Acoustic Power Flow Research Articles

Active control of higher-order acoustic modes in ducts

The active control of higher-order acoustic modes within a semi-infinite hard-walled rectangular duct is examined analytically for harmonic constant volume velocity sound sources. The effect of source location, size, strength, and relative phase upon the total mean acoustic power flow is investigated for both single and dual control source configurations, at a number of excitation frequencies. For the analysis, the primary source is mounted in the plane of the duct cross section, which may be a uniform surface of arbitrary finite impedance. It was found that the reduction in total acoustic power is dependent upon the relative location of the primary and control sources, both laterally across the wall of the duct and axially along the duct. The reduction in total acoustic power was found to be a maximum at axial source separation distances corresponding to multiples of half-wavelengths of the propagating modes, and at relative lateral locations such that the primary and control source mode shape function values were equivalent.

Two-sensor power measurements in lossy ducts.

Theory and measurements of the use of two adjacent pressure sensors to measure acoustic power flow of a simple harmonic sound wave in a duct are presented. This theory differs from the usual intensity-times-area formulation of this problem by including the phase shift between pressure gradient and velocity, which is caused by viscous drag on the gas at the duct wall. For high standing-wave ratios, the power obtained by this method differs significantly from the product of mid-duct intensity and duct area. These measurements confirm the method to an accuracy of 5%, even at high amplitudes where the acoustic flow is turbulent and the theory might not necessarily be valid.

Active control of higher‐order acoustic modes in duets

The examination of the physical mechanisms describing active control of acoustic plane waves propagating in rectangular section ducts [S. D. Snyder and C. H. Hansen, J. Acoust. Soc. Am. 86, 184–194 (1989)] has been extended to encompass the active control of higher‐order modes and has led to the development of an analytical model. The model allows calculation of acoustic power flow from both simple and finite size primary and control sources, radiation impedances of all sources with and without control sources operating, and total downstream power flow for a particular source of configuration. Taken into account in the analysis are the following: influence of secondary source location, both within the duct cross section and axially; number of secondary sources; relative source strengths; and relative phase angles between source signals. Results are presented showing the effect of various source arrangements on the optimal attenuation of downstream power flow.

Active noise control in ducts: some physical insights.

The mechanisms of active noise control in a duct are examined. Acoustical measurements are used to determine directly the acoustic power flow associated with both primary and secondary sources as a function of secondary to primary source strength ratio and volume velocity relative phase angles. A complete analytical model is also developed which allows calculation of individual source power flows and total downstream power flow as a function of source strengths and relative phase angles for finite size sources. It is evaluated for monopole and dual secondary source arrangements, but can be extended easily to any number of secondary sources. The model considers a finite size primary source in the plane of the duct cross section and evaluates the effect that the secondary sources have on the primary source power output. Measurements of individual source output powers and total downstream acoustic powers agree well with theoretical predictions. It is demonstrated that, for the monopole system, sound attenuation is achieved primarily by suppression of the primary source acoustic power output, with a little remaining power being absorbed by the secondary source. For the dual secondary source system, it is shown that the power is primarily absorbed by the secondary sources, but that, at phase and amplitude values slightly different to optimum, noise reduction is achieved by a combination of energy absorption and primary source power suppression. The analysis also demonstrates the dependence of the achievable noise reduction on secondary source size and location with respect to the primary source.

Acoustic energy propagation in noise control foams: Approximate formulas for surface normal impedance

Relatively stiff, partially reticulated polyurethane foam as used in noise control applications supports two longitudinal wave types having distinct propagation factors: the “frame” wave and the “airborne” wave. Both waves appear in both the solid and porous phases of the foam. Considered here is the division of acoustic power flow (within a semi‐infinite foam layer) between the two wave types and between the two phases. These divisions are strongly dependent on surface boundary conditions. Energy is carried predominantly by the frame wave and almost exclusively via the solid phase when the surface is scaled by an attached impermeable membrane; in this configuration foam behaves like a homogeneous elastic material having enhanced structural damping owing to the contained air. In contrast, when the surface is open, energy is carried by both wave types and is observed to oscillate between the solid and air phases. These observations have allowed the derivation of simplified formulae for the surface impedance of foam layers.

An ultrasonic power meter

A new ultrasonic power meter has been developed to measure the acoustic power flow of longitudinal vibration in a metallic rod as the product of particle velocity and vibration force. The technological difficulty that should be faced in measuring the vibration force by electrically obtaining the spatial differential coefficient of particle velocity has been overcome. The theory used here and the experimental verification of this method are also described.

Optimal crystal cuts and propagation directions for excitation of acoustic waves in LiNbO3

Acoustic power flow in a LiNbO3 single crystal was calculated to find the optimal crystal cutting orientation and the wave propagation direction for the efficient excitation of acoustic waves in the crystal. By solving the stiffened Christoffel equations and calculating the acoustic Poynting vectors with piezoelectric effect included, maximum longitudinal acoustic power flow in a 30° Z-rotated, Y-cut LiNbO3 crystal was found.

The use of finite‐element techniques in statistical energy analysis

When using the statistical energy analysis (SEA) technique to compute the structureborne and acoustic power flow through complex structures, a parameter of paramount importance is the coupling loss factor which characterizes the power flow across substructure boundaries. For many simple boundary types (e.g., plates connected to plates) the coupling loss factors are available in the literature, but in applying the SEA method to structures with more complex connections the finite element method can be used to advantage in computing these factors. The structure studied here consists of two beams, capable of supporting flexural, compressional, and torsional motion, connected by a small, builtup box which has several resonances in the frequency range of interest. The admittance matrix of the box structure was computed using NASTRAN. From this admittance matrix the coupling loss factors are computed. The resonant structure of the “coupler” (the box) is apparent in the results, which compared well with results from experiment.

A Method to Generate Conservation Laws for Coupled Transmission Systems

A systematic method is presented for generating a set of conservation laws for spatially distributed coupled linear systems. In contrast with previous practice, where energy balance equations were obtained by manipulating the fundamental equations of the interaction (the Maxwell equations or the equations of mechanics), or by determining the invariant quadratic forms of the motion, here the coupled systems equations are used as the point of departure. The results apply to lossy as well as to lossless devices. Illustrative examples examine the acoustic power flow in the surface acoustic-wave grating reflector and TE-TM-mode coupling in anisotropic dielectric waveguides.

Sound intensity measurements for describing acoustic power flow

This paper presents calculated and measured sound intensity data describing power flow in near, reflective and refractive acoustic fields. The data illustrate how the intensity vectors can show sources and sinks in an acoustic system and how near and far fields are linked together to form a continuous power flow. Some problems concerning the measuring technique are discussed.

Generation of acoustic waves by harmonic electric current sheets in the sea

The generation of acoustic waves by a harmonic electric current sheet in a conducting medium permeated by a weak static magnetic field is investigated. For a current sheet of 1 A/m, a time‐averaged acoustic power flow per unit area normal to the direction of travel of the wave of 2×10−16 W/m2 is generated in seawater. A possible source of these current‐generated acoustic signals is lightning. Because of the very large peak currents involved (∠20 kA), lightning striking the sea appears likely to be a strong source of transient acoustic signals in the lower ELF range (5–50 Hz).

Temperature variation of SAW power flow angle

The power flow angle of surface acoustic waves in quartz not on a crystalline axis of symmetry is shown to vary rapidly with temperature. Experimental results and theoretical calculations are presented demonstrating the dependence of the acoustic power flow angle on a doubly rotated cut of quartz.

Surface intensity patterns for a baffled plate

The spatial characteristics of the acoustic power flow at the surface of a baffled simply supported rectangular plate vibrating in flexural motion are studied to obtain an insight on the process of energy exchange between the plate and the acoustic medium. An expression for the local radiation efficiency as a function of space and frequency is presented and used to compute sound intensity patterns at the surface of the vibration plate, under different types of excitation of the plate‐bending motion. The space average of the local radiation efficiency is compared with published values and with measurements by the reverberant room method. Frequency averages (13 octave band) of this local radiation efficiency at points on the plate are compared with measurements by the accelerometer‐microphone method. Satisfactory agreements are obtained in all these comparisons. [Work performed at M.I.T.]

Band-limited power flow into enclosures

Acoustic power flow into enclosures is an area of continued research activity. Recent work [Pope and Wilby, BBN Report No. 3286 (1976)] resulted in band-limited power-flow formulations which account for coupling of structure and volume modes in the low-frequency regime and allow for a general description of the exciting external random pressure fields.

A Cell Model for Noise Propagation in Semi-Confined Spaces

A cell model is used to discuss noise propagation in semi-confined spaces such as industrial manufacturing plants, downtown urban areas, and open plan offices. The cell walls are formed, for example, by buildings, walls, screens, machinery, or arrays of pipes. The walls reflect, absorb, and transmit sound. The noise sources within each cell represent, for example, machines or vehicles. The noise field within each cell has both a direct and a reverberant component, the reverberant component being determined partly by the acoustic power flow between adjacent cells. The sound level is predicted both within and exterior to an array of cells. Depending on the reflection, absorption, and transmission coefficients chosen, the sound level within the cell region may be either higher or lower than the level obtained when the noise sources but no cell walls are present; the exterior noise level is always reduced by the presence of the walls. It is shown that with a suitable choice of coefficients the model predicts reasonably well the ambient noise levels measured in urban areas.

Acoustic performance tests and parameters for fluid piping system components: A critical evaluation of the state of the art: Part 2

This paper, which has been published in two parts, presents a critical evaluation of the state of the art relating to the measurement and characterisation of the acoustic performance of fluid system components, in particular of pumps and acoustic filters for liquid piping systems. The first part reviewed, in non-mathematical terms, the analysis techniques which can be used for acoustic circuits, and pointed out that the effect of any component (such as a filter) cannot be predicted accurately without making a complete circuit analysis. Various performance measurements and analytical parameters for acoustic filters were described, the theoretical relationships between ‘measured attenuation’ and ‘transmission loss’ were demonstrated, and causes for discrepancies between theoretical and measured filter performance discussed. Approaches toward acoustic characterisation of pumps and other noise sources were examined, and this lead to the conclusion that the difficulties therein have only begun to be recognised, and are far from solved. Some new suggestions for experimental approaches were presented. This second part deals more directly with practical considerations in the design of acoustic test loops for liquid piping system components. After a review of the general requirements, more detailed consideration is given to the measurement of standing waves, to entrained and entrapped air problems, to the design of practicable acoustic ‘terminations’, and to the advantages and disadvantages of plastic pipes for loop piping and filter models. Slightly more mathematical appendices deal with the acoustic impedance and acoustic velocity in fluid-filled elastic pipes, and the measurement of acoustic power flow.

Acoustic performance tests and parameters for fluid piping system components: A critical evaluation of the state of the art: Part 1

This paper, to be published in two parts, presents a critical evaluation of the state of the art relating to the measurement and characterisation of the acoustic performance of fluid system components, in particular of pumps and acoustic filters for liquid piping systems.The first part reviews, in non-mathematical terms, the analysis techniques which can be used for acoustic circuits, and points out that the effect of any component (such as a filter) cannot be predicted accurately without making a complete circuit analysis. Various performance measurements and analytical parameters for acoustic filters are described, the theoretical relationships between ‘measured attenuation’ and ‘transmission loss’ are demonstrated, and causes for discrepancies between theoretical and measured filter performance are discussed. Approaches toward acoustic characterisation of pumps and other noise sources are examined, and this leads to the conclusion that the difficulties therein have only begun to be recognised, and are far from solved. Some new suggestions for experimental approaches are presented.The second part will deal more directly with practical considerations in the design of acoustic test loops for liquid piping system components. After a review of the general requirements, more detailed consideration will be given to the measurement of standing waves, to entrained and entrapped air problems, to the design of practicable acoustic ‘terminations’, and to the advantages and disadvantages of plastic pipes for loop piping and filter models.Slightly more mathematical appendices will deal with the acoustic impedance and acoustic velocity in fluid-filled elastic pipes, and the measurement of acoustic power flow.

Perturbation Theory for Electromagnetic Coupling to Elastic Surface Waves on Piezoelectric Substrates

Starting from the fundamental acoustic and electromagnetic field equations an approximate expression is obtained for the perturbation in propagation wavenumber of a surface acoustic wave in a piezoelectric crystal. The source of perturbation is taken to be a surface spaced an air-gap distance h above the piezoelectric and is described in terms of an electrical impedance. The resulting perturbation is found in terms of the perturbing electrical impedance, an effective dielectric constant for the piezoelectric, the air-gap spacing h, and a perturbation coupling constant defined in terms of the unperturbed electric potential at the piezoelectric surface and the average acoustic power flow per unit frequency. The theory is applied to the case of a short-circuit perturbing surface and found to be in excellent agreement with certain numerical results for Y-cut Z-propagating LiNbO3 and several cuts of Bi12 GeO20. In the general case of a complex perturbing impedance, such as that exhibited by a semiconductor, the theory indicates that attenuation or gain and dispersion may be introduced by the perturbation, in close agreement with experimental observations.

Experimental Investigation of Jet Noise Generated by Cold Air Flow through Standard and Unusual Nozzles

Far-field sound-pressure levels were measured in an anechoic room for a selected number of standard and unusual nozzle types, the latter being modifications of optimum configurations previously reported in ASD-TDR-62-303. The results are reported in terms of over-all acoustic power vs mass flow, and are compared with various 8th-power relations. Spectral analyses are presented as well. An attempt is made to normalize acoustic and flow parameters with respect to size and temperature. [Supported by Propulsion Laboratory, Aeronautical Systems Division.]

Experimental Investigation of Jet Noise Generated by Cold Air Flow through a Wide Variety of Small Nozzles

Over-all sound-pressure levels were measured in an anechoic room for 20 different nozzle configurations, including converging, converging-diverging, slot, and annular types, the latter with and without center-core flow. The results are examined in terms of over-all acoustic power vs mass flow, and they are compared with various eighth-power relations. The acoustic performance of most nozzles was similar in the subsonic region. Howere, certain annular-type nozzles exhibited a marked superiority in the supersonic region. (This work was supported by Propulsion Laboratory, Aeronautical Systems Division.)