176 PhiJips tech. Rev. 37,176-179,1977, No. 7

The design and construction of anon-rectangular reverberation chamber

The rather strange structure now taking shape at thePhilips Research Laboratories complex in Eindhoven isa reverberation chamber. This is a chamber with hardsound-reflecting walls and is of great value in acousticmeasurements. The chamber now being built should beready by about March 1978; it will be used for inves-tigations connected with noise abatement. These willinclude measurements on appliances such as vacuumcleaners and washing machines, to help in the design ofquieter products, and measurements on productionmachines, so that noise can be reduced in workshopsand factories. A reverberation chamber is also neces-sary for for testing the quality of sound-absorbentmaterial.

When a reverberation chamber is available it is pos-sible to obtain a quick and reliable measurement of the

acoustic power radiated from an acoustic source. Inthe ideal case an acoustic source in a reverberationchamber produces a homogeneous and isotropicacoustic field, whose level is directly related to thepower of the source. The acoustic field is homogeneousand isotropic because a large number of standing-wavepatterns are excited simultaneously. As a result of thesuperposition of all these standing-wave patterns thereis no preferential excitation of anyone frequency, andno one place or direction is systematically favoured.The result is an almost continuous spectrum of res-onant frequencies. Any chamber in the form of arectangular parallelepiped and with a volume of200 m3

corresponds fairly well with this ideal picture at fre-quencies above about 250 Hz, i.e. at wavelengthsshorter than about IA m. For longer waves, however,

Philips tech. Rev. 37, No. 7 NON-RECTANGULAR REVERBERATION CHAMBER 177

the possible number of standing-wave patterns in sucha chamber is limited, and the chamber then has aclearly discontinuous spectrum ofresonant frequencies.It has long been known that a better approximation

to the ideal behaviour of a reverberation chamber canbe obtained at these low frequencies by making thewalls oblique in such a way that the chamber is asym-metric in all three dimensions. This has the effect ofproducing irregular spatial patterns of standing waves.Superposition of the few standing-wave patterns oc-curring at low frequencies then leads to a more homo-geneous acoustic field than in a 'rectangular' chamber.This asymmetry also has the effect of producing thedesired uniform distribution ofthe resonant frequenciesover the frequency scale.The standing-wave patterns and resonant frequen-

cies of a rectangular reverberation chamber can be cal-culated analytically [1]. This is not possible ifthe cham-ber is not rectangular. In the past this was often held tobe a major drawback of a non-rectangular chamber.Nowadays, however, the behaviour of a non-rectan-gular chamber can be calculated numerically by meansofthe finite-element method [2].

In spite of the greater technical problems, we there-fore decided to build a reverberation chamber of irreg-ular shape. In calculating the sound-pressure distribu-tion with the finite-element method the total volume ofthe chamber is divided into a large number of tet-rahedral elements, and the differential equation for theacoustic field in the chamber is replaced by a set ofequations for the field at the nodes of the tetrahedralnetwork. The results of such a numerical calculationwill be more accurate the finer the meshes of the net-work. To keep down the amount of calculation re-quired, we only considered the frequency range below

Ix=5m

IY=7mD_ _-J:::J1

(6)(;) mI

20 30 40 50 60 70 80 90 100Hz-fr

Fig. 1. Behaviour of the resonant frequency Ir of a two-dimen-sional rectangular chamber of total area 5 X 7 m2, when one ofthe short walls is rotated through an angle O. Each ofthe resonantfrequencies is characterized by a pair of numbers (nXlly) thatindicates the number of half-periods in the standing-wave patternin the x- and y-directions ofthe rectangular chamber.

125 Hz; this is the range where the various resonantfrequencies are relatively far apart.We calculated a number of standing-wave patterns

in this frequency range, for both two-dimensional andthree-dimensional chambers [3].

The first thing that we noticed during these calcula-tions was that if the angle of one of the walls waschanged slightly, the effect on the resonance spectrumwas completely unpredictable. Fig. 1 shows the cal-culated behaviour of a number of resonant frequenciesin a two-dimensional chamber, with a surface area of5X 7 m2, as one of the walls is rotated through anangle. The result of changing the angles of two wallscannot be found by superimposing the results of chang-ing the angles of each of the two walls separately. Fig. 2shows a number of calculated st~nding-wave patternsfor the two-dimensional rectangular chamber and fora non-rectangular chamber' with the same area. Athigher frequencies in particular there is hardly anyagreement between the pattern in a rectangular cham-ber and that in a non-rectangular chamber.The computer time necessary for 'calculating the

acoustic field in a single three-dimensional chamber isconsiderable, and the geometry of a three-dimensionalnon-rectangular chamber., is determined by a largenumber of parameters. The method of calculation istherefore not so suitable for calculating the optimumvalues of all these parameters, and hence the optimumshape of the chamber. It'is however possible to cal-culate the acoustic field ina given chamber. From cal-culations of this kind it can be seen quantitatively whya non-rectangular chamber is superior to a rectangularone, both in the homogeneity of the acoustic field andin the regularity of the spectrum of resonant frequen-cies in the low-frequency region.We arrived in this way at a shape that promised

acceptable behaviour even at frequencies lower than100 Hz, and which has characteristics that come withinthe limits recommended in the ISO standards [4]. Thismeans that our future measurements will be imme-diately comparable with measurements made elsewherein other reverberation chambers constructed to thesestandards. This basis for intercomparison is particularly

[1] P. M. Morse, Vibration and sound, McGraw-HiII, New York,2nd edition 1948, chapter VIII.J. W. Strutt, 3rd Baron Rayleigh, The theory ofsound, Vol. 11,Macmillan, London, 2nd edition 1896, sections 267 and 299.

[2] The principles of the finite-element method are described inthe article by J. H. R. M. Eist and D. K. Wielenga in thisvolume ofPhilips tech. Rev., p. 56 (No. 2/3).

[3] J. M. van Nieuwland and C. Weber, to be published shortly.[4] International Standard ISO 3741-1975: Acoustics - Deter-

mination of sound power levels of noise sources - Precisionmethods for broad-band sources in reverberation rooms.International Standard ISO 3742-1975: Acoustics - Deter-mination of sound power levels of noise sources - Precisionmethods for discrete-frequency and narrow-band sources inreverberation rooms.

178

(10)

o+100

fr=34.3Hz

fr =lI. 6Hz

J. M. VANNIEUWLAND eta!.

(13)

-100

(04)

fr=98.0Hz

fr=95.3Hz

Philips tech. Rev. 37, No. 7

(30)

100

fr=81.1Hz

-100

fr=102.9Hz

tr =103.9Hz

Fig. 2. Calculated sound-pressure distributions in a two-dimensional rectangular chamber andin a non-rectangular chamber of' the same area. The calculations were carried out for a numberof the lowest resonant frequencies. The resonant frequency fr is indicated in each case. Thenodallines (zero sound pressure) are the bold contours. The pressure value in relative units isindicated next to the other contours of equal sound pressure. The correspondence in shapebetween the patterns in the two chambers is soon lost at higher resonant frequencies.

tr=85.5Hz

desirable since future recommendations and specifica-tions are expected that will quantify the permittedsound levels from equipment such as domestic ap-pliances.

The shape finally chosen for the reverberation cham-ber after we had considered the results of our calcula-

A' •..... I \"'"' .._

~fl

A

tions is shown in fig. 3. The fioor is not rectangular,only two of the four side walls are perpendicular to thefioor, and the ceiling consists oftwo planes that are notparallel to the floor. The volume of the chamber is227 m3. To check the calculations we made a modelfrom concrete slabs, at a quarter of full scale, in which

Fig.3. Plan of the reverberation chamber (left) and a vertical cross-section along the line AA'(right). The concrete wall of the reverberation chamber is shown grey; the sound-insulatingbrick walls of the enclosure are shown black. To prevent external vibrations from entering thechamber through the floor, the ISO-tonne concrete chamber is mounted on 80 stee! coil springs.

Philips tech. Rev. 37, No. 7 NON-RECTANGULAR REVERBERATION CHAMBER'

.y

ty

t

50 70 90dB-Lp

50 70 90dB-Lp

50 70 90dB-Lp

Fig. 4. Distribution of the sound pressure Lp as a function of theX-, y-, and z-coordinate in the final design of our reverberation 'chamber. The solid lines give the distribution calculated for thefull-sized chamber at a frequency of 91.4 Hz, the points give themeasurements for the quarter-scale model at a frequency of365.5 Hz. In the neighbourhood of the nodallines the differencebetween measurements and calculations may be relatively large.At these positions small deviations in the location of the micro-phone used for the measurements result in large errors, and thedimensions ofthe microphone will also have an effect.

the sound pressure was measured at a large number oflocations. As can be seen infig. 4, the results of thesemeasurements are in good agreement with the calcula-tions.The chamber is built entirely of reinforced concrete.

Special precautions were taken to make the inside sur-face as smooth as possible to give the maximum soun'dreflection from the walls.The unpredictable and sometimes drastic effect of a

small change in dimensions on the characteristics ofthechamber, as mentioned earlier, meant that the dimen-sions specified in the design had to be adhered to veryaccurately in the construction. A heavy-wooden struc-ture, supported by steel girders, was therefore made forthe internal shuttering (formwork) of the concretechamber, as shown in the title photograph. This wood-en structure was later covered with a cladding of specialvery.hard smooth plywood boards. The exterior of theboarded formwork exactly followed the dimensions ofthe interior ofthe chamber.To reduce external interference as much as possible

during the measurements the entire reverberation cham-ber is enclosed inside a space with heavy brick walls.These walls are lined inside with sound-absorbingmaterial to prevent resonances inthe gap between thewalls and the outside ofthe chamber. The weight ofthechamber will be 150 tonnes, and it will stand on 80steel coil springs located around the outside edge of thebase. The natural frequency ofthe complete structure isat about 3 to 4 Hz, so that external vibrations at a fre-quency higher than about 10Hz will have no noticeableeffect on the chamber. Very high frequencies may how-ever be transmitted along the springs; to prevent this,rubber pads are placed between the springs and thefoundation. The wall of the reverberation chamber hasopenings, which can be tightly sealed, for ventilationand for introducing cables. The chamber itself and thesurrounding structure are closed with heavy sound-proofed doors.

•

J. M. van NieuwlandA. PettersonC.Weber

Dr Ir J. M. vall Nieuwland, Ing. A. Petterson and Dr Ir C. Weberare with Philips Research Laboratories, Eindhoven.

179

'.