Measurement of complex acoustic intensity in an acoustic waveguide

Abstract

Acoustic intensity is normally treated as a real quantity, but in recent years many articles have appeared in which intensity is treated as a complex quantity where the real (active) part is related to local mean energy flow, and the imaginary (reactive) part to local oscillatory transport of energy. This offers the potential to recover additional information about a sound field and then to relate this to the properties of the sound source and the environment that surrounds it. However, this approach is applicable only to a multi-modal sound fields, which places significant demands on the accuracy of the intensity measurements. Accordingly, this article investigates the accuracy of complex intensity measurements obtained using a tri-axial Microflown intensity probe by comparing measurement and prediction for sound propagation in an open flanged pipe. Under plane wave conditions comparison between prediction and experiment reveals good agreement, but when a higher order mode is present the reactive intensity field becomes complicated and agreement is less successful. It is concluded that the potential application of complex intensity as a diagnostic tool is limited by difficulties in measuring reactive intensity in complex sound fields when using current state of the art acoustic instrumentation.3

On the use of power reflection ratio and phase change to determine the geometry of a blockage in a pipe

“…The reason for this discrepancy is the approximation inherent in the volume velocity matching conditions used for the inlet and outlet plane of the blockage in the plane wave model. This is confirmed by comparing plane wave predictions with a full finite element model [20,21], which is also shown in Fig. 2.…”

“…In this article, analysis is restricted to the plane wave region only and it will be shown that this is sufficient to recover the area ratio and the length of the blockage. Whilst it is attractive to make use of higher order modes, maybe to try and recover more information about the shape of the blockage, this has been found to be very difficult to do, even under very controlled laboratory conditions [20]. This is believed to be because higher order modes are very sensitive to the boundary conditions in a duct and this sensitivity makes it difficult to develop a reliable and robust technique suitable for use under less controlled conditions, such as sewer systems [20].…”

“…Whilst it is attractive to make use of higher order modes, maybe to try and recover more information about the shape of the blockage, this has been found to be very difficult to do, even under very controlled laboratory conditions [20]. This is believed to be because higher order modes are very sensitive to the boundary conditions in a duct and this sensitivity makes it difficult to develop a reliable and robust technique suitable for use under less controlled conditions, such as sewer systems [20]. Furthermore, higher order modes are dispersive and so this makes a methodology that utilises a change in phase more difficult to implement.…”

“…Therefore, in order to investigate the effect of these errors, the plane wave based predictions will be compared against a full treatment of the problem (based on a mode matching approach) in section 3 [20,21].…”

Steering Acoustic Intensity Estimator Using a Single Acoustic Vector Hydrophone

“…Given a single source with continuous spectrum against a background of isotropic and band-limited white Gaussian noise, azimuth angle estimation can be performed using a complex acoustic intensity estimator (CAIE, also known as an acoustic energy flux estimator), which is a maximumlikelihood detector, and an azimuth angle estimator that employs a single vector hydrophone, as discussed in [14]. The use of a complex acoustic intensity estimator is further discussed in [15][16][17]. In the presence of interference or multiple sources, the acoustic energy flux is a mixture of the signals from all the sources.…”