My house is 14 yrs old. With an original tub/shower enclosure. When showering, for the first 2 minutes everything is fine. Then the water pressure drops to a trickle. Temperature doesn't change just the pressure. Shut the shower off wait 30 seconds and start it over, the pressure is fine for another 2 minutes. Problem is not the shower head, we use a detachable hose/sprayer. The faucet cartridge has been replaced. Is the problem in the shower control on the faucet where it closes off partially after two minutes or somewhere else I'd rather not know about?

I know it seems like the pressure drops but its likely the volume, not pressure that's at issue. Leave the shower on and when the pressure/volume drops try opening other fixtures like kitchen sink and bath sink. Do they have low volume too? City water or well?

Agree - it is probably the volume, other faucets pressue is OK. City water - pressure has always been low - 45-50 lbs. Also, pipes whine,and have a light vibration as the volume drops, and then stops when volume is the lowest. No such problem in any other faucet in the house, and all has worked OK, for 14 yrs.
If it is a clogged pipe, how do I unclog it?

Most of us would say 45-50 is about perfect. Does your house have a pressure reducing valve near the meter, PRV? Watts 3/4 Inch 25AUB-Z3 (0069717) Pressure Reducing Valve (Threaded F Union Inlet x NPT Threaded F Outlet) You can test you pressure with a cheap valve attached to your garden spigot