Determination of the size of an object and its location in a rectangular cavity by eigenfrequency shifts: First order approximation

Abstract

The acoustic properties of a cavity are modified when objects are placed in the cavity. Such objects modify the wave equation or boundary conditions and give rise to volumetric and scattering effects. These effects cause changes in the eigenfrequencies of the cavity. This paper describes a method of using eigenfrequency shifts for determination of the object size and location in the cavity. A theoretical and experimental determination of the object size and position in a 2-D rectangular cavity has been carried out. It is shown that the object location and size can be calculated from the measured eigenfrequencies and their mode orders under four boundary conditions. When the object is small, the object function can be expressed as a 2-D spatial Fourier series the spatial frequencies of which are related to the eigenfrequency shifts caused by the object. The theory can also be applied to determine the position of multiple objects in the cavity. Experimental results show that the accuracy of the calculated object function is dependent on the number of eigenfrequency shifts used in the calculation. The difficulties involved in the mode order identification are discussed.