Study on acoustic radiation impedance at aperture of a waveguide with circular cross section taking account of interaction between different guided modes

TL;DR

This study simulates the acoustic impedance at a waveguide aperture considering mode interactions, using the Rayleigh integral, to improve understanding of high-frequency wave radiation beyond piston approximation.

Contribution

It introduces a low-time-consuming simulation method for mode interactions at waveguide apertures applicable across wave science fields.

Findings

Rayleigh integral effectively simulates mode interactions

Piston approximation accuracy varies with mode complexity

Method applicable to acoustics, electromagnetism, and optics

Abstract

In this paper we simulated self- and mutual- acoustic impedances of guided modes at the aperture and estimated accuracy of the piston radiation approximation. We used the Rayleigh integral to simulate the interactions between different guided modes at the aperture, with low time-consuming. This kind of guided-wave technique can be utilized to solve problems in diverse fields of wave science such as acoustics, electromagnetism and optics. For acoustic waves emitted through a horn or a waveguide with an aperture much smaller than the wavelength, there are only plane wave modes in the waveguide and the aperture of horn can therefore be considered as a piston radiator. However if an acoustic wave with high frequency such as ultrasonic wave is radiated, there can exist several guided modes in the duct. For arbitrary shape and size of waveguide, interactions between different modes must be taken into account to evaluate sound field in the duct and total acoustic power from its aperture. In this paper we simulated self- and mutual- acoustic impedances of guided modes at the aperture and estimated accuracy of the piston radiation approximation. We used the Rayleigh integral to simulate the interactions between different guided modes at the aperture, with low time-consuming. This kind of guided-wave technique can be utilized to solve problems in diverse fields of wave science such as acoustics, electromagnetism and optics.