Can gravitational waves be markers for an extra-dimension?

The main issue of the present paper is to fix specific features (which turn out being independent of extradimension size) of gravitational waves generated before a dimensional compactification process. Valuable is the possibility to detect our prediction from gravitational wave experiment without high energy laboratory investigation. In particular we show how gravitational waves can bring information on the number of Universe dimensions. Within the framework of Kaluza-Klein hypotheses, a different morphology arises between waves generated before than the compactification process settled down and ordinary 4-dimensional waves. In the former case the scalar and tensor degrees of freedom cannot be resolved. As a consequence if gravitational waves having the feature predicted here were detected (anomalous polarization amplitudes), then they would be reliable markers for the existence of an extra dimension.