Other possibilities, though less likely, include:
* Worn or damaged belt: A slipping or misaligned serpentine belt can sometimes make a whistling sound.
* Power steering pump: A failing power steering pump can whine or whistle.
* Alternator: Although less common, a failing alternator could create a high-pitched whine.
To diagnose the problem: It's best to have a mechanic check it out. However, you could try to locate the source of the whistling yourself by carefully listening around the engine compartment while the car is running. Pay attention to where the sound seems to be loudest. Look for any loose or disconnected vacuum hoses.
Because vacuum leaks are common on older cars, that's the most likely culprit for a whistle upon startup.