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Chapter 8Resonant detectors for gravitational wavesand their bandwidthG PizzellaUniversity of Rome Tor Vergata and Laboratori Nazionali diFrascati, PO Box 13, I-00044 Frascati, ItalyThe sensitivity of the resonant detectors for gravitational waves (GW) isdiscussed. It is shown that with a very low-noise electronic amplifier it ispossible to obtain a frequency bandwidth up to 50 Hz. Five resonant detectorsare presently in operation, with a spectral amplitude sensitivity of the order of˜h = 3 × 10 −22 (1/ √ Hz). Initial results are presented, including the first searchfor coincidences and a measurement of the GW stochastic background.8.1 Sensitivity and bandwidth of resonant detectorsThe detectors of GW now operating [1–5] use resonant transducers (and thereforethere are two resonance modes coupled to the gravitational field) in order to obtainhigh coupling and high-Q.However, for a discussion on the detectors’ sensitivity and frequencybandwidth it is sufficient to consider the simplest resonant antenna, a cylinderof high-Q material, strongly coupled to a non-resonant transducer followed by avery low-noise electronic amplifier. The equation for the end bar displacement ξis¨ξ + 2β 1 ˙ξ + ω0 2 ξ = f (8.1)mwhere f is the applied force, m the oscillator reduced mass (for a cylinderm = M/2) and β 1 = ω 0 /2Q is the inverse of the decay time of an oscillationdue to a delta excitation.We consider here only the noise which can be easily modelled, the sum oftwo terms: the thermal (Brownian) noise and the electronic noise. The power91