Wavenumber In Water Research Articles

Luneburg Lens and Wave Theory

The wave theory for an underwater Luneburg lens is discussed in terms of a generalized wave equation, which differs from the ordinary wave equation in that it contains a term involving the gradient of the material density of the lens. We then consider the special case where, to a first approximation, the density of the lens has a constant value equal to that of water. This case is of some importance since it corresponds to the compliant tubing lens built and tested by W. J. Toulis [J. Acoust. Soc. Am. 35, 286 (1963)]. For this special case, we determine the analytic solution of the wave equation when the lens is being irradiated by plane waves, and then present the results of a numerical evaluation of that solution. In particular, we calculate the acoustic pressure field along the axis of the lens and the pressure receiving patterns. These results give us the gain and beamwidths for the range 1 ⩽ k0a ⩽ 30 (k0 the wavenumber in water, a the radius of the lens).

Experimental Determination of Mutual Radiation Impedance between Coplanar Circular Pistons

The normalized mutual radiation impedance between circular piston transducers mounted in a coplanar configuration is determined by an experimental procedure. The transducers used in the experiment are double mass-loaded ferroelectric tubes. The normalized mutual-radiation-impedance coefficients are calculated from the measured value of electrical admittance and the known freefield properties of the transducer. To simplify the interpretation of the data, lumped-constant equivalent electromechanical circuits with frequency-dependent elements are used. The equivalent circuit as synthesized from freefield measurements of the transducer is modified to include the effects of the mutual radiation impedance. The modified circuit permits its use in the analysis of arrays of transducers. By means of this method, experimental results are obtained for a 2-element array with a 30-in.-sq steel baffle plate and also with no baffle. The “ka” value of the piston radiators at velocity resonance is approximately 1.3, where k is the acoustic wavenumber in water and a is the radius of the piston. Data are presented for various center-to-center element spacing and piston-velocity ratios. The results obtained show the mutual-impedance coefficient to be practically independent of piston-velocity ratio. The experimental mechanical-radiation-impedance values agree with analytical results reported previously in the literature.