Transducer Sound Dome Interaction

The acoustic interaction of a transducer and a surrounding sound dome is analyzed by a modified separation of variables method. The theory is described for transducer and dome of general shape. If they arc concentric spheres, the method reduces to classical separation of variables. Perhaps the simplest crumple that uses the general theory in a significant way is obtained if transducer and dome are concentric spheres but the thickness of the dome varies with position. Numerical results are given for this case. For the calculations the velocity at the transducer is phased to a plane wave and its magnitude multiplied by a constant to adjust for a fixed transducer power output, which is taken as that for the no-dome case. The results show that, with a dome that has a thickness increasing uniformly from a minimum value A in the direction of the main radiated beam to a maximum value in the opposite direction, the directivity index and main beam magnitude are increased several decibels in comparison with results for a dome of constant thickness equal to the average of A and B.