Last modified: 2018-06-05
Abstract
This paper explores fluid structure acoustical interaction in the application of a musical instrument. A thin flourocarbon string with a diameter of 0.432 millimeters and length of 43 centimeters is precisely tuned and placed in a cross-flow of laminar falling water, accelerating at the rate of 9.8 meters/sec2. The string is moved down, perpendicular to the falling water, starting at near zero water velocity. Within the increasing velocity field and at incremental lengths of the string, the regions of harmonic resonance are identified and the audio is recorded. This process is repeated through a chromatic scale starting at A2-110 hertz and ending at A3-220 hertz. From this chromatic scale, two of the notes are selected for detailed analysis of the harmonic modes. The boundaries of these modes are clearly defined, and agree with the synchronization lock-in regions observed by Williamson & Roshko's 1988 research. Moreover, in a time based model, the Strouhal number lines up the periods of vortex shedding with string wavelength periods at any position, and illustrates the phase between the fluid and string interaction. As a result of the analysis, this paper will present two maps (String tuned to E3 164.81 Hz, and G#3 207.65 Hz) useful for the musician to navigate through a full range of musical notes.