A Study of an Acoustical Experimentation Chamber
The research for this paper was done during the last six months of 1981, as a contribution to the ongoing project at the University of Michigan which researches the radiative properties of the violin. As a basis for investigation, the violin is viewed as a complex oscillatory structure whose vibrational modes are composed of a superposition of normal modes. Data tabulated during the various experiments consist of graphs which are analog representations of the rms amplitude and phase of the acceleration of the violin body, the velocity of the strings, or of the pressure of the air contained inside the body. The body response is measured by accelerometers, the string response is measured by a specially built optical sensor, and the air modes are measured with microphones. Graphs of the phase and amplitude. are tabulated concurrently. The violin is excited acoustically by a sinusoidal signal which is produced by an audio oscillator which is controlled by a phase-locked loop. The frequency of the signal is stepped through a predetermined frequency range which is chosen through observation of interesting characteristics of the violin. The frequency stepping procedure allows the violin two seconds to reach steady-state oscillation before a measurement is made and the frequency is again incremented. The frequency step is on the order of one-tenth hertz. The sweep is done for each of four speakers, whose positions are known. The response of the violin is tabulated digitally in a computer data file for each step. This information is later used to produce the graphs. The sound field and the gradient of the sound field are determined by removing the violin, and placing four microphones arranged in a regular tetrahedron such that their center corresponds to the former position of the bridge. The tetrahedron consists of twelve brass tubes joined together to form a cube, upon which the microphones are mounted, such that each microphone is diagonally opposite the other three microphones. In this way, the response of the violin to a specific acoustic stimulus can be determined.
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