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Analysis of a Pseudo-Harmonic Tubular Bell

Oliver, Douglas L

Abstract Details

2017, Master of Science, University of Toledo, Mathematics.
Tubular bells, or chimes are used for ambient sounds as well as serious music. Unlike most wind or stringed instruments, a tubular bell does not have a harmonic set of overtones. The lack of harmonious overtones creates a problem with using tubular bells for serious music: there is not unanimity regarding the pitch, or musical note associated with a particular tubular bell. The Euler-Bernoulli model for vibrating thin beams was used to derive a mathematical model for vibrations of a tubular bell. Using this model, an analysis of the natural frequencies of a modified tubular bell was presented. One or more ends of the tubular bell were weighted with a mass. This mass changes the boundary conditions, and hence the ratio of the natural frequencies of the tubular bell. Values for the ratio of the mass of weight(s) to the mass of the tube were identified such that the ratio of the frequency of the first overtone to the second overtone was 2. Under these conditions, the these overtones are one octave apart. Frequency ratios predicted by the model have been compared with experimental results of a frequency analysis of the sound produced by two physical tubes. The experimental results were in good agreement with the theoretical predictions.
Alessandro Arsie (Committee Chair)
Sonmez Sahutoglu (Committee Member)
Denis White (Committee Member)
26 p.

Recommended Citations

Citations

  • Oliver, D. L. (2017). Analysis of a Pseudo-Harmonic Tubular Bell [Master's thesis, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo149980725594691

    APA Style (7th edition)

  • Oliver, Douglas. Analysis of a Pseudo-Harmonic Tubular Bell. 2017. University of Toledo, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo149980725594691.

    MLA Style (8th edition)

  • Oliver, Douglas. "Analysis of a Pseudo-Harmonic Tubular Bell." Master's thesis, University of Toledo, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo149980725594691

    Chicago Manual of Style (17th edition)