A micro-machined ultrasonic transducer is proposed. The micro-machined ultrasonic transducer includes a membrane element for transmitting/receiving ultrasonic waves, during the transmission/reception of ultrasonic waves the membrane element oscillating, about an equilibrium position, at a respective resonance frequency. The equilibrium position of the membrane element is variable according to a biasing electric signal applied to the membrane element. The micro-machined ultrasonic transducer further comprises a cap structure extending above the membrane element; the cap structure identifies, between it and the membrane element, a cavity whose volume is variable according to the equilibrium position of the membrane element. The cap structure comprises an opening for inputting/outputting the ultrasonic waves into/from the cavity. The cap structure and the membrane element act as tunable Helmholtz resonator, whereby the resonance frequency is variable according to the volume of the cavity.