The process involves transmitting an ultrasonic excitation wave having a mid-band transmission frequency (fc) and focused in a target point of a target medium (2) e.g. patients body. Transducers are fixed on a reverberating solid object (7) that provokes multiple reflections of the wave. A pulse wave of duration 1/fc entering the object leads to an acoustic transmission of duration 10/fc towards the medium. An independent claim is included for a device for focusing ultrasonic waves.