Bruel & Kjaer Type 4002 Standing Wave Apparatus

98 Pages·2017·30.19 MB·English

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♦ PDFCover Page ♦
♦ Verso Filler Page ♦
Bruel Kjaer
&
B
K
Teletechnlcal, Acouasntdi Vciablr ational
Research
Bruel &
Copen hag
STANDING WAVE
APPARATUS
--------�
No.1 Januar19y5 5
(cid:2) Verso Filler Page (cid:2)
The Standing Wave Apparatus
by
Pcr V. Bruef. D. Se.
1902
As early as Tuma*) gave a method for measuring acoustic absorption
coefficients by m ans of standing waves in a tube. This standing w�ve method
e
has been considerably d op d in the course of time, and has contributed
evel e
greatly to the v opment of effective acoustic absorbents, which are the
de el
most effective weapon at the command of modern building technique in its
fight against noise.
In Fig. 1 a sketch of the principles of the apparatus is shown. Sound of
pressure amplitude A is directed down the length of the tube by means of a
loudspeak r at one end, to strike the sample p aced at the other end. When
e l
the sound waves encounter the sample, part of the sound energy is absorbed
and another part reflected back through the tube at an amplitude B. As a result
of interference with the incident wave a partly stationary wave is formed in
the ube, which can measured by means of the microphone probe mounted
t be
in the small moveable microphon car. In it is shown how the sound
e Fig. 2
pressure develops as a function of position, both for complete reflection, that
is to say, an absorption coeffi i n = 0, and for a partly absorbing sampl .
c e t a e
The maximum spund pressures (A+B) lie at distances of one-half wavelength
from each other, and in between these maxima lie the minimum points with
amplitudes equal to (A-B). At such maxima and minima the incident sound
wave is in phase or anti-phase with the wave reflected from the sample.
l!'Q9 2105
ill.l:
I-'-""�-'-�
r -� �
-�-e-- :-
!
I ..
I
I
I
,
I_ _________________________________ ,..-i-_-'
Principle of the Standing Wave Apparatus for measuring acoustic absorp­
Fig. 1.
tion coefficients. The audio frequency generator used is the Bruel & Kjrer
B. F. O. tYPf? 1012, while as selective amplifier either Analyzer 2105 (adjustable
to any frequency between and 12,000 cis) or Analyze 2109 (for measure-
4-7 r
ments the standardized frequencies according to table J) be used.
at may
-) Tuma: Sitz. der Rais. Akad. der Wisscnschaftcn, III 2 A, p. 402 (902).
-— 1 —-
"fhe measuring apparatus measures the relation n between the sound pressure
maxima and minima tube
III tlte
n == -(-A ..- B-)- - == --Pmax .
(A-B)
pmin
The absorption coefficient of the sample is defined as the ratio between the
energy absorbed the sample and the total energy striking the sample.
by As
energy is proportional to the square of the sound pressure, we have
the (n-l)1
a == 1 _ Bt = 1 _ = _4 __
Ai n + 1
n �
+ n + 2
It is thus particularly easy to find the absorption coefficient, provided one
knows the ratio between the maximum and minimum sound pressures. By
means of suitable construction of the electronic amplifying equipment the
a
absorption coefficti ceann be read directly as a percentage on the instrument
scale.
\eVhen a sample of an acoustic absorbing material is investigated in a standing
wave apparatus, the question what kind of absorption coefficient
arises �s to
one is measuring. It is wellk no\\n fhlm tlte acoustic literattuhraet d ifefretn
laboratories often measure widely dJf'ferent absorption coefficients for the
same material, with the result that m�ny manufacturers and users of acoustic
material have certain mistrust for acoustic absorption measurements. The
a
usual .method for measuring the acoustic absorption of a materiailst he room
method, where the material is placed in an acoustically "hard" room. The
reverberation time of the room is measured both before and after the material
is placed whereafter, by using the well known Sabine formula, one can
in it,
calculate the absorption coefficient of the ma terial by dividitnhge totaalb sorp­
tion found, by the area oft he test material: It be pointed out that what is
must
really being measured in this room method is the given material's
acoustic
One ean both theoretically and practically de­
behaviour in the given room.
monstrate that even with the very sa e testm aterial the e fe is
m acoustic f ct
different in different rooms, and these rooms, is dependent on the
again, in
placing of the material on the wall or ceilIng. Furthermore, the acoustic effect
(calculated as absorption coefficient) is dependent on the superficial area
an
of the tesmt aterial in l�.e room.
Thus, with the room method, it in a way useless to speak of a definite
i�
absorption coefficient when, at the same time, one has not precisely specified
the room's size and shape, and the material's superficial area and method of
siting. The absorption coefficitesnm easured by ther oom method are thus
not only dependent on the physical constants of the absorption material,
as the mechanical construction, thickness, density, porosity, elasticity,
such
homogeneity, etc., also to a degree influenced the conditions under
but high by
the material is measured. state of is easily understood,
which This affairs
when one considers the ab�orption coefficients measured by room
that the
method are not based directly on the definition of the absorption coefficient
as the between the energy absorbed by the sample and the total energy
ratio
-— 2 —-
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.Nr·i3� . . . . . . . . . . . . . . ...... �" .. �"'l".'" llSi •
Fig�.. S ounpdr essausra e fu nction 0/t hepo sitioofn t hemi crophoncea rf(),r
diffnetrt eerminatioTness.f tre quency 100c0I s.
a) Hard termination. Thes oundp ressuirsde e pictloegadri thmically. The
djlferbeentcwee tehne1 smta ximum and the1 smti nmium isg reatetrh na
50 db,w hicchor respondst oa zero absorption of thet ublee ss t1.h3a%n
b) As a), wiht lineparre sssucrael e.
c) Witha bsorbent terminatloigaorniht,m ics cale.
d)A s witlhi nesacra le.
c),
-— 3 —-
striking only indirectly, in by means of Sabine's statistical reverbe­
it, but that,
ration formula (which postulates a series of conditions which no practical
room can satisfy) a reverberation coefficient is calcudl_a te
The matter is quite different when it comes to the Standing Wave Apparatus
method. Here, the absorption coefficient is measurdeirdec tly the basis of
on
its definition, so thatit is only dependent on the physical constants of the
material. This fact is again demonstrated if one sendsd ifferent samples to
different laboratories with the request thatth ey be measured in a Standing
Wave Apparatus. Provided thes amples areu niform, and set up in the same
way in the apparatus, the results obtainewdil l be the same. The Standing
Wave Apparatus is therefore eminently suited for the development of new
absorption materials and for continuous production control.
In recent years, with various room acoustic problems, such as the investiga­
tion of troublesome flutter echoes and similar phenomena which can arise
in radios tudios, audiloria and so on, thes ound waves in the room have been
calculated by solving the so-callweadv e e uato , which, as a boundary
q i n in
condition for the room's limiting surfaces, the specific acoustic impedance of
the wall coverings has been inserted. This is defined as the complex ratio
between the sound pressure and particle velocity att he material's surface.
The complex form of the impedance arises because there is a phase difference
between the pressure and the particle velocity of the air att hes urface. As
' a
rule the impedance is expressed as a complex numberZ == R + jX == /Z! L'(})
The unit is the Raylw,hi ch in the CGS system is g cm-2s-1, and in the MKS
system is kg m-2s-1• It is possihle to measure this complex impedance of an
absorption material by means of the Standing Wave Apparatus, as will be
described later.
Manufacturerasn d user!l, of absorption material oftenh ave use for
very
method of working out an absorbent which has a special absorption curve
a
as function of frequency. If, for example, the frequency spectrum of the
noise in a fctory hasb een measured and found to bpea rticulaarclceyn tuated
a
forc ertain frequency bands, it would be natural tot ryt op roduce an absorb­
for placing on wallasn d roof whose most powerful absorption lay just
ent
in the frequency bands in question, whereby the most effective and economic
damping would be obtained. Very often, changes in the acoustic material,
sucha sc hanging thea irsp acing bet\\-een material and supporting wallc,h ang­
ing the degree of pt�rforation, changing thet hickness of the plate and so on,
can shift the absorption maximum within very wide limits. The Standing
Wave Apparatus is indispensable for the workingo ut and checking ofs uch
investigations.
However, the Standing Wave Apparatus hasa lso very great limitations.
it is onlyp ossible to take measurements on v ry small samples, as
Thus, e it
is a condition for mode of operation of the thatt hed iameter
the appa'ratus
be less thana bout half the length}. oft he sound. Theoretically one can
o
deduce that the condition }.>1.7 D must be satisfied ino rder that plane sound
-— 4 —-
wavese xits in: thteu beI.t i st husn otp ossiblteo t ake measurementisn t he
StandiWnagv e Apparatsu on absorbentwsh ose absorptievfef ecits b ased
on thev ibratioofnl argseu rfacesa sa whole.S imilarltyh,ec onditiounnsd er
whicht hes amplesa res etu p can oftenc ause difficualst iyti, s easyw hen
inserntgi thes amplesi nt het ubet op roduces tressiens t hed ifferelnaty ers
of them ateriaaln,d thus eithecrh anget her esonancoer evenp roducer e­
sonancewsh ichd o nota ppeari n largesru rfacaer easT.h esel imitatiaornes
ofa fundamentnala turaen,d i nu singt heS tandiWnagv e Apparatuosn e must
Jearth em in mind ata llt imesa,s otherwisoen e isl iablteo obtainq uite
meaninglersess ul.t s
What demandsm ay one make of a practicSatlan dingW ave Apparatus?
The greatets possilbef requencrya ngei so fc oursed esirebdu,t o nei sl imited
asf ara st hel owerf requenclyi miits c oncernebdy reasont hatt hea pparatus
shalble a ltitel more thana quarter wavelengtlho ngT.h ati st os ay,th ati f
thea pparatussh alble heldw ithina reasonabllee ngtho,n e can hardly
measureu nder9 0-100c isU.p wardso,n e isl imitebdy then ecessity tthhea t
diameteorf thet ubes halble lesst han0 .5826 ,i nt hat therei sa possibility
fora firsttr anvserser esonancaet thisw avelengtAhs. t het ubem ethod pre­
supposeas flasto undf ielidn t hem easurintgu be'csr osss ectiotnr,a nsverse
resonancceasn n aturalnloyt b ea lloweda,s t hesweo uldg iver iset oa varying
soundp ressurien thet ube'tsr ansverdsier ectioTno. e xtendt hef requency
ranget,h ea pparatuisn i tsl atefro rmh as two measurintgu beso,n ef or the
lower frequernacnyg eo f 95-1600c is,a nd one fort heh igherf reqeuncy
rangef rom 800-6500c is.M easurementasb ovea pprox.5 ,000c ish aven o
singificanwchea tevefro rt he absorbenutsse di n practicaes, a t thees higher
frequencimeoss tm aterisa hlavea moret hans ufficieanbts orpticvaep acity.
To make do with at ubel engtohf a littmloer e than1 /w4a veleng,t ihti sa
conditiotnh att hes oundf ielhde s ymmetricatlh roughto uthe whole lentgh
oft het ube,i .et.h,a tt hes ounds ourcebe placedq uites ymmetricaatlo lnye
end of thet ubeI.f t hisi sn ott hec asei,t i sn ecessartyo e xtendt het ubeb y
at leasat hafl waveleng,t sho as to give a sufficiently uniformt ransverse
distributoifo nt hes oundp ressurien t hatp arto f thet ubei n whicht he
measuremenits t akinpgl ace.A notherco nditioins t hatt hem easurintgu be
bes ufficiesnttiltfyhf a nto a ppreciasbpluer,i oduasm pinegf fecdtism initshhe g enerated
soundw avesr eflectienngd -to-ewnidt hiint I.n p ractitchee nt,h em easuritnugb em ust
bec irculiancr r oss-sectniootsn q,u araes i ss oo ftens eena,s i ti se xceptiondailflfyi cult
tof abricaat seq uarsee ctiosnu fficiesnttilfytf h atn o significdaenflte ction/damping
effecotcsc urW.i tht het ubet erminatbeydm eanso fa soliwdh,o llrye flectievned p iece
its houlbde p ossibtloeo btaian h ighr atiboe tweetnh em aximuma ndm inimums ound
pressurae ssi,g nt hanto d ampinogc curisn e ithetrh et ube'wsa llosr t hee ndp iece.
As botht he4 002s' l oudspeaaknedrt hea udioos cillaotftoernu sedt od riviete xhibit
a quitwee aks econhda rmoniocn,e w hosem aximal ayse xactolvye rt hem inimao ft he
fundamentoafli ntereistti ,s r ecommendeidn p ractitcoeu sea frequensceyl ective
amplifiteomr e asurteh em aximum/minimurma tio.
-— 5 —-
,.
trock s• cal
•
b
Fig3. .a )P hotograapnhd d rawingosft he StandinWga veA pparatutsyp e 4002.
b)P hotographo ft hes ixd ifferenstam pleh olders belotnogt ihneag p paratus.
For thaep paratutsob e practicabilnue s ei ti si mportantth att ests amples
canb es etu p ina simplmea nnera ndt hatw,h ilsatl sot erminatitnhget ubet,h e
holedrsc ontainitnhge mf itt het ubei na n airtigmhatn ner.
Descriptoifot nh eS tandiWnag veA pparattuysp e4 002.
Fig.3 showsa photograapnhd d rawingosf t hec ommerciaflo rmo f theS tanding
Wave Apparatucso;n sistionftg w om easurintgu bewsi thd iameterosf 3 and1 0c m
andc overinfgr equenrcayn geosf 8 00t o6 ,50c0i sa nd9 5t o1 ,60c0i sr espectively.
Theset ubecsa nb ef astenteodt hel oudspeakeenrc losusruec ht hatth eya rec oaxial
witht hel oudspeakeern,s uring thetrheegb eyn eratesdo undf ielwdi thitnh et ube
isp lanef romt hes ourceA. m icrophonper obet ubei si nserttehdr ougah h olei n
thec ente-rpolep ieceo f thel oudspekaer,w itht hem icrophoniet eslfb eing
-— 6 —-