aPhysics, King Mongkut's Institute of Technology Ladkrabang
bInst. of Music, Sci. and Eng., King Mongkut's Institute of Technology Ladkrabang
Saw-u is a Thai low-pitched vertical fiddle, of which two strings are bowed to vibrate, via a bridge, a sheet of goatskin or cowhide stretched over a cavity with sound holes. This instrument is similar to Cambodian Tro-u, but distinguished from Chinese Yehu or Korean Haegeum in that animal skin is used for the interface to the bridge (rather than wood in the latter two). In the current study, the unique structure of the instrument body was investigated by establishing a mathematical model where the cavity was assumed to behave as a Helmholtz resonator interacting with a circular membrane. Two coupled equations governing the motions of the membrane and that of the air mass in the soundhole were solved based on simple assumptions. The results showed that the resonance frequencies associated with the circular modes of the membrane were shifted under the influence of the Helmholtz resonator, whereas that of the resonator would remain unchanged. Moreover, it was found that an additional circular mode may be observed near the Helmholtz resonance frequency, which may significantly influence the sound quality by reinforcing the resonance. The application of the current findings to the analysis of similar structures will also be discussed.
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