The vibrational spectrum of a tunneling junction on a clean Cu(111) surface has been characterized by vibrational density of states calculations and inelastic electron tunneling spectroscopy technique. We demonstrate that the achieved spectrum consists not only of vibrational modes excited by the tunneling electrons on the clean surface but also of modes characteristic of the structure of the tip apex. This allows to identify unequivocally the atomic structure of the tip, which is still the largest unknown parameter in a scanning tunneling microscope. This opens a new perspective in the interpretation of the measurements of vibrational modes with a scanning tunneling microscope. Additionally, it might have implications in the measurements of electron conductance through single atom or molecules contacted by the tip of scanning tunneling microscope.