosh ( mn z) mn sinh mn ( ) D mn ( ) D mn cos mπ x nπ y cos (8) Then the verge sound pressure cting on the outlet cn e otined s: P = 1 S 1 1 jkρc φ(x y ) dx dy cosh = jkz ( ) Moreover expnding the ove eqution corresponding to vrition of m nd n we hve: P = j Z where mn = mπ nπ ( ) sinh( ) m n m n m n w m= n= m n sinh m n m n m n w ( ) ( k) cos k sin ( ) sinh( ) ( n) n sinh( ) cosh m sinh( ) cosh n n= 1 n sinh( n) n n m m m= 1 m m m m ( ) sinh( ) cosh m n sinh( ) m n m n m n m n n m n (9) (1) k (11)

3 Investigtion of the Inlet nd Outlet oction on the Soundproofing Ventiltion nit The Open Acoustics Journl 14 Volume = nπ 1 nπ sin sin ( nπ ) 1 1 n 1 nπ sin sin 4 = m (1) (13) (14) (1) (16) (17) k is the wve numer nd re the volume velocity t The first term in the rcket of Eq. (1) represents the sound pressure of the plne wve nd the second one represents the sound pressure components of the higherorder mode wves respectively. The output pressure P ( ) increses when its denomintor sin(k) nd mn sinh mn re zero. Nmely t the following resonnce frequencies of sin(k) = f = η c mn sinh ( mn ) = f mn = c π ( m π ) 1 1 m 1 π sin sin mπ nπ 1 mπ sin sin S w 1 m n = 1 mπ sin sin mnπ S S 1 nπ sin sin 1 mπ 1 nπ sin sin sin sin 4 = ( n π ) 1 n 4 = ( m π ) 1 m S 1 = w m n mnπ S 1 nπ sin sin 1 nπ sin sin 1 mπ sin sin 1 mπ sin sin the inlet nd outlet the symol mens without m= n= the cses of m nd n in 1st - 3rd terms of Eq. (1). ηπ ( η = ) (18) ( η = ) (19) 3. IMPROVEMENT FOR THE SONDPROOF EFFECT Genertion mechnism of the frequencies of plne wve nd the higher order mode wve cn e understood ccording to the clcultion exmple shown in Fig. (4). The curve of Eq. (18) nd the sound pressure level of those wve components in db re shown in Fig. (4). Similrly the curve of Eq. (19) nd the sound pressure levels of ( ) (4 ) higher order modes wve components in db re shown in Fig. (4). The plne wve nd the higher order mode wves lso hve mny resonnce frequencies which occurred corresponding to the incresing vlue of in Eqs.(18) nd (19). As evident from the results the level of the ltter is significntly greter thn those of the former. Therefore it is cler tht when we re le to reduce n ritrry higherorder wve mode we will not only void resonnce generted y this mode ut lso otin low level of the entire outlet sound pressure. () () sin(k) sinh( d) Frequency (Hz) sinh( 4 d) og P ( )! (4 )! Frequency (Hz) og P 1 Fig. (4). The genertion mechnism of sound pressure in B-type SV hving dimension of =.48m =.7m nd =.9m. () Plne wve component defined y Eq. (1) () Higher order modes component defined y Eq. (1). Fig. () shows the first resonnce frequency of (m n) higher-order modes occur in A-type SV. Fig. (6) shows those of B-type SV nd the comprison etween two types of SV. Note tht the symol in this figure indicted the resonnce frequency of the plne wve defined y Eq.(18). As indicted in this figure B-type SV hs lot of resonnce frequencies of the plne wve nd higher-order mode wve in comprison with those of A-type. Therefore it cn e seen tht the soundproofing effect of A-type is etter thn B-type. Investigtion of inlet/outlet loction on S Nsu T. Iki K.nd Nishimur T.

4 4 The Open Acoustics Journl 14 Volume 7 Tsunetoshi nd Tsuyoshi () (1) (4) (1) (6) () the form of form-1 or form- s shown in Fig. (7). The remining higher order modes tht we hve to consider re ( ) ( 4) (6). When using form-1 nd ( ) (4 ) (6) when using form- respectively. Similrly low level of could e selected in n identicl mnner. (1) (3) () Frequency (Hz) Fig. (). The first resonnce frequency of (m n) higher-order modes occur in the A-type SV. () form-1 B-type SV (1) () (3) (1) (11) (1) A-type SV (1) () (3) (1) (11) (1) A Frequency (Hz) Fig. (6). Comprison of B-type nd A-type SV on the first resonnce frequency of (m n) higher-order modes. stly in order to increse the soundproofing ility let us consider the shpe nd loction of inlet nd outlet sed on the theoreticl clcultion results. For this purpose low levels of nd in Eqs. (14) nd (17) re required. When i1 = / Δ i = / Δ nd re selected Eq. (14) ecomes = mπ cos mπ sin nπ Δ nπ cos nπ sin nπ Δ () This is demonstrted when m = 1 3 or n = 1 3 ecomes zero. Furthermore if is selected for m = mn 4 6 lso ecomes zero. On the other hnd if is selected ecomes zero when n = 4 6. Therefore to void mny higher order mode wves the shpe of the inlet must e in () form- Fig. (7). A resonle shpe nd loction of the inlet nd the outlet which otined from the nlysis for oth types. 4. EXPERIMENTA RESTS An experiment ws conducted using the reverertion chmer method to verify the ctul sound ttenution chrcteristics of A-type nd B-type SV. Fig. (8) shows the experimentl setup. The volumes of the reverertion chmers were 98m 3 nd 179 m 3 respectively. The SV were instlled t the perture y csing composed of plnk. The sound source ws loudspeker fed y pink noise nd five microphones were locted on ech chmer mesuring the sptilly verged sound pressure. The pressure levels in the sending chmer were 1-1 db to chieve pressure level of 7-8 db in the receiving room. The ctul sound ttenution of the SV is estimted y the vrition from the mesurement results with nd without the SV inserted etween the two reverertion chmers. Severl SV with vrious shpes of inlet nd outlet were used during the experiment. The shpe nd position of inlets nd outlets re shown in Fig. (9). Herefter we shll refer to them s (A1) to (A) for A-type SV nd (B1) to (B3) for B-type SV respectively. Note tht S is n re of inlet or outlet nd the symol R% is defined s R%= S / S w. Additionlly (A1) (A) (B1) nd (B) re the shpes tht we considered in the theoreticl computtion nd summrized in Fig. (7). The other shpes were used to vlidte our prediction.

5 Investigtion of the Inlet nd Outlet oction on the Soundproofing Ventiltion nit The Open Acoustics Journl 14 Volume 7 Reverertion chmer microphones oud speker plnk csing Reverertion chmer SV microphones Fig. (8). Mesurement system sed on the reverertion chmer method. (A1) (A4) (B1) S = 4mm S = 4mm S = 9mm R% =. R% =. R% =. (A) (A) (B) S = 7mm S = 4mm S = 9mm R% =.1 R% =. R% =. (A3) (B3) S = 18mm S = 4mm R% =. R% =.1 Attenution (db) 1 1 S = 4mm R% =. Inlet (A) S = 7mm R% =.1 (A3) S = 18mm R% =. Outlet (A) Outlet (A3) 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (1). Mesured result of A-type SV with chnge of outlet cross-section re. Fig. (1) Mesured result of A-type SV with chnge! of outlet cross-section (A) re.! (A3)! 1 S = 4mm R% =. S = 7mm R% =.1 S = 18mm R% =. Fig. (9). Comintion of inlet nd outlet. (A1) to (A) for A-type SV with dimension of 7mm x 9mm. (B1) to (B3) for B-type SV with dimension of 9mm x 48mm. Fig. (1) shows the mesured results of A-type SV with chnges in outlet cross-section re. Noticely the soundproof effect will e decresed when opening lrge outlet to mximize ventiltion. Similr chrcteristics re shown in Fig. (11) when chnging the inlet cross-section re. Fig. (1) proves our theoreticl clcultion on the resonle shpe of the outlet s discussed in section 3. Fig. (13) shows the ttenution otined when using resonle outlet shpes (A1) nd (A). When using (A) the ttenution otined is greter thn (A1) ecuse (A) eliminted the resonnce of ( ) which ppers t 14Hz. Figs. (14 1) show the difference of A-type nd B-type when they hve the sme R% nd outlet cross-section re S respectively. Attenution otined is greter when using A-type though B-type hs higher ventiltion effect. stly the comprison etween two kinds of SV is shown in Fig. (16) when resonle shpes of inlet nd outlet were used. It is cler tht A-type induces greter soundproof effects thn B-type. Attenution (db) 1 Inlet (A) Inlet Inlet (A3) Investigtion of inlet/outl Nsu T. Iki K.nd Nishi 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (11). Mesured result of A-type SV when chnging the inlet Fig. cross-section (11) Mesured re. result of A-type SV when chnging! It should the e inlet noted cross-section tht the ove re.! experiment ws crried! out using n SV mde of steel plte tht ws not ffixed with the soring mteril. However in prctice it is necessry to use some pproprite sound soring mteril inside the SV to otin higher soundproof effect.

6 6 The Open Acoustics Journl 14 Volume 7 Tsunetoshi nd Tsuyoshi Attenution (db) 1 1 S = 4mm R% =. Inlet (A4) S = 4mm R% =. Outlet (A4) 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (1). Mesured result of A-type SV when chnging the outlet shpe. (A) etter outcomes thn A-type ecuse it could open lrge input nd output to mximize the ventiltion effect. However s vrious resonnces of plne wve nd higherorder mode wve occur inside the unit the soundproofing effect of B-type cn not e expected to e gret. The results of theoreticl clcultion nd experiments conducted led to the conclusion tht A-type SV is suitle for soundproof ventiltion unit. Attenution (db) 1 1 S = 4mm R% =. Inlet (A1) Inlet (B1) Outlet (B1) (B1) S = 9mm R% =. Attenution (db) 1 1 S = 4mm R% =. Inlet S = 4mm R% =. Outlet (A) 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (13). Mesured result when used resonle shpe (A1) nd Fig. (A) (13) outlets. Mesured result when used resonle shpe! (A1) nd (A) outlets.! CONCSION Acoustic chrcteristics of A-type nd B-type rectngulr cuoid soundproof ventiltion unit hve een considered theoreticlly nd experimentlly. Both these types hve similr dimensions with the inlet nd outlet locted on the opposite fces. It is considered tht B-type would induce 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (14). Mesured results of A-type nd B-type SV. Both types of SV hve the sme R%. Fig. (14) Mesured results of A-type nd B-type SV.! Both types of SV hve the sme (B3) R%.!! Attenution (db) 1 1 S = 4mm R% =. Inlet (A1) S = 4mm R% =.1 Inlet (B3) Outlet Investigtion (B3) of inlet/outl Nsu T. Iki K.nd Nishi 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (1). Mesured results of A-type nd B-type SV. Both types of SV hve the sme S. Fig. (1) Mesured results of A-type nd B-type SV.! Both types of SV hve the sme S.!!

7 Investigtion of the Inlet nd Outlet oction on the Soundproofing Ventiltion nit The Open Acoustics Journl 14 Volume 7 7 S = 4mm R% =. (A) (B1) S = 9mm R% =. (B) CONFICT OF INTEREST The uthors confirm tht this rticle content hs no conflict of interest. ACKNOWEDGEMENTS Declred none. Attenution (db) 1 1 S = 4mm R% =. Inlet (A1) Outlet (A) Inlet (B1) Outlet (B) S = 9mm R% =. 63 1k k 3.1k k 8k 1/3 Octve nd frequency (Hz) Fig. (16). Mesured results of A-type nd B-type SV. Both types of SV hve the sme R% nd good comintion of inlet nd outlet shpe. REFERENCES [1] Nishimur Y Nishimur S Nishimur T Yno T. Sound propgtion in soundproofing csement windows. Appl Acoust 9; 7: [] Nishimur S Nishimur T Yno T. Acoustic nlysis of ellipticl muffler chmer hving perforted Pipe. J Sound Vi 6; 97: [3] Aom M. Derivtion of four-pole prmeters for including highermode effects for expnsion chmer mufflers with extended inlet nd outlet. J Acoust Soc Am 199;137: [4] Ih JG. The rective ttenution of rectngulr plenum chmers. J Sound Vi 199; 171:93-1. [] Nishimur T Iked T. Four-pole-prmeters for n ellipticl chmer with men flow. Electron Commun Jpn 1998; 81: 1-9. [6] Nishimur T. Ando T. Iked T. Resonnce of ellipticl muffler chmer hving non-uniformly perforted pipe. Electron Commun Jpn ; 8: -8. [7] Glv R Regud P Aom M. Study of folded resontor including the effects of higher order modes J Sound Vi 4; 73: [8] Whlen TM. The ehvior of higher order mode shpe derivtives in dmged em-like structures. J Sound Vi 8; 39: [9] Crrer E Miglioretti F Petrolo M. Computtions nd evlutions of higher-order theories for free virtion nlysis of ems. J Sound Vi 1; 331: [1] Nishimur Y ung NH Nishimur S Nishimur T Yno T. The coustic desigh of soundproofing doors nd windows. Open Acoust J 1; 3: 3-7. Received: June 1 14 Revised: Octoer 3 14 Accepted: Novemer 7 14 Tsunetoshi nd Tsuyoshi; icensee Benthm Open. This is n open ccess rticle licensed under the terms of the Cretive Commons Attriution Non-Commercil icense ( which permits unrestricted non-commercil use distriution nd reproduction in ny medium provided the work is properly cited.