The pressure equalization vents of conventional microphones introduce bias errors in measurements of the sound intensity. Two error terms in the estimated active intensity are derived using a low-frequency model of microphone. The first error term is associated with the lower-limiting frequency of the microphones ͑1 to 2 Hz͒ and is proportional to the reactive sound intensity. It is shown here that the difference between limiting frequencies of the two microphones causes the second error term to be proportional to the mean-square pressure and to be of comparable importance at low frequencies. The amplitudes of errors due to the vents are analyzed in a quasistanding wave. Unlike the first error, the second can be corrected at the same time as the phase error between measurement channels, and several correction techniques are examined. For the error proportional to the reactive intensity, a correction method in a standing wave tube is suggested, using the joint measurement of several other energetic quantities. Examples of the influence of these errors on typical parameter values for half-inch microphones are presented in the case of measuring the acoustic impedance of materials using a two-microphone probe.
An experimental system has been developed for in situ measurement of the acoustical impedance of surfaces using a single microphone, pseudorandom sequences, and transfer-function techniques. It is well known that the impedance determined from two transfer functions is very sensitive to phase errors. The biased impedance has been expressed as a function of equivalent errors [J.-F. Li and J.-C. Pascal, J. Acoust. Soc. Am. 99, 969–978 (1996)]. In the system used here only one channel is used; thus the error does not include the electronic phase mismatch. However, since no experimental system is perfectly linear and repeatable, an equivalent phase error occurs. This error can be represented as the difference in phases between two average transfer functions measured sequentially at two locations. The objective of this work is to show how this error affects the impedance. The error causes a large bias at low frequencies. The results suggest that to reduce errors the distance between the two microphone locations should be large enough at low frequencies, and the number of transfer functions averaged should be as large as possible.
Spherical microphone array has been studied for various applications. In enclosed space, spherical array eliminates forward-backward grating lobes occurring in two-dimensional arrays. Beamforming and spherical harmonic decomposition are both used to map the distribution of source strength. The two approaches show similar performance at frequencies where the upper spherical harmonic order equals the product of the wave number and sphere radius. However, at lower frequencies, processing using spherical harmonics maintains the same directivity while the spatial resolution for delay-and-sum beamformer deteriorates. It has been shown that the scattering of sound by a rigid sphere improves the directivity of the same open sphere microphone beamformer, by increasing the path length travelled by incident sound. This paper concerns focused beamformer using rigid and open sphere. The concept of statistically optimized array processing (SOAP) is applied to adapt to a particular interior geometry, considering the scattered field in case of rigid sphere. The regularization process makes it possible to use a model of partially coherent sound field in the enclosed space. A deconvolution post-processing based on the knowledge of the actual steering vector leads to an efficient and robust solution to improve considerably the resolution of the source strength distribution.
Conventional data-independent beamforming with microphone array is widely used to locate sound sources and build acoustic model of equipments, engines and vehicles. The particularities of this technique are the use of a relatively few number of microphones and a simple signal processing. So, this technique is fast and easy to use. Other approaches using experimental data for computing the steering vector have been proposed to increase the resolution, for example, minimum variance method, and high-resolution methods. However these methods are often delicate to put in use in acoustic engineering where they are often reproached for lack of robustness in perturbed acoustic fields. Whereas, the most used methods nowadays are those by which the determination of the steering vector is data-independent. Among those methods we consider a method using a Statistically Optimal Array Processing (SOAP) completed by techniques of post-processing deconvolution, by which the resolution of the conventional beamforming is considerably increased, particularly at low frequencies. Some relevant indicators evaluate the performance of the proposed method by using perturbed data and by comparing between conventional and high-resolution beamformers. Examples of industrial measurements in a multi-sources environment demonstrate the practical interest of this technique.
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