John Vanderkooy

An analytic secondary source model of edge diffraction impulse responses

A new impulse-response model for the edge diffraction from finite rigid or soft wedges is presented which is based on the exact Biot–Tolstoy solution. The new model is an extension of the work by Medwin et al. [H. Medwin et al., J. Acoust. Soc. Am. 72, 1005–1013 (1982)], in that the concept of secondary edge sources is used. It is shown that analytical directivity functions for such edge sources can be derived and that they give the correct solution for the infinite wedge. These functions support the assumption for the first-order diffraction model suggested by Medwin et al. that the contributions to the impulse response from the two sides around the apex point are exactly identical. The analytical functions also indicate that Medwin’s second-order diffraction model contains approximations which, however, might be of minor importance for most geometries. Access to analytical directivity functions makes it possible to derive explicit expressions for the first- and even second-order diffraction for certain ...

An improved acoustic model for active noise control in a duct

This paper presents a model of sound propagation in a duct, for the purpose of active noise control. A physical model generally different from those explored in much of the literature is derived, with non-constant acoustic load impedance at the one end, and a coupled disturbance loudspeaker model at the other end. Experimental results are presented which validate the derived transfer function.

Dithered quantizers with and without feedback

It is shown that quantizing systems without feedback respond to the use of particular spectrally-shaped dither signals quite differently from those with feedback paths. For each type of system, conditions are given which ensure that the quantization error will be wide-sense stationary with no input dependence and with a predictable power spectral density function.<<ETX>>

Using computer algebra to explore sound-wave propagation in spherical cavities

This article shows how we have used the Maple computer algebra system to solve a classical problem in mathematical physics-that of analyzing sound-wave propagation in spherical cavities using the Fourier method to solve the wave equation. Our approach lets users easily generate and visualize solutions starting from various initial conditions for this conceptually difficult problem. To illustrate our approach, we perform a careful analysis of the propagation and reflection of spherically symmetrical sound waves for a specific initial condition.

An analytical decomposition of the Biot–Tolstoy edge diffraction model

The sound field for a rigid, infinite wedge which is irradiated from a point source has an explicit impulse response solution which has been given by Biot and Tolstoy. This solution has been the basis for methods to calculate sound fields by summing up all specular reflections from finite surfaces and edge diffraction components from finite edge segments. However, these methods have usually relied on assumptions about the solution for finite edges. In this paper an edge diffraction model is presented which uses directional edge sources and analytical expressions for the directivities are derived to give exactly the Biot–Tolstoy solution for an infinite wedge. Unlike other models, with this new model explicit expressions can be found for certain geometries, such as the on‐axis scattering from a rigid circular disc, for which both the first‐order and the second‐order edge diffraction can be derived. Furthermore, this model can be used to incorporate low‐order edge diffraction into room acoustics prediction ...

Time‐domain approaches to the edge diffraction problem: Applications to boxed loudspeakers

The classical edge diffraction problem has an exact solution for infinite and truncated wedges. There are no explicit solutions for finite wedges but approximate formulations have been presented, many of which are based on the Kirchhoff diffraction approximation. These methods fail at low frequencies and for certain geometries. A method suggested by Medwin etal . [J. Acoust. Soc. Am. 72, 1005–1013 (1982)] for finite wedges, based on the exact Biot–Tolstoy solution, has proven successful when applied to noise barrierlike geometries. They tentatively propose a method for handling multiple diffraction. In the present paper their method is tested for the application of a boxed loudspeaker, a case where multiple diffraction is clearly evident. Comparisons are made with boundary element calculations. Modifications to Medwin’s method are discussed and other methods, for example, as suggested by Vanderkooy [J. Aud. Eng. Soc. 39, 923–933 (1991)], are discussed as well. Time‐domain formulations, such as those discu...