Ricerc@Sapienza

The generation and propagation of a second harmonic water wave have been investigated in the
frequency range between 7 Hz and 60 Hz where the velocity vs. frequency curve attains its minimum
value. A model is proposed by assuming that the second harmonic is locally generated by point
sources on the wavefront of the fundamental wave, and that at any point along the propagation
direction the second harmonic be given by the cumulative contribution from all the sources up to
the considered point. In the frequency range examined the combined effects of gravity and capillarity
yield the so called resonance condition where the fundamental and second harmonic waves share
the very same phase velocity. In such a case, wave shape matching condition is maintained between
the two waves along all the propagation directions, with the amplitude of the second harmonic
only limited by the attenuation effect. Evidence is given experimentally of such effect through the
wavenumbers mismatching produced by the model vs. frequency and the detection of the maximum
distance of second harmonic amplitude from the wave source. Furthermore, it is found that the
resonance condition is a threshold effect with respect to water depth.