i nt er・noi se 94
YOKOHAMA- J APAN, AUGUST29- 31YOKOHAMA- J APAN, AUGUST29- 31YOKOHAMA- J APAN, AUGUST29- 31YOKOHAMA- J APAN, AUGUST29- 31YOKOHAMA- J APAN, AUGUST29- 31
MEASUREMENT OF EQUI VALENT ABSORPTI ON AREA OF ROOMS USI NGMEASUREMENT OF EQUI VALENT ABSORPTI ON AREA OF ROOMS USI NGMEASUREMENT OF EQUI VALENT ABSORPTI ON AREA OF ROOMS USI NGMEASUREMENT OF EQUI VALENT ABSORPTI ON AREA OF ROOMS USI NGMEASUREMENT OF EQUI VALENT ABSORPTI ON AREA OF ROOMS USI NGREFERENCE SOUND SOURCESREFERENCE SOUND SOURCESREFERENCE SOUND SOURCESREFERENCE SOUND SOURCESREFERENCE SOUND SOURCES
Masaru Koyasu *,  Hi deki  Tachi bana ** and Hi roo Yano **
* Chi ba I nst i t ut e of  Technol ogy  Tsudanuma 2- 17- 1,  Narashi no,  275 J apan
**I nst i t ut e of  I ndust ri al  Sci ence,  Uni versi t y of  Tokyo  Roppongi  7- 22- 1,  Mi nat o- ku,  Tokyo,  106 J apan
25  72. 4  72. 8  72. 9  74. 2  74. 9
1.  I NTRODUCTI ON
  The equi val ent  sound absorpt i on area i s necessary t o be measured i n t hemeasurement s of  sound t ransmi ssi on l osses of  mat eri al s,  sound i nsul at i on
ef f i ci enci es of  bui l di ngs,  and sound power l evel s of  sound sources i n di f f usesound f i el d.  I n t hese measurement s,  t he equi val ent  sound absorpt i on area i s
However,  t he reverberat i on t i me measurement  needs addi t i onal  i nst rument at i oni s desi rabl e t hat  t he equi val ent  sound absorpt i on area can be obt ai ned onl y by
sound pressure measurement  by omi t t i ng t he reverberat i on t i me measurement ,especi al l y i n t he f i el d measurement s of  sound i nsul at i on ef f i ci enci es of
bui l di ngs.  For t hi s purpose,  t wo ki nds of  t echni ques f or t he measurement  ofequi pval ent  sound absorpt i on area usi ng st at i onary and i mpul si ve ref erence
sound sources are i nvest i gat ed t heoret i cal l y and experi ment al l y i n t hi s st udy.
2.  DEFI NI TI ON OF ACOUSTI C RADI ATI ON FROM STATI ONARY AND   I MPULSI VE SOUND SOURCES
  As i s wi del y recogni zed,  t he sound radi at i on f rom st at i onary sound sources i sdescri bed i n t erms of  "sound power",  t he sound energy emi t t ed per uni t  t i me,  or
"sound power l evel " i n dB- represent at i on.
  Sound power :    ( 1)
     :  i nst ant aneous sound power,  -  :  t i me- averagi ng
Fig. 1  Definitions of Sound Power and Sound Energy
P= P t=( )()J / sW
P t( )
  Sound power l evel  :
  On t he ot her hand,  t he way of  descri bi ng t he sound radi at i on f rom i mpul si ve
( t ransi ent ,  i n general )  sound sources i s not  cl earl y def i ned.   Here,  Tachi bana etal .  [ 1]  have proposed a way of  descri bi ng t he sound radi at i on f rom t ransi ent
sound sources i n t erms of  "sound energy" and "sound energy l evel " as f ol l ows( see Fi g. 1) .
  Sound energy :( 3)
  Sound energy l evel  :( 4)
  Sound energy l evel  can be measured by si mi l ar ways as i n t he measurement  ofsound power l evel  i n a f ree f i el d or a di f f use f i el d by measuri ng t he t i me-
i nt egrat ed val ue of  sound pressure or sound i nt ensi t y i nst ead of  measuri ng t het i me- average val ue [ 1] .
3.  BASI C EQUATI ONS
  Accordi ng t o t he ways of  expressi on ment i oned above,  t he sound propagat i on
f rom a st at i onary or i mpul si ve poi nt  source i n a f ree f i el d or a di f f use f i el d canbe expressed as f ol l ows.
For a st at i onary sound source i n a f ree f i el d :
( 5) ( 6)
where,   i s t he di st ance f rom t he sound source ( m) ,          i s sound i nt ensi t y           i s sound pressure ( Pa) ,    i s t he charact eri st i c i mpedance of  ai r,    i s
sound power l evel  of  t he source ( dB) ,  and    i s sound pressure l evel  ( dB) .
( 7) ( 8)
where,     i s sound pressure exposure l evel
For a st at i onary sound source i n a di f f use f i el d :
( 9) ( 10)
where,    i s speed of  sound          i s sound energy densi t y        ,  and    i s
equi val ent  sound absorpt i on  area      ,  and
For an i mpul si ve sound source i n a di f f use f i el d :
( 11) ( 12)
Here,  i t  shoul d be not ed t hat  Eqs.  ( 6)  and ( 8) ,  and Eqs.  ( 10)  and ( 12)  are i n
compl et el y i dent i cal  f orm,  respect i vel y.
LP PPWW==−1010002log (/)
EP t dt=
∞∫( )0
LE EEEJ==−10100012log (/)
Pr Ir Pc==44
22LLr rWp=++10111002log ( /)
rrI01= m ,
()W / m2, pρcLWLp
ErI t dtrcPt dt==
∞∞∫∫4422
0ππρ( )( )LLr rWpE=++10111002log ( /)
P= cE Ad/ 4LLA SWp=+−1060log(/)
c()m / s , Ed(J / m )3A()m2S021= m
EcAEt dtAcPt dt==∞∞∫∫440
0d( )( )ρLLEpA / S=+−1060log()
Koyasu
4.  MEASUREMENT OF EQUI VALENT SOUND ABSORPTI ON AREA LEVEL
  Ordi nari l y,  t he equi val ent  sound absorpt i on area of  a room i s obt ai ned by
measuri ng reverberat i on t i me,  based on t he Sabi ne' s equat i on,  as f ol l ows.
where,     i s equi val ent  sound absorpt i on area l evel  ( dB) ,    i s vol ume of  room               i s reverberat i on t i me i n t he room     and
I nst ead of  t hi s met hod,     can al so be obt ai ned by usi ng a st at i onary sound
source or an i mpul si ve sound source accordi ng t o Eqs.  ( 10)  and ( 12) .  That  i s,
where,     i s t he mean sound pressure l evel  i n t he room ( dB) ,     i s t he meansound pressure exposure l evel  i n t he room ( dB)
  When a st at i onary sound source i s used,  t he spat i al  average of  sound pressurel evel  i s measured,  and when an i mpul si ve sound source i s used,  t he spat i al
average of  sound pressure exposure l evel  i s measured.  I n t hese measurement s,   of  t he st at i onary sound source and     of  t he i mpul si ve sound source must  be of
course cal i brat ed i n advance of  t he measurement .  The consi derat i on ment i oned above i s based on t he assumpt i on of  an i deal
di f f use sound f i el d,  but  i n t he case of  est i mat i ng t he mean sound energy densi t yf rom t he sound pressure i n act ual  measurement s t he correct i on t erm
                 ( t he Wat erhouse correct i on,    :  wavel enght ,    :  roomsurf ace,     :  room vol ume)  shoul d be added t o     and
5.  EXPERI MENTAL STUDI ES
  I n order t o exami ne t he val i di t y and appl i cabi l i t y of  t he met hods usi ng a
st at i onary sound source or an i mpul si ve sound source ment i oned above,measurement s were made i n f our rooms of  di f f erent  vol ume and acoust i c
charact eri st i c.
( 1)  Cal i brat i on of  t he ref erence sound sources  I n t hi s st udy,  a hemi - omni di rect i onal  sound source syst em composed of  si x
l oudspeakers shown i n Fi g. 2 was used as a ref erence source.  A pi nk noi se andi mpul se responses of  2- oct ave- band f i l t ers were radi at ed f rom i t  as a st at i onary
source si gnal   and i mpul si ve ones,  respect i vel y.  I n advance of  t he f i el dmeasurement s,     and    of  t hi s sound source were cal i brat ed i n a reverberat i on
room of         vol ume and 6. 1 s reverberat i on t i me ( 500 Hz)  accordi ng t o Eqs.  ( 10)and ( 12) .  The cal i brat ed sound power l evel s and sound energy l evel s i n oct ave
bands f rom 125 Hz t o 4 kHz of  t he ref erence sound source are shown i n Tabl e 1.I n t hese cal i brat i on measurement s,  reverberat i on t i me was measured by t he
convent i onal  i nt errupt ed- noi se met hod.
et al.
AVT= 0162./
LA SV VT Tab ==−−1010108000log(/)log(/)log(/)
LabV(),,mm3031VT=( ),sT01= s
LLLab =−+Wp6
LLLab =−+EpE6
++101810log (/)SVλλ
LELW220m3
  Tabl e 1  Sound power l evel  and sound energy l evel  of  t he st at i onary and           i mpul si ve ref erence sound sources
( 2)  Fi el d measurement s
  The t ri al  measurement s were made i n t he f ol l owi ng f our rooms.
AAAAA :  reverberat i on room
BBBBB :  reverberat i on room
CCCCC :  meet i ng room
DDDDD :  TV cont rol  st udi o
  I n t hese measurement s,  t he convent i onal  met hod measuri ng reverberat i on
t i me by t he i nt errupt ed noi se met hod was al so pref ormed i n addi t i on t o t he t woki nds of  ref erence sound source met hods.  I n order t o avoi d t he changes of  sound
power l evel  and sound energy l evel  of  t he ref erence source caused by t heboundary ef f ect ,  t he sound source syst em was l ocat ed on t he f l oor bei ng kept
more t han 1. 5 m away f rom any of  t he room boundari es ot her t han t he f l oor [ 2] .Through al l  measurement s,  t he sound source was l ocat ed at  a poi nt  and si x
recei vi ng poi nt s were di st ri but ed i n t he f ar f i el d f rom t he sound source i n t herecei vi ng room.     and      were obt ai ned as t he energy- mean val ues of  t he
sound pressure l evel s and sound pressure exposure l evel s,  respect i vel y,measured at  t hese recei vi ng poi nt s.
  The reverberat i on t i mes measured i n t he f our rooms are shown i n Fi g. 3.  Theroom AAAAA i s a rect angul ar reverberat i on room equi pped wi t h suspended r ef l ect ors
and has t he l ongest  reverberat i on t i me among t he al l  rooms t ested i n t hi s st udy.The room BBBBB i s a smal l  rect angul ar reverberat i on room of  whi ch f requency
charact eri st i c of  reverberat i on t i me i s t uned t o be f l at  around 1 s by soundcharact eri st i c of  reverberat i on t i me i s t uned t o be f l at  around 1 s by sound
absorpt i on t reat ment .  The room C i s a normal  room wi t hout  any speci al  acoust i c
Oct. band center freq. Hz
Stationary R.S.S.         dB
pulsive R.S.S.          dBIm
Fig. 2  Reference sound source           composed of 6 loudspeakersFig. 3  Reverberation times measured            in the four rooms under test
[]V = 220mmTsHz3,,.()s ==222323 5002
[]Vm Sm TsHz===5386510350032,.,.()[]Vm SmTsHz===12716908450032,,.()[]Vm SmTsHz===18423503750032,,.()
Koyasu et al.
Fig. 7  Measured results for Room D
Fig. 6  Measured results for Room C
Fig. 5  Measured results for Room B
Fig. 4  Measured results for Room A
t reat ment .  The rooms DDDDD i s a st udi o f or t he cont rol  of  TV programs and i s mucht reat ed wi t h absorpt i ve f i ni shi ng.
  The measurement  resul t s of  equi val ent  sound absorpt i on area l evel  f or t he
f our rooms are shown i n Fi g. 4 t o 7.  I n t he cases of  Room AAAAA and BBBBB,  t he resul t smeasured by t he t hree di f f erent  met hods are i n good agreement  wi t hi n 1 dB.  I n
t he case of  Room CCCCC,  t he agreement  of  t he t hree ki nds of  resul t s are f ai rl y goodexcept  f or 125 Hz and 4kHz bands i n whi ch about  1. 5 dB di f f erences are seen.  I n
t he case of  Room DDDDD,  t he resul t s measured by t he t wo ki nds of  ref erence soundbut  di screpanci es up t o 2 dB are seen i n 125 Hz and 2kHz bands.  These
sound f i el d i s no l onger val i d i n rooms wi t h rect angul ar shape,  smal l  vol ume andcurves t end t o bend and i t  becomes di f f i cul t  t o det ermi ne t he reverberat i on t i me,
especi al l y i n l ow f requency bands.
6.  CONCLUSI ONS
  From t he t heoret i cal  and experi ment al  i nvest i gat i ons ment i oned above,  wemay concl ude t hat  t he met hods usi ng a st at i onary ref erence sound source or an
i mpul si ve on are ef f ect i ve f or t he measurement  of  equi val ent  can be perf ormed onl yby sound pressure l evel  or sound exposure l evel  measurement  usi ng an
i nt egrat i ng- averagi ng sound l evel  met er and t heref ore t he measurementt he ref erence sound sources must  be kept  st ri ct l y const ant .
  Regardi ng st at i onary ref erence sound sources,  I SO 6926 i s now bei ngst andardi zed and t hey wi l l  be ef f ect i vel y used i n vari ous acoust i c measurement s,
f or exampl e,  sound power l evel  det ermi nat i on by t he di f f use sound f i el d met hod( I SO 3741,  3742 and 3743- 1,  J I S Z 8733) .  I n addi t i on,  i t  i s necessary t o devel op
i mpul si ve ref erence sound sources wi t h enough sound energy,  broad bandspect rum charact eri st i c and hi gh st abi l i t y.
REFERENCES
[ 1]  H. Tachi bana,  H. Yano and K. Yoshi hi sa :  Def i ni t i on and measurement  of
    sound energy l evel  of  a t ransi ent  sound source,  J . Acoust . Soc. J pn( E)  8( 6)    ( 1987)  p. 253- 240
[ 2]  H. Tachi bana and H. Yano :  Changes of  sound power of  ref erence sound    sources i nf l uenced by boundary condi t i ons measured by t he sound
    i nt ensi t y t echni que,  Proc.  of  I nt er- noi se 89 ( 1989)  p. 1009- 1012