Fabrice Silva

Approximation formulae for the acoustic radiation impedance of a cylindrical pipe

Useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and mathematical principles are met, like Hermitian symmetry for the reflection coefficient (identical behaviour of positive and negative frequencies) and causality for the impulse response. A non-causal but more accurate expression is also proposed that is suitable for frequency-domain applications. The formulae are obtained by analytical and numerical fitting to reference results from Levine and Schwinger for the unflanged case and extracted from the radiation impedance matrix given by Zorumski for the infinite flanged case.

MoReeSC: a framework for the simulation and analysis of sound production in reed and brass instruments

This paper presents a free and open-source numerical framework for the simulation and the analysis of the sound production in reed and brass instruments. This tool is developed using the freely distributed Python language and libraries, making it available for acoustics student, engineers and researchers involved in musical acoustics. It relies on the modal expansion of the acoustic resonator (the bore of the instrument), the dynamics of the valve (the cane reed or the lips) and of the jet, to provide a compact continuous-time formulation of the sound production mechanism, modelling the bore as a series association of Helmholtz resonators. The computation of the self-sustained oscillations is controlled by time-varying parameters, including the mouth pressure and the players embouchure, but the reed and acoustic resonator are also able to evolve during the simulation in order to allow the investigation of transient or non-stationary phenomena. Some examples are given (code is provided within the framework) to show the main features of this tool, such as the ability to handle bifurcations, like oscillation onset or change of regime, and to simulate musical effects.

Behavior of reed woodwind instruments around the oscillation threshold

Properties of small amplitude oscillations of the single reed woodwind instruments near the oscillation threshold are investigated. Analytical formulae with explicit dependence on the physical parameters of the instrument and instrumentist allow to determine the bifurcation point, the nature of the bifurcation, the amplitude of the first harmonics and the oscillation frequency. The model, which takes the reed dynamics into account, is entirely expressed in the frequency domain and its behaviour is analysed. An application to a model of saxophone is proposed and compared with numerical results obtained through the harmonic balance technique and a time domain simulation, showing excellent agreements.

Some simulations of the effect of varying excitation parameters on the transients of reed instruments

This paper considers the simulation of self-sustained oscillations in reed and brass instruments, based on a compact continuous-time formulation of the sound production mechanism. The control parameters such as the mouth pressure and the players embouchure, but also the acoustic resonator and the reed may vary with respect to time, allowing the analysis of transient and non-stationary phenomena like changes of regime. A particular attention is first given to staccato notes, with comparison of the evolution of the instantaneous frequency in simulations to theoretical and experimental results. This shows the importance of using realistic control parameters on the onset of the oscillations. When the acoustic resonator is modelled using a modal expansion with non-stationary resonance frequencies and damping, it is also possible to simulate and study slurs and musical effects like the wah-wah, gaining some insight on the mechanisms involved.

Idealized digital models for conical reed instruments, with focus on the internal pressure waveform

Two models for the generation of self-oscillations of reed conical woodwinds are presented. The models use the fewest parameters (of either the resonator or the exciter), whose influence can be quickly explored. The formulation extends iterated maps obtained for lossless cylindrical pipes without reed dynamics. It uses spherical wave variables in idealized resonators, with one parameter more than for cylinders: the missing length of the cone. The mouthpiece volume equals that of the missing part of the cone, and is implemented as either a cylindrical pipe (first model) or a lumped element (second model). Only the first model adds a length parameter for the mouthpiece and leads to the solving of an implicit equation. For the second model, any shape of nonlinear characteristic can be directly considered. The complex characteristic impedance for spherical waves requires sampling times smaller than a round trip in the resonator. The convergence of the two models is shown when the length of the cylindrical mouthpiece tends to zero. The waveform is in semi-quantitative agreement with experiment. It is concluded that the oscillations of the positive episode of the mouthpiece pressure are related to the length of the missing part, not to the reed dynamics.

Self-oscillations of a vocal apparatus: a port-Hamiltonian formulation

Port Hamiltonian systems (PHS) are open passive systems that fulfil a power balance: they correspond to dynamical systems composed of energy-storing elements, energy-dissipating elements and external ports, endowed with a geometric structure (called Dirac structure) that encodes conservative interconnections. This paper presents a minimal PHS model of the full vocal apparatus. Elementary components are: (a) an ideal subglottal pressure supply, (b) a glottal flow in a mobile channel, (c) vocal-folds, (d) an acoustic resonator reduced to a single mode. Particular attention is paid to the energetic consistency of each component, to passivity and to the conservative interconnection. Simulations are presented. They show the ability of the model to produce a variety of regimes, including self-sustained oscillations. Typical healthy or pathological configuration laryngeal configurations are explored.

Conical reed instruments: A hierarchy of parameters

Some aspects of sound production by wind musical instruments are rather well understood. A minimum model for reed cylindrical instruments was proposed in 1983 by Mc Intyre et al. When the reed dynamics and resonator losses are ignored, the mouthpiece pressure is a square signal. Three primary parameters are necessary: (i) the mouth pressure; (ii) the “valve” parameter (based on the reed opening and its stiffness); (iii) the length of the cylinder. The model gives a simplified shape of the waveform; the playing frequency and the amplitude are rather well predicted. For further spectrum details, it is necessary to add losses, therefore a secondary parameter, the radius. Furthermore other parameters influence the spectrum: reed dynamics, toneholes, vocal tract.... What happens for conical reed instruments? Considering the waveform of the mouthpiece pressure, a fourth primary parameter is the length of the missing part of the truncated cone. Similarly to cylindrical instruments, a secondary parameter is relat...

Corrigendum to “Approximation formulae for the acoustic radiation impedance of a cylindrical pipe” [J. Sound Vib. 322 (2009) 255–263]

The authors regret that the above-mentioned paper contains the erroneous Eq. (20) Z r (ω) = (d 1 − n 1)jka − d 2 (jka) 2 2 − (d 1 + n 1)jka + d 2 (jka) 2 (20) which should have been written as Z r (ω) = (n 1 − d 1)jka + d 2 (jka) 2 2 − (d 1 + n 1)jka + d 2 (jka) 2 (20 ′) i.e. the negative of the published expression, thus leading to the correct unit behaviour for high frequencies. This modification does not affect any other part of the paper and the results in Table (1) are still valid. To the best of our knowledge, we have not found any misuse of this formula in any citing article. The authors would like to apologize for any inconvenience caused and are grateful to Prof. James Beauchamp for drawing the attention to the above-mentioned error.

Theoretical and experimental study of glottal geometry in phonation

Most existing theoretical models of phonation assume that the vocal folds are parallel and that the glottis forms a two-dimensional channel for the flow. However, during phonation the vocal folds can be very accurately abducted or adducted using intrinsic muscles acting on the arytenoid cartilages. The resulting shape of the glottis can then vary between an almost uniform slit (when the vocal folds are parallel) to a V shape (with an angle between the vocal folds up to 20 °). Further, the vocal folds surface can present some irregularity which can be severe, in some pathological cases such as cysts or nodules. In this paper, we present a theoretical and experimental study performed in order to evaluate and to predict these geometrical effects. A theoretical model to predict the pressure losses in such a non-uniform glottis will be presented and tested against an in-vitro experimental set-up using a self-oscillating latex replica of the vocal folds. The angle between the artificial folds could be controlle...

Minimum models for self-sustained oscillations of conical reed instruments.

It is now well known that a minimum model for self-sustained oscillations of clarinet-like instruments is the iterated map model, leading to square signals. The reed is assumed to be without dynamics, while losses are ignored (or assumed to be independent of frequency). The generalization to conical instruments is not straightforward. For the present work, the minimum model is used for a truncated cone instrument, but the missing part of the cone is not assumed to be small compared to the wavelength. Thus the result should be a signal without sharp corners. However, without any kind of mouthpiece, no periodic sound can be obtained in a steady-state regime. It will be explained that the choice of a model for the mouthpiece can be done without adding any supplementary parameter (therefore a conical resonator has one parameter only more than a cylindrical one). It is shown that several choices are possible, allowing either the use of: the same inverse nonlinear characteristic than for clarinet-like instrumen...