Acoustic Potential Energy Research Articles

Active control of low-frequency random sound in enclosures

This paper evaluates the degree to which active methods can be used to reduce the level of sound-pressure fluctuations in an enclosure excited at low frequencies by a stationary random source. The spectral density of the total acoustic potential energy in the enclosure is used as a cost function for evaluating the global effectiveness of the technique. The enclosure is controlled by a secondary source whose output is constrained to act causally with respect to the primary source. The optimal causal filter relating the secondary source output to the primary source output can be deduced using classical Wiener filter theory. A numerical approach is adopted for the solution of the resulting Wiener–Hopf integral equation. It is shown that the resonances of the enclosure can be successfully suppressed by the action of the active control.

The active minimization of harmonic enclosed sound fields, part III: Experimental verification

The principle objective of this paper is to compare the measured results of active minimization experiments in an enclosed sound field with those predicted from theory. The enclosure used was essentially two dimensional over the frequency range of interest and was only lightly damped. A practical control system was built which minimized the sum of the squares of a number of microphone outputs by adjusting the outputs of a number of secondary loudspeakers at a single frequency. Various approaches to designing the algorithm which controls such a system are discussed, including matrix inversion, gradient descent methods, and pattern search methods. Although some problems with coupling between the acoustic and structural modes were initially encountered, the response of the experimental enclosure was very close to that predicted by the computer model when these problems were overcome. The pressure field inside the enclosure was measured at 200 points when excited both on resonance and off resonance, and the form of the pressure field was also found to be very similar to that predicted by the computer model. The conditions under which significant reductions in the total acoustic potential energy in the enclosure could be achieved by the action of a number of secondary sources were experimentally investigated. It was found that, in general, large reductions can be achieved only when the enclosure is excited on resonance. The secondary source does not have to be within half a wavelength of the primary to give good reductions, provided it is able to couple in to the most strongly excited modes.

The active minimization of harmonic enclosed sound fields, part II: A computer simulation

This paper is Part II in a series of three papers on the active minimization of harmonic enclosed sound fields. In Part I it was shown that in order to achieve appreciable reductions in the total time averaged acoustic potential energy, E p , in an enclosed sound field of high modal density then the primary and secondary sources must be separated by less than one half wavelength, even when a relatively large number of secondary sources are used. In this report the same theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the use of a computer model of a shallow rectangular enclosure it is demonstrated that whilst the reductions in E p which can be achieved are still critically dependent on the source locations, the criteria governing the levels of reduction are somewhat different. In particular it is shown that for a lightly damped sound field of low modal density substantial reductions in E p can be achieved by using a single secondary source placed greater than half a wavelength from the primary source, provided that the source is placed at a maximum of the primary sound field. The problems of applying this idealized form of active noise control are then discussed, and a more practical method is presented. This involves the sampling of the sound field at a number of discrete sensor locations, and then minimizing the sum of the squared pressures at these locations. Again by use of the computer model of a shallow rectangular enclosure, the effects of the number of sensors and of the locations of these sensors are investigated. It is demonstrated that when a single mode dominates the response near optimal reductions in E p can be achieved by minimizing the pressure at a single sensor, provided the sensor is at a maximum of the primary sound field. When two or three modes dominate the response it is found that if only a limited number of sensors are available then minimizing the sum of the squared pressures in the corners of the enclosure gives the best reductions in E p . The reasons for this behaviour are discussed.

The active minimization of harmonic enclosed sound fields, part I: Theory

An analysis is presented of the effectiveness with which active methods can be used for producing global reductions in the amplitude of the pressure fluctuations in a harmonically excited enclosed sound field. The total time averaged acoustic potential energy is expressed as a quadratic function of the complex strengths of a number of secondary sources of sound introduced into the enclosure. For a given number and location of secondary sources, there is a unique set of source strengths which determines the minimum value of this function. The analysis is applied to the case of a lightly damped enclosure excited by a point primary source at a frequency above the Schroeder cut-off frequency. It is demonstrated that substantial reductions in the total time averaged acoustic potential energy are possible only if the secondary sources of sound are located at a distance from the primary source which is less than half a wavelength at the frequency of interest.

Active suppression of acoustic resonance

The minimization of acoustic potential energy has been proposed as a method of actively controlling a harmonic reverberant sound field. In this paper an analysis of plane waves in a finite length duct provides insight into the physical mechanisms of this method and allows comparison with two other methods, the acoustical virtual earth and the absorbing termination. A practical technique of achieving the reduction of acoustic potential energy is presented and discussed.

Levitation using intense acoustic fields at high temperatures

Intense acoustic fields can be used to position objects without mechanical contact. This phenomenon finds application in high‐temperature materials research by enabling a specimen to be heated, melted, reacted, cooled, and solidified in a containerless state. The acoustic force vectors capable of levitating an object are given by the gradient of the acoustic potential energy density. By suitable shaping of the acoustic field, a closed energy well can be created and a small specimen captured therein. Some recent experiments were carried out in microgravity aboard the Space Shuttle in order to reduce the requirements for intense acoustic fields, typically from 145 to 165 dB, at 15 kHz. Preliminary results are presented showing successful containerless processing of glass specimens of density 5 g/cm3 at 1550 °C. Ground‐based experiments have levitated densities of 20 g/cm3 at STP and densities up to 4 g/cm3 at 1000 °C. Various results from these experiments will be presented along with a discussion of the effects of acoustic cooling, thermal perturbations of the acoustic field, and the presence of harmonics. [Work supported by NASA.]

Are acoustic intensity and potential energy density first- or second-order quantities?

A reviewer’s comment to our manuscript ‘‘Acoustic radiation produced by a beam of sound,’’ [J. Acoust. Soc. Am. 72, 1673 (1982) has prompted us to consider the question posed by the title of this manuscript, which is not an uncommon one when dealing with nonlinear problems. As might be expected, we demonstrate that the problems reside mostly with semantics. To set the record straight we define and distinguish among acoustic potential energy density, potential energy density relative to a reference state, and internal energy density, as well as intensity and acoustic intensity.