Extensions to the Mode Matching Method for Horn Loudspeaker Simulation

Abstract

For loudspeaker horns, the throat acoustic impedance and the far field directional characteristics are important measures of performance. Both quantities depend greatly on the shape of the horn, and the acoustical conditions at the mouth of the horn. The Mode Matching Method (MMM) is a semianalytical method for the simulation of sound propagation in ducts, and is the method used as the fundamental building block in this work. In previous work using this method, the horn has usually been assumed to be mounted in an infinite baffle, a condition that is not realistic for most real-world applications. Most horns are usually mounted in finite baffles or cabinets, or placed close to reflecting surfaces or in rooms. This work has therefore focused on extending the MMM to new cases closer to real-world applications. For horns without baffle, or with finite baffles or flanges, two methods have been explored; one for axisymmetric horns based on the solution for a semi-infinite unflanged duct, and one for general geometries based on edge diffraction. For horns near infinite reflecting surfaces, a method has been derived to compute the modal mutual radiation impedance. For the final radiation condition, a horn mounted in the wall of a room, two methods have been explored, where in both cases analytical expressions for radiation impedance and radiated pressure are found for shoebox shaped rooms. Experimental verification of some of the cases mentioned above is provided. The MMM is restricted to certain cross-sectional geometries; round and rectangular geometries are treated in this work. In many practical cases a rectangular horn is connected to a circular loudspeaker, and in order to simulate this and similar configuration, a method has been developed to interface the MMM with the Boundary Element Method. By modifying the MMM, it has also been possible to simulate radiation from concave structures like loudspeaker diaphragms. Using this approach it is also possible to simulate concave reflectors, as long as the source is not outside of the cavity. A final application of the MMM in this work, is the use of the method to compute the transfer function and resonance frequencies of non-shoebox shaped rooms. While the shape of the room is still somewhat restricted compared to Finite Element Method simulations, a wide range of rooms can be simulated.