  The main issue of the present letter 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 can not be resolved. As a consequence if were detected gravitational
waves having the feature here predicted (anomalous polarization amplitudes),
then they would be reliable markers for the existence of an extra dimension.
