Exploring the resonant vibration of a cello with the finite element method

Violins are precisely crafted to present their brilliant quality in sound that dates from 16th century Italy. The wood component’s Young’s modulus (E), the soundpost, and the bass bar play significant roles in the instrument’s sound production. Yet, current acoustic research mostly focuses on violins. Therefore, this research aimed to investigate resonant vibration using a cello model. We hypothesized the structural changes in the soundpost and bass bar would lead to different eigenfrequencies, in which the original structure yields the highest value compared to the rest. To accurately reveal the secrets of cellos’ acoustics, we conducted numerical and graphical simulations with the finite element method. We utilized the simulation tool to calculate the eigenfrequencies of altered structures with varying Young’s modulus and positions of the soundpost, with or without the bass bar. We identified specific vibration mode shapes across all structures and found that Young’s modulus had the greatest influence on the eigenfrequencies while removing the bass bar had the least impact. Yet, our hypothesis was not fully supported: not in all mode shapes did the original structure have the highest eigenfrequency value. Within the investigated components, we concluded that the factor affecting resonant vibration frequencies the most is Young’s modulus, then soundpost, and, finally, the bass bar. Future research extension with physical experiments should be conducted to understand and quantify the result accuracy.