Modal analysis of violins and cellos

Abstract

Normal modes of bowed string instruments are determined by the coupled motion of the top plate, back plate, enclosed air, ribs, neck, fingerboard, etc. Normal mode testing has traditionally been done using sinusoidal excitation, either mechanical or acoustical, although modal testing with impact excitation is a fast, convenient way to determine the normal modes of an instrument. Holographic interferometry provides the greatest detail about mode shapes, but the best understanding of the normal modes of an instrument results from application of more than one testing method. The normal modes in a cello are found to be quite similar to the corresponding modes of a violin, although they may appear in a different order in frequency. Modal frequencies in one cello were found to occur at 0.29 to 0.43 times the corresponding mode frequencies in a violin.