Operating an ultrasonic transmitter and receiver includes providing a MEMS composite transducer. The MEMS composite transducer includes a substrate. Portions of the substrate define an outer boundary of a cavity. A first MEMS transducing member includes a first size. A first portion of the first MEMS transducing member is anchored to the substrate. A second portion of the first MEMS transducing member extends over at least a portion of the cavity and is free to move relative to the cavity. A second MEMS transducing member includes a second size smaller than the first size of the first MEMS transducing member. A first portion of the second MEMS transducing member is anchored to the substrate. A second portion of the second MEMS transducing member extends over at least a portion of the cavity and is free to move relative to the cavity. A compliant membrane is positioned in contact with the first and second MEMS transducing members. A first portion of the compliant membrane covers the first and second MEMS transducing members. A second portion of the compliant membrane is anchored to the substrate. Electrical pulses are sent to the first MEMS transducing member which causes the first MEMS transducing member and the compliant membrane to vibrate. The vibrations of the first MEMS transducing member and the compliant membrane are transmitted to an object. Echo signals are received from the object. The received echo signals are converted into electrical signals by the second MEMS transducing member.