Plane Rigid Baffle Research Articles

Interface reflection wave of axisymmetric directional spherical-wave

The sound radiation field of a circular piston source in an infinite plane rigid baffle can be approximated as an axisymmetric directional spherical-wave. The interface response expressions of the axisymmetric directional spherical-wave for the piston parallel with the interface has already been obtained in previous studies. On condition that the distance from the piston center to the interface is much greater than the piston radius, we first derive the conical wave expansion of the axisymmetric directional spherical-wave which is obtained by using the conical wave expansion of the homogeneous spherical-wave and the formula of the axisymmetric directional spherical-wave excited by a circular piston in an rigid infinite plane, and then derive the expression of the interface reflection wave of the axisymmetric directional spherical-wave for the piston non-parallel to the interface. The expression of the interface reflection wave is simplified into a simplified expression by saddle point method on condition that the source distance is much larger than the acoustic wavelength. The simplified expression is not only simple in the calculation, but also clear in the physical meaning. The simplified expression shows that the interface reflection wave of the axisymmetric directional spherical-wave can be regarded as the product of the axisymmetric directional spherical-wave excited by the piston mirror image and the reflection coefficient. The calculations show that when the piston radius is smaller than the acoustic wavelength, the reflected wave is less sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is weak. When the piston radius is greater than the acoustic wavelength, the reflected wave is very sensitive to the angle included between the piston and the interface and the azimuth of the receiving point, and the directivity of the reflected wave is strong. Increasing the angle included between the piston and the interface, the reflected wave and its directivity both first increase and then decrease. The reflected wave is largest and the directivity of the reflected wave is strongest when the angle included between the piston and the interface is equal to that between the interface normal and the connecting line between the mirror image of the piston center and the receiving point.

An extended lumped-element model and parameter estimation technique to predict loudspeaker responses with possible surround-dip effects

Lumped-element models have long been used to estimate the basic vibration and radiation characteristics of moving-coil loudspeakers. The classical low-frequency model combines and simplifies several important driver elements, predicting only a single mechanical resonance wherein the diaphragm (e.g., cone and dust cap) and the inner portion of the surround move together as an effective piston. Even if the diaphragm maintains piston-like motion with increasing frequency, the flexible surround eventually vibrates out of phase, producing another resonance whereby a noticeable "surround dip" may occur in the radiated pressure spectrum. The classical model is unable to predict this behavior. This paper explores an extended lumped-element model that better characterizes the distinct diaphragm, surround, spider, and other properties of a loudspeaker in a plane rigid baffle. It extends effective modeling to mid frequencies and readily predicts a surround dip in the radiated response. The paper also introduces a method to estimate model parameters using a scanning laser Doppler vibrometer, a surround resonance indicator function, and a constrained optimization routine. The approach is validated by its ability to better predict on-axis pressure responses of several baffled loudspeakers in an anechoic environment.

Radiation impedance matrices for rectangular interfaces within rigid baffles: Calculation methodology and applications

The coupling of sound fields through a finite-sized aperture in a plane rigid baffle where the region (half-space) on one side is unbounded can be described by an integral equation which constitutes a boundary condition for the field on the other side of the aperture. Such a boundary condition, when the pressure and the normal velocity are expanded in basis functions defined over the aperture, can be recast into a matrix form relating the coefficients of the basis functions in the expansions, the principal feature being a matrix of fourfold (double-area) integrals analogous to those encountered in studies of radiation from flexible pistons in rigid baffles. A substantial analytical reduction to sums of single nonsingular integrals is derived for the elements of this radiation impedance matrix when the aperture is rectangular and the basis functions are expressible as a sum of products of exponential functions of the Cartesian coordinates of the aperture plane, with the exponential coefficients being arbitrary complex numbers. The validity of the result is substantiated by its reduction to previously published results for less general cases. Its utility is demonstrated with the example of diffraction by a square hole in a screen.

Radiation impedance matrix of a rectangular aperture, with arbitrary vibration, in a rigid baffle

The present paper shows that multidimensional integrals associated with radiation from a rectangular surface in a plane rigid baffle can be reduced to one-dimensional integrals. If the vibrational excitation is expanded into a summation over a set of basis functions, the surface pressure and velocity may be related by an infinite matrix. Each element of the matrix is expressed as a quadruple integral. The numerical evaluation of such integrals, although possible, is prohibitively time consuming for many practical applications. However, for some choices of the basis functions, each quadruple integral may be reduced analytically to single integrals. Explicit expressions are given for square surfaces and with the basis functions taken as products (or sums of products) of trigonometric functions. Numerical results agree well with previous results published in the literature for the pressure distribution over a surface when the vibration is uniform.

A criterion for an energy vortex in a sound field

Measurements with intensity meters have shown that energy vortices exist in certain sound fields. In these vortices, sound energy flows around closed paths, in the steady state. Vortices occur in some sound fields (e.g., that of a point source near a reflecting edge), but not in others (e.g., that of a plane rigid piston in a plane rigid baffle). It is shown that in a two-dimensional or axisymmetric sound field, a necessary and sufficient condition for a vortex to exist is the presence of an isolated maximum or minimum in the stream function. Two examples are given for a vortex in (a) a duct of square cross section, and (b) the field of two monopole sources, one of which just extinguishes the other. Some relations for the interaction between two monopole sources are also given.

Ultrasound fields in attenuating media.

For medical ultrasonic imaging and for nondestructive testing, the attenuation of pressure waves and the resulting shift in wave velocity are important features in commonly used transmission media such as biological tissue. An algorithm for the numerical evaluation of pressure field distributions generated by ultrasonic transducers is presented. The attenuation and dispersion of the sound transmission medium are taken into consideration. The sound fields are computed numerically for continuous wave as well as pulse excitation. The transducer has plane or gently curved geometry and is embedded in a plane rigid baffle. The numerically determined pressure fields are presented as 3D plots, as gray-scale images for a fixed time stamp (like a snapshot), or as isobars regarding the maximum values over time for each local point in the area under investigation. The algorithm described here can be utilized as a tool for design of ultrasound transducers, especially array antennas.

Calculation of the external‐ear directional filter function of the KEMAR manikin

In order to assess the quantitative reliability of the calculation of sound diffraction by the external ear using the boundary‐integral‐equation method [S. Koshigoe and A. Tubis, J. Acoust. Sac. Am. Suppl. 1 73, S76 (1982)], we calculate the directional filter function for the KEMAR manikin external ear. The calculations are based on the assumptions of blocked meatus conditions and the embedding of the external ear in a plane rigid baffle. [Work supported by NSF.]

Sound Field of a Pulsed, Planar, Straight-Edged Radiator

Assuming pulsed or CW conditions, theoretical expressions are derived for the farfield of an arbitrary plane straight-edged radiator, vibrating with spatially uniform velocity within an infinite plane rigid baffle. The results are then specialized to radiators whose shapes are regular polygons. The farfield is made up of components, termed “transmission replica pulses,” which are shown to act, in general, as if they originated at the corners of the radiators. Examples of pulsed field structure and of CW directivity curves of polygonal radiators are presented.

Numerical computation of the radiation impedance of a rigid annular ring vibrating in an infinite plane rigid baffle

An expression for the radiation impedance of a rigid annular ring vibrating with uniform amplitude in a close-fitting infinite plane rigid baffle is presented. An algorithm for the numerical evaluation of this expression by electronic computer is included in the form of an Algol 60 procedure. A selection of numerical results obtained is included.

Variational Finite-Element Calculation of the Acoustic Response of a Rectangular Panel

The problem of the acoustic response of a structure falls into three parts. (1) The response of the structure to given acoustic excitation, when the effect on the vibration of the resultant acoustic radiation is ignored. This part of the problem is usually solved by using a normal-mode approach, and has usually therefore been carried out only for simply supported plates, for which the normal modes are simple functions. (2) The determination of the acoustic radiation from a given structural vibration. Numerous workers have calculated the total radiated energy and/or the radiation-intensity-distribution pattern for different vibrating surfaces. (3) The effect of the radiation on the response of the plate. This aspect is usually ignored, and when the acoustic medium is air, it is in any case, an effect that is usually negligible. When it is included, the problem is closed (in the sense that it has a feedback loop) and its theoretical analysis involves the use of integral equations. Morse has recently solved the complete problem for the case of a circular membrane set in an infinite plane rigid baffle. In this paper, a variational principle derived in an earlier paper [J. Sound Vibration 4, 233 (1966)] is used in conjunction with a finite element method to calculate the response of a rectangular panel set in an infinite plane rigid baffle. The method can be applied with equal ease to plates with different boundary conditions, and the effect of the acoustic radiation on the plate vibration is considered in full.

Generation of an acoustic pulse by a baffled circular piston

The generation of acoustic disturbances in a fluid of semi-infinite extent by the motion of a circular piston surrounded by a plane rigid baffle has been studied quite extensively (see (1), (2), (3), (4) and further references given in these papers). Attention has been devoted mainly to the case in which the piston executes a harmonic oscillation of small amplitude, and only comparatively recently has Oberhettinger (2) demonstrated how the time-harmonic solution can be used to solve the more general problem in which the normal velocity of the piston is an arbitrary function of time. The purpose of the present paper is two-fold. Firstly, we point out that for arbitrary normal motion of the piston the " baffled piston problem " can be solved directly, and in a particularly simple manner, by means of a technique involving integral transforms which has been applied by Mitra (5) and Eason (6) to the study of shear wave propagation in an elastic half-space. Secondly, we give a more detailed account than appears to be available in the literature of the structure of the sound pulse generated by the arbitrary normal motion of a baffled piston.

Numerical Methods for the Computation of Acoustic Radiation Functions

During the last decade, the large scale digital computer has become available to almost all scientists. The speed and accuracy of such machines has led some people to use mathematical methods that are not always appropriate. The primary purpose of this paper is to discuss some numerical methods for the improvement of the convergence of series encountered in acoustical theories. This paper is restricted to general comments and a discussion of one special case, namely the mutual mechanical impedance between circular pistons in an infinite plane rigid baffle, which has been represented by Pritchard as a double or single series of Bessel function products. If the separation of the two pistons is large as compared with the diameter of the pistons, the series can be represented to sufficient accuracy by its partial sum of a very few terms. On the other hand, if the separation is only slightly greater than the diameter, a large number of terms must be included in the partial sum. Methods for reducing the numerical computations and/or improving the accuracy of results have been studied. An integral method has been used with excellent success.

Near-Field and Far-Field Radiation from an Experimental Electrically Steered Planar Array

Current interest in electrically steered transducers has led to new experimental and theoretical work. Several years ago extensive measurements were made on a large planar broadside array. Experimental results in the near and far fields agreed to excellent accuracy with theory based upon the assumption of an infinite, plane rigid baffle. This paper includes new experimental results for a similar transducer array which was electrically steered to seven different angles from broadside to endfire. These results are compared with theory based upon the infinite baffle assumption. It is demonstrated that both near-field and far-field errors increase as the steering angle approaches the endfire case. It is concluded that the effects of a finite baffle must be considered in any theory that is to be used for arrays steered to large angles from broadside. This observation is also important relative to radiation impedance computations.