An approximate method for determining the maximum amplitude of higher-order duct modes

Abstract

Previous investigations have used Hankel transforms to establish the amplitudes of the wave fields resulting from arbitrary angle impingement on a circular orifice in a baffle. Investigations have also been undertaken on the effects of model coupling between the higher modes in the orifice. In particular, these studies concentrated on establishing the contributions at the cut-on wave number for a particular mode. This work is extended to introduce a method of simply approximating the complex amplitude of the forward and backward waves in the duct at the cut-on wave number, based only on the modal wave number. The interest focuses on the cut-on wave number because the forcing functions for the various fields will be at a maximum at cut-on. This technique is established by observing the relationships between the peak values of the driving functions and the modal wave number. If simple approximations are established for the in-duct field, it is also possible to approximate the maximum amplitude of the scattered field.