The metre

A musical wind instrument transforms a constant pressure input from the player's mouth into a fluctuating pressure output in the form of a radiating sound wave. In reed woodwind and brass instruments, this transformation is achieved through a nonlinear coupling between two vibrating systems: the flow control valve formed by the mechanical reed or the lips of the player, and the air column contained by the pipe. Although the basic physics of reed wind instruments was developed by Helmholtz in the nineteenth century, the application of ideas from the modern theory of nonlinear dynamics has led to recent advances in our understanding of some musically important features of wind instrument behaviour. As a first step, the nonlinear aspects of the musical oscillator can be considered to be concentrated in the flow control valve; the air column can be treated as a linear vibrating system, with a set of natural modes of vibration corresponding to the standing waves in the pipe. Recent models based on these assumptions have had reasonable success in predicting the threshold blowing pressure and sounding frequency of a clarinet, as well as explaining at least qualitatively the way in which the timbre of the sound varies with blowing pressure. The situation is more complicated for brass instruments, in which the player's lips provide the flow valve. Experiments using artificial lips have been important in permitting systematic studies of the coupling between lips and air column; the detailed nature of this coupling is still not fully understood. In addition, the assumption of linearity in the air column vibratory system sometimes breaks down for brass instruments. Nonlinear effects in the propagation of high amplitude sound waves can lead to the development of shock waves in trumpets and trombones, with important musical consequences.     

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.     

Vibration characteristics of pipe organ reed tongues and the effect of the shallot, resonator, and reed curvature

Pipe organ reed pipes sound when a fixed-free curved brass reed mounted on a shallot connected to a resonator is forced to vibrate by an impressed static air pressure. Five sets of experiments were performed in order to investigate the influence of the most important parameters which could affect the tone of a reed pipe. First, the phase difference between the pressure variation in the shallot and the boot, and its relationship to the motion of the reed tongue were analyzed to compare their phases and their spectra. Next, the frequency dependence of the reed on three basic parameters (reed thickness, its vibrating length, and the imposed static air pressure) was investigated in an attempt to determine an empirical equation for the frequency. For each trial, two of the variables were kept constant while the third was altered in order to construct an equation giving frequency as a function of the three variables. Third, experiments were conducted using three different types of shallots: the American (or English) style, the French style, and the German style. The results show that for each shallot, the frequency increases linearly with thickness and linearly with air pressure (over the normal operating range of the reed). For each of the shallots, frequency varies inversely with length when the other variables are held constant. The effect on the reed spectrum of using the three different types of shallot was also investigated, as was the effect of reducing the interior volume of each type. Progressively filling the shallot interior generally decreases the frequency of the vibrating reed. The effect of the resonators on frequency and spectrum was studied because the resonator is an integral part of the resulting tone; virtually every reed stop has some type of resonator. The resonator tends to raise the Q of the impedance peaks and reduce the fundamental frequency. Finally, the influence of the type and degree of curvature on reed vibration was briefly examined; increasing the reed curvature tends to decrease the vibration frequency and increase the sound intensity by creating a richer spectrum.     

管束穿孔板的管腔耦合共振吸声机理研究

为了揭示管束穿孔板共振吸声结构的吸声机理,利用热黏性条件下基于有限元算法的管束穿孔板仿真模型,研究了平面声波正入射条件下,管束穿孔板内部声场分布特征,并利用阻抗管对吸声系数的理论仿真结果进行了试验验证.结果表明,管束穿孔板在低频主要靠腔体共振吸声,在高频主要靠管共振吸声,管束穿孔板整体呈现出较为明显的管腔耦合共振吸声特征。管束穿孔板共振时管中声强和质点法向振速较大,高频次吸声峰频点处管中和腔中均有驻波形成,频率越高驻波数量越多.管束穿孔板的耦合共振受到管长、腔深、穿孔率和管内径等参数变化的影响,管长对高频耦合共振的影响最大,管长增大使高频主吸声峰频点移向低频,并使相邻主吸声峰之间的间距减小.      

传统笙的物理模型及声音合成方法

为研究传统笙的物理结构与音色之间的关系,提出了传统笙的物理模型及声音合成方法。在簧舌振动模型的基础上,结合指孔和音窗的传输矩阵计算方法,建立了笙管的等效电路,并将二者结合,得到笙的完整物理模型。为了验证模型的有效性,设计了一套笙的实验系统,实现了对笙管发声过程中特征量的多通道同步测量。通过对比实验和模型仿真结果的时频域特点以及与音色相关的特征量,分析了模型的性能.结果表明,该模型可较好地模拟传统笙管的发声过程,合成笙样本能够较准确的反映真实笙样本的音色特征。      

Reed vibration in lingual organ pipes without the resonators

Vibrations of plucked and blown reeds of lingual organ pipes without the resonators have been investigated. Three rather surprising phenomena are observed: the frequency of the reed plucked by hand is shifted upwards for large-amplitude plucking, the blown frequency is significantly higher than the plucked one, and peaks halfway between the harmonics of the fundamental frequency appear in the spectrum of the reed velocity. The dependence of the plucked frequency on the length of the reed reveals that the vibrating length at small vibrations is 3 mm shorter than the apparent free length. The frequency shift for large-amplitude plucking is explained by the periodic change of the vibrating length during the oscillation. Reed vibrations of the blown pipe can be described by a physical model based on the assumption of air flow between the reed and the shallot. Aerodynamic effects may generate and sustain the oscillation of the reed without acoustic feedback. The appearance of subharmonics is explained by taking into account the periodic modulation of the stress in the reed material by the sound field. Therefore, a parametric instability appears in the differential equation of vibration, leading to the appearance of subharmonics.     

Numerical simulations of fluid-structure interactions in single-reed mouthpieces

Most single-reed woodwind instrument models rely on a quasistationary approximation to describe the relationship between the volume flow and the pressure difference across the reed channel. Semiempirical models based on the quasistationary approximation are very useful in explaining the fundamental characteristics of this family of instruments such as self-sustained oscillations and threshold of blowing pressure. However, they fail at explaining more complex phenomena associated with the fluid-structure interaction during dynamic flow regimes, such as the transient and steady-state behavior of the system as a function of the mouthpiece geometry. Previous studies have discussed the accuracy of the quasistationary approximation but the amount of literature on the subject is sparse, mainly due to the difficulties involved in the measurement of dynamic flows in channels with an oscillating reed. In this paper, a numerical technique based on the lattice Boltzmann method and a finite difference scheme is proposed in order to investigate the characteristics of fully coupled fluid-structure interaction in single-reed mouthpieces with different channel configurations. Results obtained for a stationary simulation with a static reed agree very well with those predicted by the literature based on the quasistationary approximation. However, simulations carried out for a dynamic regime with an oscillating reed show that the phenomenon associated with flow detachment and reattachment diverges considerably from the theoretical assumptions. Furthermore, in the case of long reed channels, the results obtained for the vena contracta factor are in significant disagreement with those predicted by theory. For short channels, the assumption of constant vena contracta was found to be valid for only 40% of the duty cycle.     

A methodological and preliminary study on the acoustic effect of a trumpet player's vocal tract

A methodological study is presented to examine the acoustic role of the vocal tract in playing the trumpet. Preliminary results obtained for one professional player are also shown to demonstrate the effectiveness of the method. Images of the vocal tract with a resolution of 0.5 mm (2 mm in thickness) were recorded with magnetic resonance imaging to observe the tongue posture and estimate the vocal-tract area function during actual performance. The input impedance was then calculated for the player's air column including both the supra- and subglottal tracts using an acoustic tube model including the effect of wall losses. Finally, a time-domain blowing simulation by Adachi and Sato [J. Acoust. Soc. Am. 99, 1200-1209 (1996)] was performed with a model of the lips. In this simulation, the oscillating frequency of the lips was slightly affected by using different shapes of the vocal tract measured for the player. In particular, when the natural frequency of the lips was gradually increased, the transition to the higher mode occurred at different frequencies for different vocal-tract shapes. Furthermore, simulation results showed that the minimum blowing pressure required to attain the lip oscillation can be reduced by adjusting the vocal-tract shape properly.     

点簧簧片振动特性数值分析*

簧片是笙等中国传统簧管类乐器的核心部件之一。通过点簧工艺可调整簧片振动频率,点簧簧片的差异对整体乐器的声音效果具有重要影响。针对点簧簧片的振动特性问题,对其建立非均匀截面并具有质量负载的振动模型,采用有限元方法计算点簧簧片的固有频率。大量算例分析了点簧质量、位置以及簧片的边界条件对振动频率的影响,研究发现:若点簧质量不变,位置越靠近自由端调整频率越大,但同时应考虑对高阶频率的激发避免影响音色;若位置相同,点簧质量与频率改变近似成正比,由此可方便调整簧片振动频率。该文研究结果初步揭示了点簧簧片振动规律,可为制作、复原传统簧管类乐器中簧片的点簧工艺过程提供物理依据。     

Acoustics of Chinese woodwind reed instrument Sheng

I.IntroductionTheancientfolkwindinstrumentShengwasfounda1readyintheShangDynasty3000yearsago.AtraditionalShenghasl7bambooreed-pipes.IthasbeendevclopedintothepresentShengwithdifferentkindsofstructure.TherichsoundofShengisbri1liantandhar-monious.ThespecialityofShengisthatsevera1tonescanbep1ayedinharmonyandsomechords.Inthispaperitisana1yzedthattheprincip1esandacousticcharacteristicsofShengbasedonthe17lreed-pipeSheng.II.Acousticequiva1cntcircuitInFig.lisshowna17rced-pipeShengwithnames0fvari…     

基于四水听器的充水弹性管声速测量方法

实验室中水声材料声学参数的测量主要在水声声管中进行。管内平面波声速是正确测量这些参数的基础。该文提出一种基于四水听器结合不同边界的测量充水弹性管中声速的新方法。该方法利用4个固定位置处的水听器,采用最小二乘的方法,使得两组水听器分别得到的声管末端入射波声压差值的平方最小的声速即为管内平面波声速。该方法利用单频信号,在每一频率点均可测得声速,可以在任一种声管末端边界下进行测量,同时无需知道各水听器到边界的精确距离,在文中的3种边界下声速测量结果具有很好的一致性,实验操作简单、误差很小。该方法的仿真结果与管内声速的理论值吻合得很好,同时实验测量结果与仿真值之间的误差很小,证明了方法的准确性以及鲁棒性,为声管声速测量提供一个很好的思路。     

笙的簧片物理参数与音色相关性的初步研究

为了改善笙的声音品质,本文研究了笙的簧片物理尺度与笙的音色之间的相关性。在提出笙的物理模型并验证其有效性的基础上,固定音高,改变簧舌的厚度、长度以及缝隙宽度,合成一组笙的声样本。通过对偶比较法以及多维尺度法分析笙的音色空间,根据簧舌参数及音色特征量解释该音色空间的物理意义,并从发声原理比较簧舌参数对音色的作用。结果表明,音高一定时,簧舌宽度对音色的作用可忽略,厚度(及长度)和缝隙宽度对音色的作用相似,但影响方式不同。改变簧舌物理参数所形成的二维音色空间与声音的对数起振时间、频谱丰富性以及频谱不规则度有关。起振特征与频谱丰富性特征存在共变关系,通过改变这两个特征,能够改变音色的明亮度和柔软度。     

声学二维平面周期结构的吸声性能建模

声学周期结构兼具优化室内声场环境,节约建筑吸声材料的特性而在现代建筑中广泛使用。针对二维平面周期结构的声场优化特性,建立了一种吸声系数计算模型。首先,根据边界条件理论推导了吸声系数的线性方程组,继而通过数值分析方法进行求解,最后在驻波管和混响室中分别进行实验验证。实验结果表明,测量的吸声系数和理论计算曲线吻合良好,该模型可以准确测算二维平面周期结构的吸声系数。同时分析表明:在平面周期结构中,相同吸声材料面积情况下,吸声材料占比越大,吸声效果越好;在相同吸声材料面积和占比情况下,材料边缘长度越长,高频段吸声效果越好;随着材料边缘长度的减少,边缘效应影响减弱。      

The simulation of acoustic radiation from a moving line source with variable speed

The purpose of this work is to simulate and investigate the sound field generated by a moving line source with finite length and variable speed. Expect for the variation of the acoustic pressure at the specific field point, the distribution of the surface pressure along the surface of the line source was also considered. For achieving this purpose, a numerical method which combines the Time Domain Boundary Element Method (TDBEM) and moving sound source theory was developed in the present work. After comparing the results with the constant and the variable speed case, it showed that the effect of the variable speed not only influenced the variation rate of the frequency modulation, i.e., Doppler effect, but also the time about the maximum acoustic pressure being observed. In addition, the simulation results also presented that the difference as to the amplitude variation of the acoustic pressure still existed between the moving case and the stationary case even if the length of the line source is very long.     

线阵波束形成声强缩放方法估算声源的辐射声功率

为了解决波束形成声源识别过程中声源辐射声功率定量计算的问题,给出了阵型简洁、便于组合的线阵声强缩放模型。通过推导线阵的声强缩放系数,建立起线阵波束输出结果与声源辐射声功率之间的换算关系。无论是线阵还是平面阵的声强缩放方法,对于偏离阵列中心位置较远处的声源进行辐射声功率估算时都存在较为明显的误差。通过理论推导和仿真模拟计算,研究了同一单极子点声源在不同位置处的声功率估算偏差随频率、幅度的变化规律,发现该估算偏差只与声源偏离位置有关,而与声源自身的强度信息无关的结论,据此给出了相应的声功率估算修正方法。半消声室实验结果和声压法测量结果对比表明:修正后的线阵声强缩放方法用于中高频声源的辐射声功率计算时,单频声源的估算误差不超过1.0 dB,宽带声源的估算误差不超过1.8 dB。      

散射条件下声源分离及参数获取的平行障板方法*

声纳系统或水声设备湿端不可避免存在某些散射体,克服散射体干扰对声源本身辐射特性进行测量目前还缺乏简捷有效的方法。依据刚性圆盘散射规律,通过有限元建模分析了与观察方向平行布设的刚性圆盘对声源辐射特性的影响规律,结果表明：在满足远场条件时,在较小的允许误差范围内观察轴线上声压幅值分布与引入平行障板无关。并在此基础上尝试提出一种简捷有效的平行障板方法,实现散射条件下声源分离与参数获取。通过有限元仿真分析,在1~20kHz频率范围内,半径0.4m厚8mm的钢板对脉动圆管声源级分离测量引入误差在±0.6dB以内。     

Oscillatory limited compressible fluid flow induced by the radial motion of a thick-walled piezoelectric tube

A simple oscillatory, slightly compressible, fluid flow model in a thick-walled piezoelectric tube used in a drop-on-demand inkjet print head is developed from the point of view of fluid-structure interaction to take account of pressure wave propagation and pressure loading opposing wall motion. A frequency sweep is performed computationally using the model revealing the first acoustic fluid-structure resonance frequency and the influence of fluid viscosity. The validity of the model, with given information on the speed of sound in a fluid, is evaluated by comparing the theoretically predicted resonance frequency to the experimentally measured resonance frequency. In addition, the intrinsic speed of sound can be easily computed using the measured acoustic resonance frequency and this computed speed of sound agrees closely with speeds of sound reported in the literature.     

微通道脉冲管中He气交替振荡的分子动力学模拟

使用非平衡分子动力学模拟方法分析了微通道脉冲管(MPT)中由正弦速度活塞提供驱动力时He气交替振荡的微观动力学过程,并对MPT的冷却机制进行了分析.结果表明,MPT的压缩和膨胀过程之间存在一个交替的振荡过程,两个过程具有不对称的属性分布,膨胀过程具有比压缩过程更大的轴向压力梯度.当充气压力较低时,循环时间对冷端温度的影响很小,但是当充气压力高于20 bar时,冷端温度对时间较为敏感,随着时间的减少,冷端温度进一步降低,而冷端瞬时平均温度随着充气压力的增加而增加.另外,压比随着时间的减少而增加,并且明显不受充气压力的影响,但它会在MPT的轴向上产生较大的温度梯度.综上所述,在热端使用不同形式的换热器和调相元件会释放或回收额外的声功率.固定工作模式和尺寸参数的MPT具有最佳频率,可以在冷端获得最低的空载温度.仿真结果增进了对脉冲管制冷机的认识,并为微通道脉冲管制冷机的优化设计提供理论支持.     

Direct computation and aeroacoustic modelling of a subsonic axisymmetric jet

A numerical algorithm for acoustic noise predictions based on solving Lilley's third order wave equation in the time-space domain is developed for a subsonic axisymmetric jet. The sound field is simulated simultaneously with the source field calculation, which is based on a direct solution of the compressible Navier-Stokes equations. The computational domain includes both the nearfield and a portion of the acoustic farfield. In the simulation, the detailed sound source structure is provided by the nearfield direct numerical simulation (DNS), while the sound field is obtained from both the DNS and the numerical solution to the non-linear Lilley's equation. The source terms of Lilley's equation are used to identify the apparent sound source locations in the idealized axisymmetric low-Reynolds number jet. The sound field is mainly discussed in terms of instantaneous pressure fluctuations, frequency spectra, acoustic intensity and directivity. A good agreement is found between the predictions from the axisymmetric Lilley's equation and the DNS results for the sound field. Limitations and perspectives of the simulation are also discussed.