Vibration Of Musical Instruments Research Articles

Characterization of bridge motions on the violin using polymer sensor technology

Recent developments in minimally invasive polymer-film sensors permit the in-situ detection of mechanical vibrations in musical instruments without significantly disturbing the acoustics of the instrument. As an example, we present measurements of vibrations of a violin between the feet of the bridge and the top plate. To this end, calibrated fluoropolymer-film sensors were matched to the geometry of the bridge feet. The forces exerted on the top plate by either bridge foot can be measured separately during excitation of a string with the bow. The differences in amplitude and phase between bass and treble foot vibrations exhibit the distinctly asymmetrical nature of bridge motions, which of course also depend on the string and the note that are being played, respectively. In comparison with the simultaneously detected string vibrations and the radiated sound, the filter characteristics of the bridge are clearly identified in the spectral representation. As the bridge is also the main agent for the coupling from the body to the string, it is suggested that the observed variations in bridge motion are closely connected to the fact that the playability of a violin changes sometimes quite drastically from note to note.

Some optical methods for modal analysis of musical instruments.

Because of their high spatial resolution, optical methods have become important for modal analysis of vibrations in musical instruments. Among optical methods for modal analysis are time-average holographic interferometry, pulsed TV holography, disital speckle interferometry, and scanning vibrometry. We review briefly principles and applications of optical methods for modal analysis.

Limit cycles in nonlinear excitation of clusters of classical oscillators

In this paper we develop a numerical procedure for detecting the existence of limit cycles in nonlinear excitation of clusters of classical harmonic oscillators. Our technique is able to compute also the main parameters of a limit cycle, that is the amplitudes and the period. The numerical method, based on the propagation matrix formalism, is transparent and easy to apply. It may find application in various areas where nonlinear excitations are involved, e.g., sound and mechanic vibrations in musical instruments, ground vibrations in volcanic areas, and sea tides.

A hot topic in musical acoustics: Phase coherent representation of radiated sound fields.

A technique used to study normal‐mode vibrations in musical instruments is modal analysis. This experimental method analyzes a series of transfer functions which relate the frequency spectra of a number of impact points to the spectrum of a fixed response point, and subsequently presents the motion of the structure at the various normal‐mode frequencies in computer animation. This approach is extended to represent a radiated sound field by using a fixed excitation point on the musical instrument as the reference signal and monitoring the sound field with a microphone at a number of predetermined points. This makes it possible to relate the phase of the sound field to the phase of the vibrating structure responsible for generating that field. Animated illustrations will be shown for the air column in a wind instrument and for the sound field of a concert grand piano.

Chaos in the classroom: Exposing gifted elementary school children to chaos and fractals

A unit of study for gifted 4th and 5th graders is described on the subject of mathematical periodicity and chaos and the underlying physical processes which produce these phenomena. A variety of hands-on experiments and the use of various data analysis tools and computer aids provide students with powerful raw material for their analysis, interpretation, and understanding. The concepts of simple periodic motion (e.g., a pendulum), complex superposition of motions (e.g., the vibrations in musical instruments), and chaotic sequences (e.g., stock prices) are covered, with numerous practical examples. Opportunities to involve related activities emphasizing language arts, history, and graphic art are included. The student response to the material is documented.

Modal analysis of vibrations in musical instruments

Modal analysis describes the properties of an elastic structure in terms of its modes of vibration. Videotape is a convenient medium for presenting the results of experimental modal analysis of structural vibrations, both in a lecture and in the laboratory. Some modes of vibration of several musical instruments, including a guitar, a handbell, a Caribbean steel drum, a snare drum, and a plane soundboard, will be demonstrated on videotape.