In slowly flaring horns the wave fronts can be considered approximately plane and the input impedance can be calculated with the transmission line method (short cones in series). In a rapidly flaring horn the kinetic energy of transverse flow adds to the local inertance, resulting in an effective increase in length when it is located in a pressure node. For low frequencies corrections are available. These fail at higher frequencies when cross-dimensions become comparable to the wavelength, causing resonances in the cross-direction. To investigate this, the pipe radiating in outer space is modelled with a finite difference method. The outer boundaries must be fully absorbing as the walls of an anechoic chamber. To achieve this, Berenger's perfectly matched layer technique is applied. Results are presented for conical horns, they are compared with earlier published investigations on flanges. The input impedance changes when the largest cross-dimension (outer diameter of flange or diameter of the horn end) becomes comparable to half a wavelength. This effect shifts the position of higher modes in the pipe, influencing the conditions for mode locking, important for ease of playing, dynamic range and sound quality.
The aim of this paper is to present a way of ranking the nonlinearities of electrodynamic loudspeakers. For this purpose, we have constructed a nonlinear analytic model which takes into account the variations of the small signal parameters. The determination of these variations is based on a very precise measurement of the electrical impedance of the electrodynamic loudspeaker. First, we present the experimental method to identify the variations of these parameters, then we propose to study theoretically the importance of these nonlinearities according to the input level or the input frequency. We show that the parameter which creates most of the distortions is not always the same and depends mainly on both the input level and the input frequency. Such results can be very useful for optimization of electrodynamic loudspeakers.