Modal analysis of the violoncello
Research on th e acoustics of violins has been progressing for nearly 200 years, and conclusions developed from experiments on th e vibrational modes of violins have been well documented. The violoncello has not received th e same a ttention, however. The objectives of this project were to investigate th e modes of th e cello, to compare and contrast the modes of the cello to those of th e violin, and to suggest a system of nomenclature for th e vibrational modes observed in th e cello. This thesis discusses th e experiments, data, results and conclusions on a school-grade cello owned by th e author. To perform a modal analysis, the cello was driven into sinusoidal vibrations by three separate methods: 1 ) a mechanical bridge drive, 2 ) an internal oscillating sound pressure, and 3) an external sound field. To help find the resonance frequencies of the cello, sound spectra and accelerance spectra were recorded. Holographic interferometry images of th e cello, driven at its resonance frequencies, revealed how th e cello was moving at these frequencies from which a classification of th e modes of vibration of th e cello was made. The modes of vibration were determined by holographic interferometry using all three driving methods over a frequency range of 90 Hz to 400 Hz. Experiments were also performed to find th e cavity air modes. By damping out the vibrations of the cello body, th e vibrational modes of the air inside the cavity were determined. The modes found in the cello were compared to modes found in violins, and a system of mode nomenclature is suggested.