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

本计画是一项关于弦乐器，特别是曼陀林的声学特性的实验研究，为本科生提供研究经验与训练。乐器可以被认为是一个耦合振荡器系统。在曼陀林的例子中，琴弦被设置成用拨子振动，并包含一系列谐波频率的能量。乐器的琴桥被琴弦设置为振动，并反过来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;两个表面都使乐器体内的空气振荡。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。他正在测量桥处的机械阻抗输入、车身的结构模态形状以及板与空气腔之间的耦合。拟议工作的最终目标是了解乐器的机械性能及其结构如何决定和弦的特性，并确定曼陀林和其他弦乐器的琴桥设计的潜在改进。耦合振子理论和共振现象是动力学中应用广泛的中心课题。曼陀林为动力学的应用提供了一个丰富而迷人的实验竞技场，并且可以使用本科物理系可用的仪器进行测量。该项目将通过吸引他们对动手研究的兴趣，然后提供严格的方法培训，为本科生提供变革性的经验。该项目的一个重要成果是投资于我国下一代STEM劳动力。 学生将接触到各种各样的实验技术和科学仪器，以及先进的理论概念，所有广泛适用于整个物理和工程。 在研究曼陀林的声学时，PI和他的学生将使用高速视频详细研究双弦的耦合，并阐明这些相互作用的音乐含义。这些结果也将为其他双弦乐器，如鲁特琴，乌德琴和12弦吉他提供帮助。 对声音频谱和琴桥阻抗的测量结合联合收割机来表征机械能从弦运动通过琴桥到乐器主体运动的传递，最终产生声音。详细了解桥梁的机械性能和由此产生的声谱之间的联系的实验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法进行研究。 曼陀林低频板模态耦合的研究？的正面和背面的亥姆霍兹模式，由于体内空气的振荡将比较吉他的经典研究。

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.