The effect of acoustic impedance in any air-columns is accountable for the frequency of output sound. With noncylindrical air-columns, non-uniform cross-section area, the impedance varies continuously. An example of any instrument shows the complexity of varying impedance. In this research, advantage of having access to the impedance probe helped in developing experiment on determining the effect of acoustic impedance on output sound. The impedance probe set up with 3D printed trumpet mouthpieces scans the full frequency and records air pressure as information useful to determine the impedance. In the mist of the unfortunate days, the impedance probe was no longer accessible. Though approximation of the results can be calculated with numerical methods. The impedance value for an entire mouthpiece can be approximated by slicing the air-column into cylinders. Calculations are performed in MATLAB and are similarly as with the impedance probe which a scan from 50Hz to 2000Hz with increment is performed. Resonance information for different dimensions of approximated mouthpiece is recorded. The impedance probe experiment and the numerical calculations shows a comprehensible method of understanding the dimensions of producing a musical sound. Physicists and experimental musicians can benefit from the approach to explore the possibilities and new understandings of music.
Author: Haoyu Tian
Faculty Advisor: Herbert Jaeger, Department of Physics
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