Sounds as though the diverter is the cause of the noise. Replacing this diverter should take care of the issue.
Depending on which type of spout/diverter you have .... either simply unscrewing the spout or another type has a set screw on the underside needs to be removed.

Before installing the new spout/diverter clean the copper pipe with some emery cloth to make it nice and shinny to help the O ring seal better.