A wave generator has a wave emitter including an elongated dispersive waveguide and a source operatively connected to a first end of the waveguide. The source covers at least partially a surface area thereof. A signal generator is in operative connection with the transducer to create electrical signals. A computer is in operative connection with the signal generator to cause it to generate the electrical signals. A mechanical input wave is created by the source at the first end of the waveguide. The mechanical input wave is constructed independently of data related to a mechanical wave received from a source in the medium and taking into account the different predetermined propagation velocities of at least two component waves of the mechanical input wave so that they combine with each other at a second end of the waveguide to form the desired mechanical output wave in the medium.