含有侧孔阵列圆柱管的发声频谱

利用末端导纳匹配方法和格林函数方法,对含有侧孔的律管进行了声学谱分析,得到了均匀侧孔长管在两个音阶上的共振频谱。发现了随有效管长的均匀递减,其发声频率的递增是不均匀的。主要共振效应发生在离吹孔最近的侧孔处,随着共振频率的升高,气流更加集中地在第一侧孔辐射能量,次共振几乎可以忽略。附管上的侧孔对共振频率影响甚微,但是对音色、音强以及各侧孔的透射率都有一定的影响。该理论给出的共振频率与数值模拟结果符合地很好,第一音阶和第二音阶的平均偏差分别为5.03%和2.23%。由此认为末端导纳匹配方法适用于各类含有侧孔的管状发声物声学特性的研究。 

Tonal spectra of cylindrical tube with uniform lattice of side holes

By using the end admittance matching method and the Green function method,we analyze the acoustic spectrum of the tube with side holes.The resonance spectrum of a designed cylindrical tube with uniform lattice of tone holes is shown over two-octave range.It is found that with the uniform decrease of the effective length,the increase of the sound frequency is uneven.The main resonance effect occurs at the nearest side hole to the blow hole.With the increase of the resonance frequency,the airflow radiates energy more intensively at the first side hole,and the secondary resonance can be almost negligible.The side hole on the attached tube has little effect on the resonant frequencies,but has certain influence on the timbre,intensity and the transmission distribution of each side hole.The theoretical results show perfect agreement with the numerical simulation results,with the average deviation of the first-order and the second-order being 5.03%and 2.23%,respectively.Thus we validate the feasibility of the method for future modeling of tube-like instruments with side holes.