| Summary: | 碩士 === 國立宜蘭大學 === 森林暨自然資源學系碩士班 === 101 === The basic acoustic mechanism of most musical instruments consists of an object that makes sound and a resonator that amplifies sound. Thus, instruments such as the xylophone and marimba not only have bars but also tube resonators at the bottom. Being hollow with nodes, the bamboo cavity possesses a natural frequency, which will resonate with the matching frequency of an external sound, making it a suitable choice as a tube resonator. There are three objectives to this Study. The first objective is to find out the effect on resonance frequency of the boundary conditions of a transverse resonator and the length of its opening, and applying this result on the experiment to test the use of bamboo tube. The second objective is to find out the relationship between the fundamental frequency and overtones of resonance frequency in relation to changes in boundary conditions of a T-shape resonator. The third objective is to compare the resonance effect of different types of resonators and analyze the composition of the overtone series.
The test materials used for simulating transverse resonator and T-shape resonator in this Study are four PVC tubes of different sizes, i.e. 3.83cm (1( 1)⁄4 inch), 4.46cm (1( 1)⁄2 inch), 5.74cm (2 inches) and 7.25cm (2( 1)⁄2 inches). All four sizes are used to make transverse resonator to simulate the effect of various boundary conditions and opening lengths on the resonance frequency. Only the 7.25cm (2( 1)⁄2 inches) tube is used to make a T-shape resonator to simulate the effect of tube length on resonance frequency. A signal generator is used to create a frequency range of 1~6000Hz. When the cavity of the tube resonator responds to specific frequencies in the range of frequencies generated, a spectrum analyzer may be used to test and record the resonance frequencies of the tube resonator. After detecting the frequencies, the relationship between frequencies and boundary conditions may then be analyzed. In the resonance effect test, bars A2 (Triple tuning) and A4 (Double tuning) are used to analyze the resonance response of three types of tube resonator, i.e. vertical resonators, transverse resonators and T-shape resonators.
Observation of the relationship between boundary conditions and frequencies indicates that: (1) When the lengths and openings of the transverse resonators are constant, the larger diameter will have a lower frequency. (2) When the diameters and openings of the transverse resonators are constant, the longer tube will have a lower frequency. There is a high correlation between length and resonance frequency. The R2 values of all four tube diameters are 0.9866, 0.9881, 0.9788 and 0.9762 respectively. (3) When the lengths and diameters of transverse resonator are the same, there is a high correlation between the opening length and resonance frequency, indicating that the greater the opening and the closer the edge of the hole is to both sides of the opening, the higher the frequency. The result of testing with bamboo tube shows similar increase in frequency. However, the results obtained from following the opening method are all 10% lower than the target frequency. More fine-tuning is required in order to reach the target frequency. (4) When the length of the bottom tube of the T-shape resonator is constant, the length of the top tube is inversely related to the resonance frequency, and the ratio of fundamental frequency to overtone gradually rises from 1: 3.18. When the ratio of the length of top tube to bottom tube is 1: 2, the ratio of fundamental frequency to overtone is 1: 4.
Results from observing the resonance effect of different types of tube resonator show that: (1) Two types of tube resonator made from PVC tube will create resonance with bars in the resonance effect test. (2) The T-shape resonator, with fundamental frequency and overtone adjusted to a ratio of 1:4, shows significant response at fourfold frequency, which will cause a louder timbre. The resonance response of a transverse resonator and vertical resonator is equivalent. Both resonator respond to fundamental frequency but transverse resonator has a smaller response in the overtone series, which will cause a deeper and gentler timbre.
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