Theoretical and experimental study of wave propagation in brass musical instruments

The concept of input impedance is a very useful representation of the resonance characteristics of an acoustic horn. A large part of this work discusses its theoretical and experimental determination. It is demonstrated that higher modes, waves with a non-uniform pressure distribution on the plane perpendicular to the axis of the instrument, should be used in the theory of wave propagation in musical instruments featuring a flared bell as an improvement on assuming plane wave propagation. The impedance at the output end of an acoustic horn is known as the radiation impedance. The existing method for the calculation of the multimodal radiation impedance of a cylindrical tube terminated in an infinite baffle is reviewed. New work is then presented for the calculation of the radiation impedance of a rectangular duct terminated in an infinite baffle. An existing method for calculating the input impedance of an acoustic horn of cylindrical cross-section starting from the radiation impedance is utilised. The method is then formulated for horns of rectangular cross-section. Pressure field calculations are also presented.

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