aPhysics, King Mongkut's Institute of Technology Ladkrabang
bInst. of Music, Sci. and Eng., King Mongkut's Institute of Technology Ladkrabang
Abstract :
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.