Principles of wide bandwidth acoustic detectors and the single-mass dual detector

We apply the standard theory of the elastic body to obtain a set of equations describing the behavior of an acoustic gravitational wave detector, fully taking into account the three-dimensional properties of the mass, the readout, and the signal. We show that the advantages given by a dual detector made by two nested oscillators also can be obtained by monitoring two different acoustic modes of the same oscillator, thus easing the detector realization. We apply these concepts and by means of an optimization process we derive the main figures of such a single mass dual detector designed specifically for the frequency interval 2-5 kHz. Finally we calculate the standard quantum limit sensitivity of this detector.