2000 discovery II. High pitch noise coming from passenger side engine at cold startup. Nis that normal?

 

Is this a california car? Sounds like you are talking about SAI (secondary air injection).

It's like an old smog pump they had in the early 80s only instead of belt drive, it's electric. Sounds somewhere in between a dust buster and a shop vac.

 

It sounds like the air injection. Check the filter in it, they fall apart with age and may be why the pump is noisy.

 

There is a "how to" in the write up section on what to do.

 

These guys are right, Secondary Air Injection pump is what the noise is. To your question, "is it normal?" Yes! It runs for a certain amount of time at start up and blows air down the exhaust manifolds to heat up the cats. Sort of sounds like a turbine winding down when it shuts off, Some people have had good luck quieting it a bit by replacing the air filter on the pump where it draws air in, per the write-up and how-to section.