Is this a shower in a tub? or a dedicated shower? If in a tub with a diverter in the tub filler spout, that is probably where the sound is coming from. Most spouts do not have replacement parts available for them - it is usually fairly easy to replace the whole thing, though.
If it is a dedicated shower valve I've heard that a loose washer can cause this. If so, then it can (usually) be repaired.
One of the pros may have some other ideas.