Advanced Mathematical Methods for Scientists and Engineers

Applied Hydraulic Transients

This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass–spring, modal, wave digital, finite difference, digital waveguide and source–filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.

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Discrete-time modelling of musical instruments

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 o...

Interaction of reed and acoustic resonator in clarinetlike systems.

http://www.cell.com/article/S240584402200041X/pdf

Hemp as a potential raw material toward a sustainable world: A review

Using an automated clarinet playing system, the frequency f, sound level L, and spectral characteristics are measured as functions of blowing pressure P and the force F applied by the mechanical lip at different places on the reed. The playing regime on the (P,F) plane lies below an extinction line F(P) with a negative slope of a few square centimeters and above a pressure threshold with a more negative slope. Lower values of F and P can produce squeaks. Over much of the playing regime, lines of equal frequency have negative slope. This is qualitatively consistent with passive reed behavior: Increasing F or P gradually closes the reed, reducing its equivalent acoustic compliance, which increases the frequency of the peaks of the parallel impedance of bore and reed. High P and low F produce the highest sound levels and stronger higher harmonics. At low P, sound level can be increased at constant frequency by increasing P while simultaneously decreasing F. At high P, where lines of equal f and of equal L are nearly parallel, this compensation is less effective. Applying F further from the mouthpiece tip moves the playing regime to higher F and P, as does a stiffer reed.

/pdf/the-clarinet-how-blowing-pressure-lip-force-lip-position-and-4e04r56hhi.pdf

The clarinet: how blowing pressure, lip force, lip position and reed "hardness" affect pitch, sound level, and spectrum.

The purpose of this study is to determine the key properties of Australian hemp particles which are used for manufacturing hempcrete. Hemp characteristics have a wide variability due to the influence of the environment conditions in various farmed areas. This study focuses on the measurements of the mechanical, thermal and acoustic performances of three Australian hemp: unretted hemp hurd, retted hemp hurd, and hemp fines. Hemp hurd is usually used in non-load bearing building walls, and hemp fine, which is the by-product of hemp manufacturing industry, is usually incorporated into a render. The experimental results show that the main impact of the retting process is a decrease in bulk density and leading to an improvement in thermal and acoustic properties. Without compaction, the bulk density is ranged from 97 and 118.8 kg.m−3, the max sound absorption coefficient from 0.88 and 0.99, and the thermal conductivity from 64 to 97 mW.m-1. K-1. Hemp fines have excellent thermal and acoustic properties and appear to be an efficient aggregate to produce an insulating render. Australian hemps investigated in this study have shown very similar characteristics to European hemps.

Physical properties of Australian hurd used as aggregate for hemp concrete

This article proposes a characterisation of the double-reed in quasi-static regimes. The non-linear relation between the pressure drop $\Delta p$ in the double-reed and the volume flow crossing it $q$ is measured for slow variations of these variables. The volume flow is determined from the pressure drop in a diaphragm replacing the instrument's bore. Measurements are compared to other experimental results on reed instrument exciters and to physical models, revealing that clarinet, oboe and bassoon quasi-static behavior relies on similar working principles. Differences in the experimental results are interpreted in terms of pressure recovery due to the conical diffuser role of the downstream part of double-reed mouthpieces (the staple).

Quasi-static non-linear characteristics of double-reed instruments

This article proposes a characterization of the double reed in quasistatic regimes. The nonlinear relation between the pressure drop, Δp, in the double reed and the volume flow crossing it, q, is measured for slow variations of these variables. The volume flow is determined from the pressure drop in a diaphragm replacing the instrument’s bore. Measurements are compared to other experimental results on reed instrument exciters and to physical models, revealing that clarinet, oboe, and bassoon quasistatic behavior relies on similar working principles. Differences in the experimental results are interpreted in terms of pressure recovery due to the conical diffuser role of the downstream part of double-reed mouthpieces (the staple).

https://hal.archives-ouvertes.fr/hal-00083699/document

Quasistatic nonlinear characteristics of double-reed instruments

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.

André Almeida

Papers

The clarinet: how blowing pressure, lip force, lip position and reed "hardness" affect pitch, sound level, and spectrum.

Physical properties of Australian hurd used as aggregate for hemp concrete

Quasi-static non-linear characteristics of double-reed instruments

Quasistatic nonlinear characteristics of double-reed instruments

Response of an artificially blown clarinet to different blowing pressure profiles.