Finn Jacobsen

A comparison of two different sound intensity measurement principles

The dominating method of measuring sound intensity in air is based on the combination of two pressure microphones. However, a sound intensity probe that combines an acoustic particle velocity transducer with a pressure microphone has recently become available. This paper examines, discusses, and compares the two measurement principles with particular regard to the sources of error in sound power determination. It is shown that the phase calibration of intensity probes that combine different transducers is very critical below 500 Hz if the measurement surface is very close to the source under test. The problem is reduced if the measurement surface is moved further away from the source. The calibration can be carried out in an anechoic room.

Near field acoustic holography with particle velocity transducers

Near field acoustic holography is usually based on measurement of the pressure. This paper describes an investigation of an alternative technique that involves measuring the normal component of the acoustic particle velocity. A simulation study shows that there is no appreciable difference between the quality of predictions of the pressure based on knowledge of the pressure in the measurement plane and predictions of the particle velocity based on knowledge of the particle velocity in the measurement plane. However, when the particle velocity is predicted close to the source on the basis of the pressure measured in a plane further away, high spatial frequency components corresponding to evanescent modes are not only amplified by the distance but also by the wave number ratio (kz∕k). By contrast, when the pressure is predicted close to the source on the basis of the particle velocity measured in a plane further away, high spatial frequency components are reduced by the reciprocal wave number ratio (k∕kz). ...

The coherence of reverberant sound fields

A new method of measuring spatial correlation functions in reverberant sound fields is presented. It is shown that coherence functions determined with appropriate spectral resolution contain the same information as the corresponding correlation functions, and that measuring such coherence functions is a far more efficient way of obtaining this information. The technique is then used to verify theoretical predictions of the spatial correlation between various components of the particle velocity in a diffuse sound field. Other possible applications of the technique are discussed and illustrated with experimental results obtained in an ordinary room.

A note on the calibration of pressure-velocity sound intensity probesa)

A pressure-velocity sound intensity probe is a device that combines a pressure microphone with a particle velocity transducer. Various methods of calibrating such sound intensity probes are examined: a far field method that requires an anechoic room, a near field method that involves sound emitted from a small hole in a plane baffle, a near field method where the sound is emitted from a hole in a spherical baffle, and a method that involves an impedance tube. The performance of the two near field methods is examined both in an anechoic room and in various ordinary rooms. It is shown that whereas reflections from the edges from a plane baffle disturb the calibration, the method based on a spherical baffle gives acceptable results in a wide frequency range even when the calibration is carried out in a small office, provided that the distance between the hole and the device under test is about 5cm.

Beamforming with a circular microphone array for localization of environmental noise sources

It is often enough to localize environmental sources of noise from different directions in a plane. This can be accomplished with a circular microphone array, which can be designed to have practically the same resolution over 360°. The microphones can be suspended in free space or they can be mounted on a solid cylinder. This investigation examines and compares two techniques based on such arrays, the classical delay-and-sum beamforming and an alternative method called circular harmonics beamforming. The latter is based on decomposing the sound field into a series of circular harmonics. The performance of the two signal processing techniques is examined using computer simulations, and the results are validated experimentally.

A NUMERICAL AND EXPERIMENTAL INVESTIGATION OF THE PERFORMANCE OF SOUND INTENSITY PROBES AT HIGH FREQUENCIES

The influence of scattering and diffraction on the performance of sound intensity probes has been examined using a boundary element model of an axisymmetric two-microphone probe with the microphones in the usual face-to-face arrangement. On the basis of calculations for a variety of sound field conditions and probe geometries it is concluded that the optimum length of the spacer between the microphones is about one microphone diameter; with this geometry the effect of diffraction and the finite difference error almost counterbalance each other up to about an octave above the frequency limit determined by the finite difference approximation. This seems to be valid under virtually any sound field condition that could be of practical importance in sound power determination. The upper frequency limit corresponds to about 10 kHz for an intensity probe with 12-in. microphones, which means that it should be possible to cover most of the audible frequency range, say, from 50 Hz to 10 kHz, with a single probe conf...

A method of measuring the dynamic flow resistance and reactance of porous materials

Abstract A method of measuring the frequency dependent flow resistance and reactance of porous materials in a duct is presented and examined. The method involves measuring the transfer function between the signals from two microphones placed on either side of a sample of the material. The validity of the method is tested by comparing measured values of the surface impedance of the material with values predicted from the measured flow resistance and reactance.

A note on acoustic decay measurements

Abstract Two sources of experimental errors in acoustic decay measurements are investigated: smoothing produced by the averaging device and “ringing” of the bandpass filter. Both linear and exponential averaging are considered. It is concluded that if it is only the average slope of the decay curve which is of interest, it suffices that the integration time of the detector is less than one quarter of the reverberation time of the system under test (with linear averaging), that the “reverberation time” of the detector is less than the half of the reverberation time of the system (with exponential averaging), and that the product of the filter bandwidth and the reverberation time of the system is at least 16. The requirements are much stronger if the important initial part of the decay is needed, however.

A note on the concept of acoustic center

The acoustic center of a reciprocal transducer is defined as the point from which spherical waves seem to be diverging when the transducer is acting as a source. This paper examines various ways of determining the acoustic center of a source, including methods based on deviations from the inverse distance law and methods based on the phase response. The considerations are illustrated by experimental results for condenser microphones.

Sound field reconstruction using acousto-optic tomography

When sound propagates through a medium, it results in pressure fluctuations that change the instantaneous density of the medium. Under such circumstances, the refractive index that characterizes the propagation of light is not constant, but influenced by the acoustic field. This kind of interaction is known as the acousto-optic effect. The formulation of this physical phenomenon into a mathematical problem can be described in terms of the Radon transform, which makes it possible to reconstruct an arbitrary sound field using tomography. The present work derives the fundamental equations governing the acousto-optic effect in air, and demonstrates that it can be measured with a laser Doppler vibrometer in the audible frequency range. The tomographic reconstruction is tested by means of computer simulations and measurements. The main features observed in the simulations are also recognized in the experimental results. The effectiveness of the tomographic reconstruction is further confirmed with representations of the very same sound field measured with a traditional microphone array.