Diffuse Sound Field Research Articles

Loudspeaker testing in reverberant rooms

In the diffuse sound field of a reverberant room acoustical intensity is directly proportional to the acoustical power emitted by a source and inversely proportional to absorption in the room. If the room and microphone characteristics are known, pressure response curves of loudspeakers can be plotted which are proportional to the total acoustical power radiated by the loudspeakers. The instrumentation procedures used in mean energy density (MED) testing are described in detail with particular emphasis on the facility at the Jensen Manufacturing Company, and the role of MED measurements in the evaluation of loudspeakers is discussed.

Angular Distribution of the Normal Modes of Vibration in Rectangular Rooms

In rooms used for making sound power measurements as well as for testing acoustical materials diffuse sound fields are postulated. In addition to the requirement for a large number of properly spaced normal modes, good diffusion also requires uniform angular distribution of the modes. Hence, the design and evaluation of reverberant rooms requiring diffuse sound fields require knowledge of the angular distribution of the normal modes as well as their frequency distribution. The angular distribution of the normal modes is determined in one portion of the computer program discussed in the companion paper on the frequency distribution of normal modes in rectangular rooms. This is done by computing the angle each mode makes with the short axis of the room and counting the number which lie within each 10° class interval for each half octave. The criterion used is based on the ratio between the actual number and the ideal number in each class interval. This will be done for the same range of dimension ratios and frequencies used for computing the frequency distributions. The development of the angular distribution criterion will be discussed, and preliminary results will be presented.

Reciprocity Calibration of Microphones in a Diffuse Sound Field

Microphones can be calibrated by a primary technique in a diffuse sound field. The formula for the diffuse-field voltage response is derived from the well-known relationship for a reciprocal transducer in free space. It is shown that the reciprocity parameter for a diffuse-sound field follows from that for free space by replacing the distance by the “diffuse-field distance” of a point source. This distance depends only on the total absorption in the reverberation room. The experimental procedure is described in some detail and the results of the diffuse-field calibration of a Western Electric 640 AA condenser microphone are presented.

Errata: Absorption of Sound by a Strip of Absorptive Material in a Diffuse Sound Field [J. Acoust. Soc. Am. 31, 595 (1959)

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Absorption of Sound by a Strip of Absorptive Material in a Diffuse Sound Field

The random incidence sound absorption coefficient is calculated for a narrow strip of absorbing material set in an otherwise reflecting plane. The assumptions made are that the material is of the locally reacting type, with a real normal admittance. The effect of an imaginary component of admittance is discussed qualitatively. The results show the increase in absorption coefficient that occurs at small widths due to diffraction. Consideration is also given to the absorption of rectangular patches having both dimensions in the diffraction range. The standard reverberation room measurement of sound absorption is examined.

On the New Reverberation Chamber with Nonparallel Walls (Studies on the Measurement of Absorption Coefficient by the Reverberation Chamber Method, II)

The details of the new reverberation chamber are given. It has a volume of 513 m 3 and is surrounded by nonparallel walls. The results of model room experiments previously reported have been used to determine the shape and volume of this chamber. At 500 cps., the reverberation time of empty chamber was 22 seconds. The position of the microphone and the sound absorbing material did not affect the reverberation time of this chamber. This fact would show that the sound field of this chamber would fulfill the requisite for the diffuse sound field which is the premise of the reverberation chamber method.

Direct Measurement of the Acoustic Ratio

A direct measurement of the acoustic ratio Q—i.e., the ratio of reverberant sound energy density in an enclosure to the direct sound energy density—by a correlation technique is shown to be possible. Results of such measurements in several rooms are found to agree fairly well with values obtained from the reverberation time through the formula Q = 4πTR2/13.8V, which is based on the Sabine theory of the diffuse reverberant sound field.

Attenuation of Ear Protectors by Loudness Balance and Threshold Methods

The attenuations of two earmuffs and two earphone sockets were measured by three methods. Two of these methods used a loudness-balance procedure in which the subject, upon removal of the ear protectors, adjusted the ambient sound level to match the loudness to that which existed previously. This procedure was used with half-octave bands of thermal noise in a diffuse sound field and also with pure tones in free-field. The third method was the absolute-threshold-shift method using pure tones in free field and a clinical audiometric procedure. At the low and high frequencies, results of the threshold method indicated an average of six decibels greater attenuation than was measured by the loudness-balance thermal noise diffuse field method. Since the latter method simulates actual usage more closely than the former, it is recommended that a safety factor be applied to threshold results in estimating the protection afforded in high noise ambients by earmuffs and receiver sockets.

Sones, Spectra, and Summation

The current assumption that the loudness in sones of a noise is the sum of the loudnesses in the separate octave bands is shown under direct test to be grossly wrong. These tests show that the loudnesses in octave bands can be combined according to the formula St = Sm + F(ΣS − Sm) where St is the loudness (in sones) of the total noise, Sm is the loudness of the loudest band, ΣS is the sum of the loudnesses of all the bands, and F is a factor that may vary between zero and one. It turns out that under a wide variety of conditions the factor F has the value of 0.27. Consequently, the rule for combining the loudnesses in octave bands is simply this: to the loudness in sones of the loudest band add 0.27 times the sum of the sones in the remaining bands. In order to facilitate the determination of the loudness level (in phons) of the octave bands, equal loudness contours for octave bands were measured in a diffuse sound field. These contours differ markedly from the well-known contours for pure tones. Since loudness in sones S is related to loudness level in phons P by the relation, log S = 0.03P − 1.2, a chart can be constructed from which the loudness of a noise can be computed under the foregoing rule of summation.

Attenuation of Ear Protectors by Loudness Balance Methods

The attenuation of several ear protectors has been measured by a loudness balance technique in which the subject, upon removal of the device, raised the ambient sound level to match loudness to that which existed while wearing the ear protectors. Results were obtained for half-octave bands of thermal noise in a diffuse sound field and for single frequency tones in free field. Attenuation measured by the former method was less at both low and high frequencies than for the latter. Both loudness balance methods gave lower values than had been anticipated from published data based on the absolute threshold method.

Articulation Scores for Two Similar, Reverberant Rooms, One with Polycylindrical Diffusers on Walls and Ceiling

Two rooms of about the same dimensions, one a rectangular parallelopiped, and one having polycylindrical walls and ceiling, were measured for reverberation times and for speech articulation. No significant differences were found in either characteristic. Since one of the rooms should provide a more diffuse sound field than the other, it can be tentatively concluded that diffusion may have little influence on speech intelligibility. Both rooms exhibited rather poor articulation scores as might have been predicted from their reverberation times.

Interference Patterns at Boundaries in Reverberant Sound Fields

Starting with the definition of a diffuse sound field as having equal energy density at all points, the waves converging on any point being random in phase and direction, an analysis is given showing that a reflecting boundary large compared with the wavelength destroys the diffuseness of such a field by setting up an interference pattern. For a perfectly reflecting plane surface, the interference pattern can be expressed analytically as a mean square sound pressure varying as [1 + (sin2kx/2kx)] where x is the distance from the surface and k is the wave number. Similarly, the mean square particle velocity varies as 1 − sin2kx2kx + 1k2x2(sin2kx2kx − cos2kx), and the combination of these two expressions gives a mean energy density variation with distance proportional to 1 + (1/2k2x2)[(sin2kx/2kx) − cos2kx]. Thus the energy level at the surface is about 2.2 db higher than at points further away where the interference pattern is negligible. The effects of such interference patterns on transmission loss and reverberation room measurements are discussed. The patterns are not much affected by the frequency band widths habitually used in room acoustics. Experimental confirmation of the theory is given.

Acoustic Absorption Coefficients at High Frequencies

The measurement of the acoustic absorption coefficient by a steady state method was carried out at frequencies of 9, 20, and 30 kc for seven different materials. This involved the construction of a sound chamber with facilities for creating a diffuse sound field and a sample area where materials could be mounted. The average intensity in the chamber was measured with the sample area covered with the material under test and the results compared with similar measurements when the area was covered successively with a material of negligible absorption and when it was open to the air outside. The expression giving the absorption coefficient in terms of these three relative intensity readings is derived.

Acoustic Absorption Coefficients at High Frequencies

The measurement of the acoustic absorption coefficient by a steady state method was carried out at frequencies of 9, 20, and 30 kc for seven different materials. This involved the construction of a sound chamber with facilities for creating a diffuse sound field and a sample area where materials could be mounted. The average intensity in the chamber was measured with the sample area covered with the material under test and the results compared with similar measurements when the area was covered successively with a material of negligible absorption and when it was open to the air outside. The expression giving the absorption coefficient in terms of these three relative intensity readings is derived.

The measurement of sound absorption coefficients

Standardised absorption measurements in reverberation rooms suffer from relatively low reproducibility, especially at low frequencies and for highly absorptive samples. In these conditions, complete sound field diffusivity cannot be achieved. However, recent research has demonstrated that the theoretical diffuse absorption emerges as the ensemble average across a wide range of rooms with different geometries, even at very low frequencies. The present study aims to investigate the influence of the room geometry, sound source positioning, and presence of panel diffusers on the sound absorption values obtained in a specific reverberation room, as well as on the difference between those values and the theoretical diffuse values. The focus is on the lowest frequency bands.A numerical simulation approach is proposed, in which the room without sample is modelled in full detail using the finite element method and coupled to the sample with a Rayleigh–Ritz approach. The measurement of diffuse sound absorption is simulated in an efficient way using a stationary power balance approach. This approach is validated against measured data and against a detailed simulation of the impulse response. From the parametric study conducted with the model, it can be concluded that, for highly absorptive samples, good agreement with the theoretical diffuse absorption values can be obtained for certain room designs. In these rooms, the measured absorption is also less sensitive to the number and positioning of sources and diffusing elements.