RUI: Musical Acoustics: Coupled Oscillators, Mandolin Bridges, and Holographic Interferometry

该项目是对弦乐器（特别是曼陀林）声学特性的实验研究，为本科生提供研究经验和培训。乐器可以被认为是耦合振荡器的系统。就曼陀林而言，琴弦通过拨片进行振动，并包含一系列谐波频率的能量。琴马通过琴弦产生振动，然后将能量传递到曼陀林的前板。前板辐射声音，但也通过乐器的肋骨耦合到后板；两个表面都会使仪器体内的空气产生振荡。因此，该仪器被建模为通过桥、肋或通过板与空气之间的直接接触彼此耦合的谐振子的集合。 PI 正在研究两个已调音的琴弦之间的耦合、它们与琴马和音板的耦合相互作用，以及两斜率衰减。他正在测量桥上的机械阻抗输入、主体的结构模态形状以及板与气腔之间的耦合。拟议工作的最终目标是了解乐器的机械特性及其结构如何决定音乐和弦的特征，并确定曼陀林和其他弦乐器琴桥设计的潜在改进。耦合振子理论和共振现象是动力学领域的核心且广泛应用的主题。曼陀林为动力学应用提供了一个丰富而迷人的实验舞台，并且可以使用本科物理系可用的仪器进行测量。该项目将通过激发本科生对实践研究的兴趣，然后提供严格的方法培训，为本科生提供变革性的体验。该项目的一个重要成果是投资于我国下一代 STEM 劳动力。 学生将接触到各种实验技术和科学仪器以及先进的理论概念，所有这些都广泛适用于整个物理和工程学。 在研究曼陀林的声学效果时，首席研究员和他的学生将使用高速视频对双弦耦合进行详细研究，并阐明这些相互作用的音乐含义。这些结果还将为其他双弦乐器提供线索，例如鲁特琴、乌德琴和 12 弦吉他。 声谱和琴马阻抗的测量相结合，可表征机械能从琴弦运动通过琴马到最终产生声音的乐器主体运动的传递。详细了解桥梁机械性能与声谱之间联系的实验旨在确定桥梁设计的潜在改进之处。由此产生的身体运动的细节、振动模式将使用全息干涉测量法进行研究。 对曼陀林前后表面的低频板模式与由于体内空气振荡而产生的亥姆霍兹模式的耦合的研究将与吉他的经典研究进行比较。

This project is an experimental investigation of the acoustic properties of string instruments, in particular of the mandolin, which provides research experiences and training for undergraduate students. A musical instrument can be thought of as a system of coupled oscillators. In the case of the mandolin, the strings are set into oscillation with a plectrum and contain energy in a harmonic series of frequencies. The bridge of the instrument is set into vibration by the strings and in turn conveys the energy to the front plate of the mandolin. The front plate radiates sound but also couples to the back plate through the ribs of the instrument; both surfaces set the air inside the body of the instrument into oscillation. The instrument is thus modeled as a collection of harmonic oscillators coupled to each other through the bridge, ribs, or by direct contact between plate and air. The PI is studying the coupling between two tuned strings, their coupled interaction with the bridge and soundboard, and the two-slope decay. He is measuring the input of mechanical impedance at the bridge and the structural modal shapes of the body and the coupling between the plates and the air cavity. The ultimate objective of the proposed work is to understand how the mechanical properties of the instrument and its construction determine the character of the musical chords and identify potential improvements in bridge design for the mandolin, and other string instruments. The theory of coupled oscillators and the phenomenon of resonance is a central and broadly applicable subject in dynamics. The mandolin provides a rich and fascinating experimental arena for the application of dynamics and one that is accessible to measurement with instrumentation available to undergraduate physics departments. This project will provide transformative experiences to undergraduate students by captivating their interest in hands-on research and then providing rigorous training in its methods. A significant outcome of this project is to invest in the next generation of our nation's STEM workforce. The students will be exposed to a wide variety of experimental techniques and scientific instruments as well as advanced theoretical concepts, all broadly applicable throughout physics and engineering. In investigating the acoustics of the mandolin, the PI and his students will carry out a detailed study of the coupling of the doubled strings using high-speed video, and the musical implications of these interactions will be elucidated. These results will also shed light on other musical instruments with doubled strings, such as the lute, oud, and 12-string guitar. Measurements of the sound spectrum and bridge impedance combine to characterize the transfer of mechanical energy from string motions through the bridge to the motions of the instrument body that ultimately produce sound. Experiments to understand in detail the connection between the mechanical properties of the bridge and the resulting sound spectrum aim to identify potential improvements in bridge design. Details of the resulting body motions, the modes of vibration, will be studied using holographic interferometry. A study of the coupling of low-frequency plate modes of the mandolin?s front and back surfaces with the Helmholtz modes due to oscillations of air within the body will be compared to the classic studies of guitars.