Effect of Transverse Acoustic Flow on the Input Impedance of Rapidly Flaring Horns

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.