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

本项目是对弦乐器，特别是曼陀林的声学特性进行实验研究，为本科生提供研究经验和训练。乐器可以看作是一个耦合振荡器系统。在曼陀林的情况下，弦被设置成振荡与一个拨子和包含能量的谐波频率系列。乐器的桥由琴弦设置成振动，然后将能量传递给曼陀林的前板。前板辐射声音，但也通过仪器的肋部耦合到后板；两个表面都使仪器内部的空气产生振荡。因此，该仪器被建模为谐波振荡器的集合，通过桥、肋或板与空气之间的直接接触相互耦合。PI正在研究两个调谐弦之间的耦合，它们与桥和音板的耦合相互作用，以及双斜率衰减。他正在测量桥上的机械阻抗输入和车身的结构模态形状以及板与空腔之间的耦合。这项工作的最终目的是了解曼陀林的机械性能及其结构如何决定和弦的特征，并确定曼陀林和其他弦乐器的桥设计的潜在改进。耦合振子和共振现象的理论是动力学中的一个核心和广泛应用的课题。曼陀林为动力学的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。该项目将通过吸引本科生对动手研究的兴趣，然后提供严格的方法培训，为本科生提供变革性的体验。这个项目的一个重要成果是投资于我们国家下一代的STEM劳动力。学生将接触到各种各样的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。在曼陀林的声学研究中，PI和他的学生将使用高速视频对双弦的耦合进行详细研究，并阐明这些相互作用的音乐含义。这一结果也将对琵琶、乌德琴、12弦吉他等其他双弦乐器有所启发。声谱和桥阻抗的测量结合起来表征了从弦运动到琴体运动的机械能的传递，最终产生声音。通过实验详细了解桥梁的力学性能和由此产生的声谱之间的联系，旨在确定桥梁设计的潜在改进。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学进行研究。曼陀林低频板模耦合的研究？钢琴的前后表面由于琴身内空气的振荡而产生亥姆霍兹模态，将与经典的吉他研究相比较。

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.