ARTICLES

Anomalous solutions to simple wave equations
Neville H Fletcher

Designing idiophones with tuned overtones
K.A. Legge and J. Petrolito

Branched Ducts and The didjeriduo
Markus Schneider, John Smith and Joe Wolfe

Opinion evidence for practitioners
Donald Woolford

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ANOMALOUS SOLUTIONS TO SIMPLE WAVE EQUATIONS

Vol. 35, No. 2 pp 41 - 43 (2007)
ABSTRACT: Standard fourth and sixth-order differential wave equations for beams and for pairs of fluid-couple plates are shown to give rise to apparently anomalous solutions describing waves that grow in amplitude in the direction of propagation and htus violate conservation of energy when the propagating medium is semi-infinite, despite the fact that the original equations conform to this principle. The second-order wave equation for a string does not have these problems, nor do they occur in the other cases if the propagating medium is finite in extent and has simple boundary conditions at both ends. This apparent paradox can be resolved by consideration of the group velocity, which is shown to be negative in the case of the anomalous waves, thus preventing them from propagating into the half-space of the medium.

DESIGNING IDIOPHONES WITH TUNED OVERTONES

Vol. 35, No. 2 pp 47 - 50 (2007)
ABSTRACT: The design of a musical instrument is normally the preserve of the specialist instrument maker using empirical techniques developed over centuries. The analysis of instruments and the sounds they produce is undertaken by mathematicians and scientists. Recent advances in computational power and numerical techniques have provided the opportunity for analysis of physically complex vibrating structures. Moreover, these same numerical techniques can also be used to design vibrating physical structures. In this paper, we consider the application of constrained optimisation to the design of tuned beams, plates and bells.

BRANCHED DUCTS AND THE DIDJERIDUO

Vol. 35, No. 2 pp 51 - 55 (2007)
ABSTRACT: Branched ducts can produce a range of resonances and antiresonances, which may be varied by changing the termination condition. One example of the use of such branching is the forked didjeridu or didjeriduo, an unusual instrument occasionally made when a forked section of a tree is suitably eaten by termites. A single player may select the mouthpiece, then produce changes in pitch and timbre, either by adjusting lip tension to select different bore resonances, or by using the heel of his hand to close the other mouthpiece. It is even possible for two players to play the same instrument simultaneously. Here we present detailed measurements of the acoustic input impedance of a forked didjeridu and employ numerical modelling to explain the major features. The modelling gives insights into the behaviour of branched ducts in general.

A DISCUSSION OF OPINION EVIDENCE FOR PRACTITIONERS

Vol. 35, No. 2 pp 56 - 57 (2007)
ABSTRACT: This paper discusses expert opinion in dispute resolution and comments on procedures in the Commonwealth and in New South Wales. It briefly reviews science, opinion evidence and admissibility and some differences between science and law.