67 research outputs found
Response of an artificially blown clarinet to different blowing pressure profiles
Using an artificial mouth with an accurate pressure control, the onset of the
pressure oscillations inside the mouthpiece of a simplified clarinet is studied
experimentally. Two time profiles are used for the blowing pressure: in a first
set of experiments the pressure is increased at constant rates, then decreased
at the same rate. In a second set of experiments the pressure rises at a
constant rate and is then kept constant for an arbitrary period of time. In
both cases the experiments are repeated for different increase rates. Numerical
simulations using a simplified clarinet model blown with a constantly
increasing mouth pressure are compared to the oscillating pressure obtained
inside the mouthpiece. Both show that the beginning of the oscillations appears
at a higher pressure values than the theoretical static threshold pressure, a
manifestation of bifurcation delay. Experiments performed using an interrupted
increase in mouth pressure show that the beginning of the oscillation occurs
close to the stop in the increase of the pressure. Experimental results also
highlight that the speed of the onset transient of the sound is roughly the
same, independently of the duration of the increase phase of the blowing
pressure.Comment: 14 page
Resonance modes in a 1D medium with two purely resistive boundaries: calculation methods, orthogonality and completeness
Studying the problem of wave propagation in media with resistive boundaries
can be made by searching for "resonance modes" or free oscillations regimes. In
the present article, a simple case is investigated, which allows one to
enlighten the respective interest of different, classical methods, some of them
being rather delicate. This case is the 1D propagation in a homogeneous medium
having two purely resistive terminations, the calculation of the Green function
being done without any approximation using three methods. The first one is the
straightforward use of the closed-form solution in the frequency domain and the
residue calculus. Then the method of separation of variables (space and time)
leads to a solution depending on the initial conditions. The question of the
orthogonality and completeness of the complex-valued resonance modes is
investigated, leading to the expression of a particular scalar product. The
last method is the expansion in biorthogonal modes in the frequency domain, the
modes having eigenfrequencies depending on the frequency. Results of the three
methods generalize or/and correct some results already existing in the
literature, and exhibit the particular difficulty of the treatment of the
constant mode
Interaction of reed and acoustic resonator in clarinetlike systems
Sound emergence in clarinetlike instruments is investigated in terms of
instability of the static regime. Various models of reed-bore coupling are
considered, from the pioneering work of Wilson and Beavers ["Operating modes of
the clarinet", J. Acoust. Soc. Am. 56, 653--658 (1974)] to more recent modeling
including viscothermal bore losses and vena contracta at the reed inlet. The
pressure threshold above which these models may oscillate as well as the
frequency of oscillation at threshold are calculated. In addition to Wilson and
Beavers' previous conclusions concerning the role of the reed damping in the
selection of the register the instrument will play on, the influence of the
reed motion induced flow is also emphasized, particularly its effect on playing
frequencies, contributing to reduce discrepancies between Wilson and Beavers'
experimental results and theory, despite discrepancies still remain concerning
the pressure threshold. Finally, analytical approximations of the oscillating
solution based on Fourier series expansion are obtained in the vicinity of the
threshold of oscillation. This allows to emphasize the conditions which
determine the nature of the bifurcation (direct or inverse) through which the
note may emerge, with therefore important consequences on the musical playing
performances
Contribution to harmonic balance calculations of self-sustained periodic oscillations with focus on single-reed instruments
International audienceThe harmonic balance method Í‘HBMÍ’ was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion Í‘square signalsÍ’ of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring
Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet
International audienceThis paper investigates the modal analysis of wind instruments as seen from the input of their air column. Beside the treatment of analytical models, a particular emphasis is given to the analysis of measured input impedances. This requires special care because the measurements cover only a limited frequency band and are affected by some unknown errors. This paper describes how the Prony analysis and the Least Squares Complex Exponential (LSCE) classical techniques can be used in this context and how the main pitfalls can be avoided in their application. A physically acceptable method of reconstruction of the low frequency band is proposed. A technique using fictitious points in the high frequency range is described in order to ensure the passivity of the resonator in the whole frequency band. The principles of a real-time synthesis of clarinet sounds based on the modal representation of the resonator is given as an application, with a method to efficiently handle the modal representation during the transition between fingerings
Approximation of 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 & Schwinger for the unflanged case and extracted from the radiation
impedance matrix given by Zorumski for the infinite flanged case.Comment: Journal of Sound and Vibration (2008) accepte
Iterated maps for clarinet-like systems
The dynamical equations of clarinet-like systems are known to be reducible to
a non-linear iterated map within reasonable approximations. This leads to time
oscillations that are represented by square signals, analogous to the Raman
regime for string instruments. In this article, we study in more detail the
properties of the corresponding non-linear iterations, with emphasis on the
geometrical constructions that can be used to classify the various solutions
(for instance with or without reed beating) as well as on the periodicity
windows that occur within the chaotic region. In particular, we find a regime
where period tripling occurs and examine the conditions for intermittency. We
also show that, while the direct observation of the iteration function does not
reveal much on the oscillation regime of the instrument, the graph of the high
order iterates directly gives visible information on the oscillation regime
(characterization of the number of period doubligs, chaotic behaviour, etc.)
Idealized digital models for conical reed instruments, with focus on the internal pressure waveform
International audienceTwo models for the generation of self-oscillations of reed conical woodwinds are presented. They use the fewest parameters (of either the resonator or the ex-citer), whose influence can be quickly explored. The formulation extends iterated maps obtained for loss-less 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 characteristics 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
Propagation of acoustic waves in two waveguides couples by perforations. I. Theory.
International audienceThe problem of propagation in two guides coupled by perforations, important for a perforated tube muffler, is discussed. At low frequencies, if the distance between perforations is sufficiently large, a discrete model can be used. An exact equivalent circuit for a perforation is obtained by using a modal theory and a matrix formalism. A series inductance due to the existence of antisymmetric field in the perforation is proven to exist, completing the perforation shunt impedance concept. This model is directly exploitable for lattice analysis. For homogeneous lattices (i.e. with identical propagation in the two guides), either regular or irregular, two modes exist: a planar mode and a "flute" mode, either propagating or evanescent. Cutoff frequencies of periodic lattices are found to depend on either the shunt inductance or the series inductance (the first cutoff depending on the shunt one). In homogeneous lattices, a new type of evanescent waves can exist, with non-zero energy flux, equal and opposite in sign in each guide. Finally, the effect of mean flow in such a lattice is discussed
Idealized digital models for conical reed instruments, with focus on the internal pressure waveform
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