Whine sounds can come from a large variety of sources... typical sources though are:
* anything with a bearing, especially one that is loaded constantly like the idler pulley. Other items hard on bearings include alternators and water pumps... anything driven by the serpentine belt. Sometimes you can hear noise coming from the cooling fan on the front of an alternator; there isn't much that can be done about this as it's a result of the fan design, not of a failed part. When the water pump bearing fully goes bad you'll hear a sound like marbles rolling around a large empty coffee can. It's a very distinctive sound usually accompanied by a few drops of anti-freeze slowly leaking from the bottom/front of the water pump.
* electric power steering pump. Actually, any power steering pump but electric ones are prone to a humming sound. Often these are temperature sensitive too; when very cold the fluid can be thicker and thus harder to pump. Air in the system, or the wrong fluid (many cars use auto transmission fluid instead of power steering fluid) will lead to whine noises. Often the power steering system will have a bleed port (just like brake caliper bleed ports, typically located on the steering rack/gearbox) to remove air. Cycling the steering
wheel stop-to-stop slowly a few times is often enough to bleed a system, especially when it's done after a long drive that heated the fluid.
* fuel pumps though usually that is a noise from the rear of the vehicle; on many cars it is especially noticeable when the engine is running with the gas cap removed - such cars have the pump IN the fuel tank, rather than near it. Fuel rapidly flowing from the pump, to the fuel pressure regulator (little beer keg/UFO shaped thing on the top of the engine at the ends of the "fuel rails" feeding the injectors), and then back to the tank can whine if there are restrictions (kinks/dents in the pipes) or flashing bits (manufacturing defects leaving extra metal inside the pipes/connectors, metal slivers from machining, etc) in the pipes/hoses.
Want to hear some horrible noises? Get a "mechanic's stethoscope" which is a stethoscope with a metal rod as a pick-up instead of the cold-to-the-touch end of a typical doctor's stethoscope. You can make one with a small diameter rubber tube (e.g. vacuum or windshield washer hose) and a metal rod, skinny screw, screwdriver shank, etc, stuck into the end of the tube. Touch various engine parts (while the engine is idling) with the metal end... you'll hear a lot of "whooshing" sounds, rhythmic pulses (marbles rolling around fast in a coffee can), clacking of injectors, clacking of valves and rocker arms, etc. Just don't touch anything actually moving or that is exhaust-pipe hot! Replace the metal rod with a small funnel and use that to localize mystery sounds you can hear un-aided. Works surprisingly well. And then you can have the dealer tech listen as well.
mike c.