Wave Propagation and Radiation in a Horn: Comparisons Between Models and Measurements

Abstract

The modeling of wave propagation in ah orn is still problematic as the limit of plane wave approximation is known butn om ethod is provent og ivea ccurate results. This paper proposes to evaluate the error induced by both ap lane wave model and as pherical model. These models use aT ransmission-Matrix Method based on either plane or quasi-spherical propagation and loaded with twod i ff erent radiation impedances. This study is done on twomusical instruments horns, one from atrumpet and the other from atrombone, whose geometry is known to within at enth of millimetre. The respective influence of both propagation and radiation is observed by comparing the input impedance measured on each of the twohorns with the impedance calculated with both models. Differences between models and measurements are quantified and an extension to awhole trombone is also done. The spherical model approximates the behaviour of the horn with an improvedaccuracyand differences between the model and the measurement do not rise above 25 cents. PACS no. 43.20.Mv,43.75Fg 158 ©S.Hirzel Verlag · EAA Eveno et al.:P ropagation and radiation in ahorn ACTA ACUSTICA UNITED WITH ACUSTICA Vol. 98 (2012)

Finite difference time domain simulation for the brass instrument bore

“…The frequencies of the first seven maxima and minima of the input impedance curve for each instrument are given in Table I, along with percent difference in frequencies, as well as difference in magnitude, in dB. The frequencies match in most cases to under a percent, and amplitudes to within a dB or less; as such, these results are similar to those obtained using frequency domain methods such as the transmission line matrix method, 9 in the present case of a simple plane wave model.…”

“…The model presented here assumes simple planar wave propagation-various one-parameter generalizations of Webster's equation exist, 26 including spherical wave propagation, which is well known to produce superior results; 8,9 such generalizations do not pose any major difficulties in the present context of FDTD methods. Models of viscothermal losses have been presented, to different degrees of approximation; some, such as model A, are not suitable for time domain discretization.…”

“…At the radiating end of the bore, as in previous studies, 8,9 approximations to the radiation impedance formula due to Levine and Schwinger 27 in the case of an unflanged circular pipe will be employed here. It is important, in FDTD simulations (as opposed to the case, in, e.g., frequency domain methods) that the approximation to the impedance is positive real, and thus passive.…”

“…As the bore is often characterized in terms of an impedance/admittance pair, frequency domain techniques have naturally long been applied for the analysis of both brass and woodwind instruments, 7,8 and are often used to calculate the input impedance of the bore directly. A recent comparison of various models using frequency domain methods (the transmission line matrix method) is provided by Eveno et al 9 In sound synthesis applications for wind instruments, transmission line models (including methods employing wave variables such as digital waveguides [10][11][12] and other related methods 13 ) are commonly used, as are modal methods. 14 Finite difference time domain (FDTD) methods, popularly used in electromagnetics simulation, 15,16 are a good match to the simulation problem for an acoustic tube in 1D.…”

The Relationship Between Bore Resonance Frequencies and Playing Frequencies in Trumpets

“…Measuring and computing wind musical instruments input impedance is nowwell mastered [1,2,3,4,5,6]. As part of alarger project aimed toward helping instrument makers to design and characterise their musical instruments, this work focuses on howthe bore resonance frequencies, taken from the input impedance, can be related to the playing frequencies.…”