Some characteristics of the concert harp's acoustic radiation

The way a musical instrument radiates plays an important part in determining the instrument's sound quality. For the concert harp, the soundboard has to radiate the string's vibration over a range of 7 octaves. Despite the effort of instrument makers, this radiation is not uniform throughout this range. In a recent paper, Waltham and Kotlicki [J. Acoust. Soc. Am. 124, 1774-1780 (2008)] proposed an interesting approach for the study of the string-to-string variance based on the relationship between the string attachment position and the operating deflection shapes of the soundboard. Although the soundboard vibrational characteristics determine a large part of the instrument's radiation, it is also important to study directly its radiation to conclude on the origins of the string-to-string variation in the sound production. This is done by computing the equivalent acoustical sources on the soundboard from the far field sound radiation measured around the harp, using the acoustic imaging technique inverse frequency response function. Results show that the radiated sound depends on the correlation between these sources, and the played string's frequency and location. These equivalent sources thus determine the magnitude and directivity of each string's partial in the far field, which have consequences on the spectral balance of the perceived sound for each string.     

Acoustics of the jarana jarocha

Some acoustical measurements on the jarana jarocha primera (first), a traditional Mexican instrument, a “one-piece” body instrument, in the coastal region of the Gulf of Mexico, are presented. Experimental mobility function, radiativity function, and some radiation patterns were obtained. Harmonic analysis and visualization techniques using both the finite element method and laser speckle-Chladni methods were made to obtain the lower deflection shapes of the soundboard. The experimental analysis using mobility function measurements of the lower resonances shows behaviour very similar to that observed in the classical guitar.     

Experimental study of AO and T1 modes of the concert harp

String instruments are usually composed of a set of strings, a soundboard, and a soundbox with sound holes, which is generally designed to increase the sound level by using the acoustic resonances of the cavity. In the case of the harp, the soundbox and especially the sound holes are primarily designed to allow access to the strings for their mounting. An experimental modal analysis, associated to measurements of the acoustic velocity in the holes, shows the importance of two particular modes labeled A0 and T1 as it was done for the guitar and the violin. Their mode shapes involve coupled motions of the soundboard's bending and of the oscillations of the air pistons located in the sound holes. The A0 mode is found above the frequency of the lowest acoustically significant structural mode T1. Thus, the instrument does not really take advantage of the soundbox resonance to increase its radiated sound in low frequencies. However, contribution of mode A0 is clearly visible in the response of the instrument, confirming the importance of the coupling between the soundboard and the cavity.     

Experimentally based description of harp plucking

This paper describes an experimental study of string plucking for the classical harp. Its goal is to characterize the playing parameters that play the most important roles in expressivity, and in the way harp players recognize each other, even on isolated notes--what we call the "acoustical signature" of each player. We have designed a specific experimental setup using a high-speed camera that tracks some markers on the fingers and on the string. This provides accurate three-dimensional positioning of the finger and of the string throughout the plucking action, in different musical contexts. From measurements of ten harp players, combined with measurements of the soundboard vibrations, we extract a set of parameters that finely control the initial conditions of the string's free oscillations. Results indicate that these initial conditions are typically a complex mix of displacement and velocity, with additional rotation. Although remarkably reproducible by a single player--and the more so for professional players--we observe that some of these control parameters vary significantly from one player to another.     

琵琶的声学特性

本文给出中国民族弦乐器琵琶的基本声学特性。分析了琴面板、琴马的振动模式和琴体振动声辐射的频率特性。从用琵琶弹七声音阶音得到的声频谱得出的频谱包络来分析琵琶声频谱的规律,基本上是每千赫频段内有个主要的包络峰。文中还给出演奏琵琶的指法弹和挑,实音和虚音的特点。     

Physics-based modeling techniques of a twelve-string Portuguese guitar: A non-linear time-domain computational approach for the multiple-strings/bridge/soundboard coupled dynamics

The Portuguese guitar is a pear-shaped instrument with twelve metal strings which is widely used in Portuguese traditional music. Unlike most common guitars, it has a curved top-plate and a specific violin-like bridge which is not rigidly fixed to the soundboard of the instrument. From the dynamical point of view, if the bridge transmits the strings vibrations to the instrument body in order to maximize the radiated energy, it also couples all the component parts of the instrument which therefore interact by structural coupling. This can originate various audible effects such as beating behavior and the excitation of numerous sympathetic resonances enhanced by the large number of strings of the instrument, and this is certainly why the Portuguese guitar has such distinct sound compared to other guitars. In this paper, a fully coupled time-domain model of the Portuguese guitar is developed and a series of simulations are presented to emphasize the various coupling phenomena involved in sound production. To reproduce the main musical features, the model includes the coupled dynamics of the twelve strings supported by a bridge which interact with the body of the instrument, described through Finite-Element modeling of the soundboard of a typical Portuguese guitar. Further simple models have been devised for the string/fret interaction and the pluck excitation. Since nonlinear effects are quite apparent in the behavior of string musical instruments, the string dynamics is modeled by the Kirchhoff–Carrier equations which describe large-amplitude string vibrations, and includes the coupling between both polarizations of string motion. The coupling between the strings and the soundboard at the bridge is provided by a model of the bridge kinematics, built on the basis of simple geometrical rationale, so that the two perpendicular string motions can exchange energy back and forth. By a close examination of the energy transfers between the various subsystems of the model, we first assess the correct behavior of the physical model and then examine the respective influence of the string nonlinearity and the bridge on the nonplanar motion of the string. The fully coupled model which pertains to the restricted group of studies which deals with the complete physical-based modeling of a multi-stringed instrument, captures many important phenomena observed in practice, among which the pitch glide effect and the mutual excitation of sympathetic vibrations.     

Violin f-hole contribution to far-field radiation via patch near-field acoustical holography

The violin radiates either from dual ports (f-holes) or via surface motion of the corpus (top+ribs+back), with no clear delineation between these sources. Combining "patch" near-field acoustical holography over just the f-hole region of a violin with far-field radiativity measurements over a sphere, it was possible to separate f-hole from surface motion contributions to the total radiation of the corpus below 2.6 kHz. A0, the Helmholtz-like lowest cavity resonance, radiated essentially entirely through the f-holes as expected while A1, the first longitudinal cavity mode with a node at the f-holes, had no significant f-hole radiation. The observed A1 radiation comes from an indirect radiation mechanism, induced corpus motion approximately mirroring the cavity pressure profile seen for violinlike bowed string instruments across a wide range of sizes. The first estimates of the fraction of radiation from the f-holes F(f) indicate that some low frequency corpus modes thought to radiate only via surface motion (notably the first corpus bending modes) had significant radiation through the f-holes, in agreement with net volume changes estimated from experimental modal analysis. F(f) generally trended lower with increasing frequency, following corpus mobility decreases. The f-hole directivity (top/back radiativity ratio) was generally higher than whole-violin directivity.     

A platform for manipulation and examination of the acoustic guitar: The Chameleon Guitar

A platform for manipulation and examination the acoustic guitar is presented, based on a novel guitar design – the Chameleon Guitar – featuring a replaceable acoustic resonator functioning as the soundboard of the instrument. The goal of the design process is to create a tone as sonically close to that of a traditional guitar as possible, while maintaining an easily replaceable soundboard. An iterative, data driven approach was used, each design step coming under examination from one or more measurement tools: finite-element method, acoustic impulse testing, and laser vibrometry. Ideal resonator geometry, bridge location, and piezoelectric sensor positions were determined. The finished instrument was then examined with laser vibrometry to confirm earlier results, evaluate the behavior and chosen sensor positions for various tonewoods, and examine the acoustic effects of adding sensors and wax finish. The conclusions drawn are diverse and point to the significance of attention to detail in each step of instrument construction. For example, when changing instrument material from one softwood to another, ideal locations for piezoelectric sensors are subject to change. We conclude that detailed acoustic analysis can significantly aid in the construction of new instruments by quantifying the impact of instrument geometry and material properties.     

Application of holographic interferometry to the vibrational analysis of the harpsichord

This paper presents an original piece of research using holographic interferometry as a quantitative optical diagnostic. The object under investigation was the soundboard of a harpsichord. The results obtained show that it is possible to measure the spatial vibrational behaviour of the whole soundboard with an accuracy of better than 170 nm. Several features which characterize the vibration behaviour of the soundboard have been visualized including a discontinuity created by a crack which has resulted in a phase change of the interferometric fringes. Finally, the theoretical model response of the harpsichord soundboard is determined and compared to our holographic measurement.     

板结构的声辐射模态分析及其高分辨率法向振动速度重建

提出了一种基于声辐射模态的速度基向量构建方法,该速度基向量不受网格划分的影响,可用于高分辨率的板结构法向振动速度重建。首先对板表面稀疏网格的声辐射模态进行计算,再以声辐射模态和模态系数构建板法向振动速度分布的基向量,然后由声场测量声压求解基向量系数,最后由该系数和加密网格的速度基向量重建高分辨率的板法向振动速度分布。以简支板声源进行仿真计算,当测量声压信噪比为30 dB时,低频的法向振动速度重建误差最低可达3.7%;以固支板声源在消声室中进行实验验证,131.5 Hz振动频率下的重建误差低于7%。该方法实现了只需要少量声压测量点即可精确重建板声源更高分辨率的法向振动速度分布。     

Experimental validation of a collocated PVDF volume velocity sensor/actuator pair

The active control of sound transmission through a rectangular panel is experimentally verified. The control system is based on a collocated volume velocity sensor/actuator pair which measures and excites the first radiation mode of the panel. Suppression of the first radiation mode is an efficient strategy to control the low frequency sound radiation from the panel. This configuration leads to a simple single-input single-output control system, to which feedback control can be applied.Two implementations of the volume velocity sensor/actuator pair are tested. First, a polyvinyledene fluoride polymer (PVDF) volume velocity actuator foil with shaped electrodes is used in combination with an identical PVDF volume velocity sensor foil. Due to the mechanical coupling between the PVDF sensor and actuator foil, it is shown that a direct velocity feedback control scheme is not feasible because higher order structural modes will be destabilized. Instead integral force feedback is applied, such that the open-loop transfer function has a roll-off towards higher frequencies. Experiments show that this control strategy results in a reduction of the sound pressure in the receiving room of 10 dB at the first structural resonance without spillover to higher order modes. Due to the roll-off towards high frequencies, the control over higher order modes remains limited. Second, a discrete volume velocity sensor is constructed by summing the signals from 12 point sensors placed on the panel. The volume velocity actuator consists of two PVDF foils, glued on each side of the panel and driven in opposite phase. Direct volume velocity feedback is applied to this system, which is minimum phase. This control system is capable of reducing the sound pressure in the receiving room below 300 Hz by 10-15 dB without spillover to higher order modes.     

Hawking Radiation from the Higher-Dimensional Schwarzschild de Sitter and Anti-de Sitter Black Holes via Covariant Anomaly

Very recently, a conceptually clean and economical anomaly cancellation method, based on the initial work of Robinson and Wilczek, on Hawking radiation was proposed. On the basis of this formalism, we investigate Hawking radiation from the higher dimensional Schwarzschild de Sitter and Anti-de Sitter black holes. To describe the observable physics in de Sitter space, we construct the effective field theory between the event horizon and cosmological horizon. Our result shows that when the underlying diffeomorphism symmetries are saved at the quantum level, Hawking radiation, from not only the event horizon but also the cosmological horizon in the higher dimensional space time, can be determined by the covariant compensating fluxes of energy momentum tensor. Meanwhile, we also discuss the exact radiation spectrum by incorporating the self-gravitational interaction and back reaction of the outgoing modes.     

Janus-Helmholtz换能器的弱辐射耦合机理与带宽特性

针对Janus-Helmholtz (JH)换能器频带内响应起伏较大、模态耦合机制尚不明确的问题,提出了振动模态声辐射独立建模方法。该方法建立换能器各个振动模的独立有限元模型,在仿真计算中将位移载荷直接加载在辐射面上,分析振动模的辐射声场。通过各个结果的对比分析,观察到JH换能器声辐射模态的弱耦合规律,最终给出JH换能器带宽特性的合理物理解释,即JH换能器在同一纵向振子激励下,由于不存在声输出明显干涉加强的模态耦合,因此难以得到通常意义上响应起伏小于3 dB的宽带工作性能。以控制工作频带内响应起伏较小为前提,将拓宽工作频带作为设计目标,优化设计了 JH换能器结构参数。实验中换能器样机的发射电压响应测试结果与仿真计算相吻合,实测谐振频率为1350 Hz与2450 Hz,谐振频率下发射电压响应分别为143 dB,141 dB,在频带1200~3300 Hz范围内响应起伏12 dB,最大声源级204 dB,实现了宽带大功率发射的特性。     

The violin: Chladni patterns,plates, shells and sounds

In this article we consider the vibrations and radiated sound of the bowed violin. The vibrations are discussed in terms of the normal modes of the instrument involving the coupled vibrations of the bowed string, the supporting bridge, the hollow shell comprising the body of the instrument and, ultimately, the acoustic modes of the performance space in which the instrument is played. We show that damping plays an important role in characterizing the normal modes in what can be distinguished as weak and strong coupling limits. The historic and modern application of Chladni pattern measurements to enhance our understanding of the acoustics and as an aid to the making of violins is highlighted, alongside the modern equivalents of experimental modal and computational finite-element analysis. The symmetry-breaking properties of the internal soundpost is shown to have a profound affect on the intensity and quality of sound radiated by the bowed instrument.     

The near-ground structure of the nocturnal sound field

The near-ground behavior of the low-frequency (100 Hz to 500 Hz) sound field in the nocturnal sound duct is studied theoretically and experimentally. In the first few meters of the atmosphere, narrow-band sound fields are found to have a characteristic vertical structure. The sound field is the superposition of a "surface mode," whose magnitude decreases monotonically with altitude, with a sum of "higher modes," each of whose magnitudes has a pronounced minimum a few meters from the ground at approximately the same height. The surface mode attenuates to negligible levels after a few hundred meters from the source. Consequently, more than a few hundred meters from a narrow-band source, there is a "quiet height" at which the sound level is reduced by 10 to 15 dB relative to its value on the ground. The narrow-band quiet height is shown to be a robust feature of nocturnal sound propagation.     

Non-Axisymmetric Oscillation of Acoustically Levitated Water Drops at Specific Frequencies

A category of non-axisymmetric oscillations of acoustically levitated water drops was observed. These oscillations can be qualitatively described by superposing a sectorial oscillating term upon the initial oblate shape resulting from the effect of acoustic radiation pressure. The oscillation frequencies are around 25 Hz for the 2-lobed mode and exactly 50 Hz for the 3- and 4-1obed modes. These oscillations were excited by the disturbance from the power supply. For the same water drop, higher mode oscillations were observed with more oblate initial shape, indicating that the eigenfrequencies of these non-axisymmetric oscillations decrease with increasing initial distortion. The maximum velocity and acceleration within the oscillating drop can attain 0.3 m·s^-1 and 98.7 m·s^-2 respectively, resulting in strong fluid convection and enhanced heat and mass transfer.     

Propagation of short pulses in a medium with frequency dispersion

Propagation of short pulses of electromagnetic radiation in a transparent medium with a frequency dispersion is considered for the linear and nonlinear modes. The role of back reflection of radiation in the spectral regions with the negative dielectric constant was clarified. For the nonlinear mode, the exact form of the stationary solitary wave whose profile includes a point with infinite steepness is found.     

Parametric plate-bridge dynamic filter model of violin radiativity

A hybrid, deterministic-statistical, parametric "dynamic filter" model of the violin's radiativity profile [characterized by an averaged-over-sphere, mean-square radiativity (R(ω)(2))] is developed based on the premise that acoustic radiation depends on (1) how strongly it vibrates [characterized by the averaged-over-corpus, mean-square mobility (Y(ω)(2))] and (2) how effectively these vibrations are turned into sound, characterized by the radiation efficiency, which is proportional to (R(ω)(2))/(Y(ω)(2)). Two plate mode frequencies were used to compute 1st corpus bending mode frequencies using empirical trend lines; these corpus bending modes in turn drive cavity volume flows to excite the two lowest cavity modes A0 and A1. All widely-separated, strongly-radiating corpus and cavity modes in the low frequency deterministic region are then parameterized in a dual-Helmholtz resonator model. Mid-high frequency statistical regions are parameterized with the aid of a distributed-excitation statistical mobility function (no bridge) to help extract bridge filter effects associated with (a) bridge rocking mode frequency changes and (b) bridge-corpus interactions from 14-violin-average, excited-via-bridge (Y(ω)(2)) and (R(ω)(2)). Deterministic-statistical regions are rejoined at ~630 Hz in a mobility-radiativity "trough" where all violin quality classes had a common radiativity. Simulations indicate that typical plate tuning has a significantly weaker effect on radiativity profile trends than bridge tuning.