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.