Matching of Fundamental Modes at a Junction of a Cylinder and a Truncated Cone; Application to the Calculation of Some Radiation Impedances

Kergomard, Jean; Lefebvre, Antoine; Scavone, Gary P.

doi:10.3813/aaa.918912

Cited by 7 publications

(4 citation statements)

References 16 publications

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“…The effect of the plane is interpreted by Dalmont as a correction ∆m r of the radiation inertance without plane m r0 (unflanged pipe). If the plane distance h p is short in comparison with the radius opening r o (h p ≪ r o ), the inertance correction is approximately proportional to the inverse of this distance: The junction of a cylinder and a truncated cone, studied by Kergomard et al [21], is also comparable to the problem studied here. Indeed, the case where the truncated cone is semi-infinite is equivalent to a cylinder surrounded by an inclined wall (Fig.…”

Section: Simplification and Generalizationsupporting

confidence: 56%

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An Inclined Plane: A Simple Model for the Acoustic Influence of the Flutist's Face

Ernoult¹,

Cuadra²,

Fabre³

2018

Acta Acustica united with Acustica

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In some flute-like instruments, the musician places their mouth near an open-end of the pipe, which modifies the radiation of the pipe and its acoustic resonances. To improve the prediction of this modification, this work presents a study on the effect of an inclined plane at the end of a radiating pipe. The radiation impedance is first measured for different positions of the plane. After verifying that the plane mainly adds an inertance to the radiation, a new simpler and more convenient measurement method is proposed. The behavior observed in these measurements is generalized with the use of finite element simulations. Finally, a global low-frequency model of the effect of an inclined plane on both the imaginary and the real part of the radiation impedance is proposed. This model is consistent with the well-established radiation impedances for unflanged and flanged pipes.

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Section: Simplification and Generalizationsupporting

confidence: 56%

“…It is only valid for acute cones (θ ≤ π).If the angle of the cone is sufficiently wide, this expression can be approximated for low frequencies by the expression of Eq. (2), leading to an inertance m (cone) r and a coefficient ζ (cone) [21]:…”

Section: Simplification and Generalizationmentioning

confidence: 99%

An Inclined Plane: A Simple Model for the Acoustic Influence of the Flutist's Face

Ernoult¹,

Cuadra²,

Fabre³

2018

Acta Acustica united with Acustica

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show abstract

“…Thus, if this volume is set by means of a cylindrical mouthpiece, a new parameter is introduced (either the length y of the mouthpiece or its cross section area S m ) and this leads to the first model, described in the present section. The matching of the plane waves in the cylindrical mouthpiece with the spherical waves in the cone can be done with an excellent precision, 22 but for the present purpose, the continuity of the flow rate and mean pressure is assumed between the output of the cylinder and the input of the cone. Fig.…”

mentioning

confidence: 99%

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

Kergomard

Guillemain

Silva

et al. 2016

The Journal of the Acoustical Society of America

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Two models for the generation of self-oscillations of reed conical woodwinds are presented. They 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 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 semiquantitative 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.

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“…At the open end, the radiation is modeled by the dimensionless radiation impedance Z R given by Silva et al [23] (see also [24]) as a fraction of two polynomials N R (ω)/D R (ω). Then, accounting for the transfer matrix between the input and the output of the pipe, the dimensionless input impedance can be expressed as the ratio of two functions Z(ω) = N (ω)/D(ω), N and D having zeros only (i.e., no poles)…”

Section: Example: the Cylindrical Pipementioning

confidence: 99%

Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

Taillard¹,

Silva

Guillemain

et al. 2018

Applied Acoustics

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Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet. Applied Acoustics, Elsevier, 2018, 141, pp.271 -280 AbstractThis 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. A musically relevant example finally illustrates the possibilities of the modal analysis applied to wind instruments.

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Matching of Fundamental Modes at a Junction of a Cylinder and a Truncated Cone; Application to the Calculation of Some Radiation Impedances

Cited by 7 publications

References 16 publications

An Inclined Plane: A Simple Model for the Acoustic Influence of the Flutist's Face

An Inclined Plane: A Simple Model for the Acoustic Influence of the Flutist's Face

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

Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

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