Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach

Waveguide model of the hearing aid earmold system

BACKGROUND: The earmold system of the Behind-The-Ear hearing aid is an acoustic system that modifies the spectrum of the propagated sound waves. Improper selection of the earmold system may result in deterioration of sound quality and speech intelligibility. Computer modeling methods may be useful in the process of hearing aid fitting, allowing physician to examine various earmold system configurations and choose the optimum one for the hearing aid user. METHODS: In this paper, a computer model adequate for this task is proposed. This model is based on the waveguide modeling method. The waveguide model simulates the propagation of sound waves in the system of cylindrical tubes. Frequency response of the hearing aid receiver is simulated in the model and the influence of the ear canal and the eardrum on the earmold system is taken into account. The model parameters are easily calculated from parameters of a physical hearing aid system. Transfer function of the model is calculated and frequency response plots are obtained using the Matlab system. RESULTS: The frequency response plots of the earmold model were compared to the measurement plots of the corresponding physical earmold systems. The same changes in frequency responses caused by modification of length or diameter of a selected waveguide section, are observed in both measurement data of a real earmold system and in computed model responses. CONCLUSION: Comparison of model responses obtained for various sets of parameters with measurement data proved that the proposed model accurately simulates the real earmold system and the developed model may be used to construct a computer system assisting the physician who performs earmold system fitting

Audibility of dispersion error in room acoustic finite-difference time-domain simulation as a function of simulation distance

Finite-difference time-domain (FDTD) simulation has been a popular area of research in room acoustics due to its capability to simulate wave phenomena in a wide bandwidth directly in the time-domain. A downside of the method is that it introduces a direction and frequency dependent error to the simulated sound field due to the non-linear dispersion relation of the discrete system. In this study, the perceptual threshold of the dispersion error is measured in three-dimensional FDTD schemes as a function of simulation distance. Dispersion error is evaluated for three different explicit, non-staggered FDTD schemes using the numerical wavenumber in the direction of the worst-case error of each scheme. It is found that the thresholds for the different schemes do not vary significantly when the phase velocity error level is fixed. The thresholds are found to vary significantly between the different sound samples. The measured threshold for the audibility of dispersion error at the probability level of 82% correct discrimination for three-alternative forced choice is found to be 9.1 m of propagation in a free field, that leads to a maximum group delay error of 1.8 ms at 20 kHz with the chosen phase velocity error level of 2%.Peer reviewe

Time domain wave separation using multiple microphones

Methods of measuring the acoustic behavior of tubular systems can be broadly characterized as steady state measurements, where the measured signals are analyzed in terms of infinite duration sinusoids, and reflectometry measurements which exploit causality to separate the forward and backward going waves in a duct. This paper sets out a multiple microphone reflectometry technique which performs wave separation by using time domain convolution to track the forward and backward going waves in a cylindrical source tube. The current work uses two calibration runs one for forward going waves and one for backward going waves to measure the time domain transfer functions for each pair of microphones. These time domain transfer functions encode the time delay, frequency dependent losses and microphone gain ratios for travel between microphones. This approach is applied to the measurement of wave separation, bore profile and input impedance. The work differs from existing frequency domain methods in that it combines the information of multiple microphones within a time domain algorithm, and differs from existing time domain methods in its inclusion of the effect of losses and gain ratios in intermicrophone transfer functions.Publisher PDFPeer reviewe

A single microphone capillary-based system for measuring the complex input impedance of musical wind instruments

Capillary-based systems for measuring the input impedance of musical wind instruments were first developed in the mid-20th century and remain in widespread use today. In this paper, the basic principles and assumptions underpinning the design of such systems are examined. Inexpensive modifications to a capillary-based impedance measurement set-up made possible due to advances in computing and data acquisition technology are discussed. The modified set-up is able to measure both impedance magnitude and impedance phase even though it only contains one microphone. In addition, a method of calibration is described that results in a significant improvement in accuracy when measuring high impedance objects on the modified capillary-based system. The method involves carrying out calibration measurements on two different objects whose impedances are well-known theoretically. The benefits of performing two calibration measurements (as opposed to the one calibration measurement that has been traditionally used) are demonstrated experimentally through input impedance measurements on two test objects and a Boosey and Hawkes oboe

On the numerical solution of the 2d wave equation with compact fdtd schemes

This paper discusses compact-stencil finite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and efficiency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also discusses the relevance to digital waveguide mesh modelling, and highlights the optimally efficient explicit scheme

Modelling the Mechanical Response of the Reed-mouthpiece-lip System of a Clarinet. Part I. The Finite-difference Approach

The motion of a clarinet reed that is clamped to a mouthpiece and supported by a lip is simulated in the time domain using finite difference methods. The reed is modelled as a bar with non-uniform cross section, and is described using a one-dimensional, fourth-order partial differential equation. The interactions with the mouthpiece lay and the player's lip are taken into account by incorporating conditional contact forces in the bar equation. The model is completed by clamped-free boundary conditions for the reed. An implicit finite difference method is used for discretising the system, and values for the physical parameters are chosen both from laboratory measurements and by accurate tuning of the numerical simulations. The accuracy of the numerical system is assessed through analysis of frequency warping effects and of resonance estimation. Finally, the mechanical properties of the system are studied by analysing its response to external driving forces. In particular, the effects of reed curling are investigated

Modelling the mechanical response of the Reed-mouthpiece-lip system of a clarinet : Part I. A one-dimensional distributed model

The motion of a clarinet reed that is clamped to a mouthpiece and supported by a lip is simulated in the time domain using finite difference methods. The reed is modelled as a bar with non-uniform cross section, and is described using a one-dimensional, fourth-order partial differential equation. The interactions with the mouthpiece lay and the player's lip are taken into account by incorporating conditional contact forces in the bar equation. The model is completed by clamped-free boundary conditions for the reed. An implicit finite difference method is used for discretising the system, and values for the physical parameters are chosen both from laboratory measurements and by accurate tuning of the numerical simulations. The accuracy of the numerical system is assessed through analysis of frequency warping effects and of resonance estimation. Finally, the mechanical properties of the system are studied by analysing its response to external driving forces. In particular, the effects of reed curling are investigated