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Physical Modeling of Musical Sound Sources


Subsections

The Sound of Oscillating Air Jets: Physics, Modeling and Simulation in Flute-like Instruments

Patricio de la Cuadra

Flute-like instruments share a common mechanism that consists of blowing across one open end of a resonator to produce an air jet that is directed towards a sharp edge. Analysis of its operation involves various research fields including fluid dynamics, aero-acoustics, and physics. An effort has been made in this study to extend this description from instruments with fixed geometry like recorders and organ pipes to flutes played by the lips. An analysis of the jet's response to a periodic excitation is the focus of this study, as are the parameters under the player's control in forming the jet.

The jet is excited with a controlled excitation consisting of two loudspeakers in opposite phase, which not only provides accurate control over the excitation but also allows for repeatability of the experiments. A Schlieren system is used to visualize the jet, and image detection algorithms are developed to extract quantitative information from the images. In order to study the behavior of jets observed in different flute-like instruments, several geometries of the excitation and jet shapes are studied. The obtained data is used to propose analytical models that correctly fit the observed measurements and can be used for simulations.

The control exerted by the performer on the instrument is of crucial importance in the quality of the sound produced for a number of flute-like instruments. The case of the transverse flute is experimentally studied. An ensemble of control parameters are measured and visualized in order to describe some aspects of the subtle control attained by an experienced flautist. Contrasting data from a novice flautist are compared. As a result, typical values for several non-dimensional parameters that characterize the normal operation of the instrument have been measured, and data to feed simulations has been collected.

The information obtained through experimentation is combined with research developed over the last decades to put together a time-domain simulation. The model proposed is one-dimensional and driven by a single physical input. All the variables in the model are expressed in terms of pressure which allows for implementation and control in real-time. The model provides both a testbed to compare and validate measurements as well as a highly configurable and real-time musical instrument.

Reference: Forthcoming dissertation

Technique for Creating, Evaluating and Refining Digital Synthesis Models of Cetacean Acoustic Signals

Michael Gurevich

Cetacean acoustic signals (whale song) present an interesting challenge for physical modeling. The exact mechanisms of sound production in whales are still unknown, and have been a long-standing, often controversial subject of research among bioacousticians. To further complicate matters, nasal and laryngeal anatomy varies considerably between the two major groups of whales, the mysticetes (baleen whales, e.g. humpback and blue whales) and the odontocetes (toothed whales, e.g. dolphins and sperm whales). Several mechanisms of sound production have been proposed, but none have been proven conclusively.

Beginning with newly-identified structures in odontocetes thought to be homologous to human vocal folds, this research will create basic digital synthesis models of proposed production mechanisms using digital waveguide filters. The output of the models will be analytically compared with recorded cetacean signals to try to refine the models, by estimating parameters and hopefully adjusting entire model segments. Comparisons of the refined models with recorded whale song will indicate which models are best suited to the real signals, which will provide evidence of the true acoustic mechanisms found in cetaceans.

Beyond developing novel synthesis models, a future goal of this research is to help address the increasing ecological concern of anthropogenic sound in the ocean. It has been estimated that the overall background sound level in the ocean increased by 10 dB in just 25 years. Recent cetacean deaths and strandings have coincided with high-intensity SONAR activity, and other noise sources including boat noise and air-guns used in oil exploration have been shown to affect cetacean behaviour. The long-term goal of this work is to combine source synthesis models with existing models of the oceanic sound channel and cetacean hearing to create a complete digital communication simulation. With a complete model, it will be possible to test the acoustic interactions between anthropogenic sources and cetacean communication signals. Using these results, behavioural scientists will be better able to predict how anthropogenic sound may adversely affect whales.

Digital Waveguide Modeling of Acoustic Systems

Julius Smith

Digital Waveguide Filters (DWF) have proven useful for building computational models of acoustic systems which are both physically meaningful and efficient for applications such as digital synthesis. The physical interpretation opens the way to capturing valued aspects of real instruments which have been difficult to obtain by more abstract synthesis techniques. Waveguide filters were initially derived to construct digital reverberators out of energy-preserving building blocks, but any linear acoustic system can be approximated using waveguide networks. For example, the bore of a wind instrument can be modeled very inexpensively as a digital waveguide. Similarly, a violin string can be modeled as a digital waveguide with a nonlinear coupling to the bow. When the computational form is physically meaningful, it is often obvious how to introduce nonlinearities correctly, thus leading to realistic behaviors far beyond the reach of purely analytical methods.

In this context, a waveguide can be defined as any medium in which wave motion can be characterized by the one-dimensional wave equation. In the lossless case, all solutions can be expressed in terms of left-going and right-going traveling waves in the medium. The traveling waves propagate unchanged as long as the wave impedance of the medium is constant. At changes in the wave impedance, a traveling wave partially transmits and partially reflects in an energy conserving manner, a process known as ``scattering.'' The wave impedance is the square root of the ``massiness'' times the ``stiffness'' of the medium; that is, it is the geometric mean of the two sources of resistance to motion: the inertial resistance of the medium due to its mass, and the spring-force on the displaced medium due to its elasticity.

Digital waveguide filters are obtained (conceptually) by sampling the unidirectional traveling waves which occur in a system of ideal, lossless waveguides. Sampling is across time and space. Thus, variables in a DWF structure are equal exactly (at the sampling times and positions, to within numerical precision) to variables propagating in the corresponding physical system. Signal power is defined instantaneously with respect to time and space (just square and sum the wave variables.) This instantaneous handle on signal power yields a simple picture of the effects of round-off error on the growth or decay of the signal energy within the DWF system, as well as other nonlinearities. Because waveguide filters can be specialized to well studied lattice/ladder digital filters, it is straightforward to realize any digital filter transfer function as a DWF. Waveguide filters are also related to ``wave digital filters'' (WDF) which have been developed primarily by Fettweis. Using a ``mesh'' of one-dimensional waveguides, modeling can be carried out in two and higher dimensions. In other applications, the propagation in the waveguide is extended to include frequency dependent losses and dispersion. In still more advanced applications, nonlinear effects are introduced as a function of instantaneous signal level.

Digital waveguide filters can be viewed as an efficient discrete-time ``building material'' for acoustic models incorporating aspects of one-dimensional waveguide acoustics, lattice and ladder digital filters, wave digital filters, and classical network theory.

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