PMUT acoustic transducer formed in a body of semiconductor material having a face and accommodating a plurality of first buried cavities, having an annular shape, arranged concentrically with each other and extending at a distance from the face of the body. The first buried cavities delimit from below a plurality of first membranes formed by the body so that each first membrane extends between a respective first buried cavity of the plurality of first buried cavities and the face of the body. A plurality of piezoelectric elements extend on the face of the body, each piezoelectric element extending above a respective first membrane of the plurality of first membranes. The first membranes have different widths, variable between a minimum value and a maximum value.