Theory of Acoustic Resonator

1 Acoustic Normal Modes in a Sphmeal and Cylindrical Restmator 

The kinetic ener produced by the absorption of a modulated beam of light in a resonator causes the excitation of acoustic normal modes in the cavity. The rimple theoretical approach considered in this section is that of a lossless gas in a rigid container with perfectly insulating walls. This simple model yields reasonable values for the eigenfrequencies of the resonator. However, for an accurate description of experimentally determined resonance frequencies and the corresponding Q factors, dissipation effects, deviations of the cavity from the ideal geometry, etc. must be taken into account. The advances made in recent years in an understanding of these loss mechanisms will be discussed in the next section. 

The resonator with the highest symmetry is the spherical resonator. A treatment of oscillations in a spherical cavity was already given by Rayleigh in 1894 A recent discussion may be found in Ref. In the simple loss-free model, sound is described by the homogeneous wave equation  

In the following only radial modes of the spherical cavity are considered for which m = 0. With the solution 

The index n is used to label the successive roots of this equation. The values of the first roots a are listed in Table 2. The eigenfrequencies of the radial modes of a spherical resoottra cn be cafculated with these a valtms using the equation  

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In this article, experiments with gases employing a resonant photoacoustic cell are reviewed. In the next chapter the physical processes occurring in an acoustic resonator are analysed. The third chapter describes experimental setups and components used in resonant photoacoustic spectroscopy. In chapter four the theory of acoustic resonators is outlined and the loss mechanisms which dampen the... 

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