Booth Id:
PHYS009
Category:
Physics and Astronomy
Year:
2023
Finalist Names:
Tanaka, Shodai (School: Sapporo Kaisei Secondary School)
Abstract:
Flageolet harmonics is a playing technique on bowed string instruments, in which a player
lightly touches a nodal point on a string with their finger. Previous studies have reported that
the harmonic sound sustains for a short time after the finger is removed from the string
during flageolet harmonics was performed on bowed string instruments. However, the
mechanism of this harmonics-sustaining phenomenon and the parameter dependency of its
sustaining time remain unclear. The purpose of this study is to mathematically investigate
the dependence of sustaining time on parameters, and thereby, to elucidate the mechanism
of the harmonics-sustaining phenomenon.
To this end, a mathematical model was devised by adding terms representing the effects of
a bow and a finger to the one-dimensional wave equation. Subsequently, numerical
simulation was performed to analyze the behavior of the model.
The devised model successfully reproduced the harmonics-sustaining phenomenon in
which the parameter dependence of sustaining time was qualitatively consistent with the
author’s empirical observations. It was found that the parameter dependence of sustaining
time follows the power law. Furthermore, dimensional analysis was performed, yielding the
proposing of a formula which expresses the relationship between the sustaining time and the
maximum and minimum bow force required to generate Helmholtz motion. As the result, it
was predicted that the essence of the parameter dependency of sustaining time is “how the
bow obstructs the string behavior”.
This study provides a scientific explanation of the harmonics-sustaining phenomenon for
the benefit of all players and lovers of bowed string instruments.
Awards Won:
Acoustical Society of America: First Award of $1,500. In addition, their School will be awarded $200, and their Mentor will be awarded $500.
Third Award of $1,000