VEHICLE WHISTLING NOISE

Customers noticed such problems and asked questions like this:

My car makes whistling noise while driving?

Why does my car make a whistling noise?

Things That Make A Vehicle Whistle While It Works?

Car Making Whistling Noise?

What's that high-pitched whistle coming from my car?

My car's strange whistling noise?

car makes humming noise when driving?

whistling noise when accelerating?

loud humming noise while driving car?

car makes whining noise when accelerating?

my car is making a whistling noise when i accelerate?

car making whistling noise when driving?

what does it mean when your car makes a whistling noise?

whistling noise from car that stops when i brake?

The fan belt can cause a whistling noise while running. You might want to check it out to see if it is correctly tensioned. Other causes of a whistling sound could be a vacuum leak, or sticking idle control system.
If the engine idles abnormally high when you first crank it up, then the malfunction is definitely in the idle system.
If the whistling gets louder or changes pitch with increase in RPM, then it is a fan belt. I t may even stop altogether, and start back when you come to a slowdown.

Another concern would be leaks from the supercharger, if it has one on this particular engine.

Easy step by step guide on how to fix an automotive engine whistle, this information is displayed in order of probability and pertains to most vehicles.

Difficulty Level - 3

Start with the vehicle parked on level ground, engine off and the emergency brake set, using a basic set of tools wearing safety gloves and eye-wear protection.

Step 1 - When a vacuum hose or tube fails it can make a whistling noise which could vary with engine speed. Learn more

ENGINE VACUUM LEAK

Step 2 - If a battery connection becomes corroded or if the battery is starting to fail, it can cause the alternator to overwork which creates a whistling, whining style of noise. Learn more

BATTERY CORROSION

NON ENGINE PROBLEM - When a door seal fails it can create a whistling noise as air enters the passenger compartment, these whistling noises can be difficult to find. If needed have a passenger ride along while running their hands along the area the noise is being generated from, this will pinpoint the location.

DOOR SEAL

Helpful Information

Some whistling noises are simple to fix, while others are a little more difficult to find and can be aligned with the engine speed.
The source of the whistle is sometimes an overworked alternator. This electrical component keeps the battery charged and provides power for lights and accessories. High resistance between the alternator and battery increase its workload, causing a noise that varies with engine speed. To stop this noise, car owners should inspect electrical wires and connections. Any corroded connections should be cleaned, and worn wired should be replaced.
Worn fan-belt pulleys make a sound that increases with speed. Worn belts also create a whistling noise. Belts should be inspected for signs or wear and replaced if necessary. Pulleys should be tight with little horizontal movement. Belts should be adjusted to the factory-recommended tension.

Noises that only occur as the car is moving are sometimes due to worn window seals. As the vehicle moves down the road, it forces air through these small openings, resulting in the whistle. Windows that are not fully closed increase the chances of whistling. Any worn seals should be replaced, and windows should be tightly closed. If the noise continues, door seals should be inspected for any small holes that allow air to pass.
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For Fan belt making Whistling noise

Yes, it is a straightforward repair. There is even a TSB about the belt being noisy. It says to get a Scotchbrite pad, and 'clean' the pulleys with it, among a few other things to check. Here is a copy of it:
August 2005
Technical Service
SI M 11 02 05
Engine
SUBJECT
Drive Belt Noise
MODEL
R50 (Cooper), R52 (Cooper Convertible) with W10 engine produced from April 2005 to present.
R52 (Cooper S Convertible), R53 (Cooper S) with W11 engine produced from April 2005 to present.
SITUATION
Customer complains the engine exhibits a high-pitched squeal from the engine accessory drive belt. The noise can occur at all engine speeds, mostly occurring in the 2500-RPM range.
CAUSE
Root cause is under investigation.
PROCEDURE
One of the following could be the cause of the complaint. Please follow the procedures outlined below in order.
1. Alternator Alignment

a. Loosen the 3 mounting bolts that attach the alternator to the mount two revolutions, do not remove the drive belt during this process. Leaving the drive belt in place causes a natural alignment of the alternator.

b. Retighten the bolts and torque to the specifications listed below for each model.

Cooper S (R52, R53)
Repair Instruction 12 31 020 Removing and installing/replacing alternator
M8 Bolts = 25 Nm
Cooper (R50, R52)
Repair Instruction 12 31 020 Removing and installing/replacing alternator
M6 Bolts = 10 Nm
Drive belt removal MINI Copper S vehicles equipped with W11 engine and F21 6 Speed automatic transmission only
Removing the drive belt on a W11 engine equipped with the F21 Automatic Transmission requires modification to the current tool 11 8 410. The two dowel pins on the tool need to be shortened approximately 5 mm. After the tool is modified it can still be used on all of the models, a new tool will not be developed. The Repair Instruction RA 11 50 020 will be updated in the September Release on TIS to reflect the modifications necessary to fit this application.
2. Rust Or Flaking Paint On The Pulleys

a. Inspect all pulleys for rust or flaking paint in the belt contact surface. Removal of the drive belt will be necessary, refer to Repair Instruction RA 11 28 010 (W10 engine) or RA 11 50 020 (W11 engine).

b. Using a 3M Scotch Brite pad or similar pad, clean the pulley until the rust or flaking paint is removed.

c. Before reinstalling drive belt, inspect the belt for damage, foreign material in contact surface and length of the belt. Compare the belt length to a new belt from parts, replace as necessary or reinstall old belt.

3. Drive Belt Is hopping Or The Belt Tensioner Is Binding

a. Inspect belt tensioner using special tool to release the belt tension. Removal of the drive belt may be necessary, refer to Repair Instruction RA 11 28 010 (W10 engine) or RA 11 50 020 (W11 engine).

b. If the tensioner feels soft or appears to be binding and will not re-apply proper tension to the drive belt, replace as necessary.

c. Before reinstalling drive belt, inspect the belt for damage, foreign material in contact surface and length of the belt. Compare the belt length to a new belt from parts, replace as necessary or reinstall old belt.

4. Supercharger Difficult To Turn (W11 Engine Only)

a. In some circumstances this could be caused by a difficult to turn or binding Supercharger. Do not replace the supercharger, submit a PuMA case to the Drivetrain Group with "Belt Noise, Supercharger Binding" in the subject field and wait for a response.

Note :Under no circumstances should the drive belt be replaced with an aftermarket drive belt. If the vehicle is not equipped with a J o h n C o o p e r Works Kit then the special belt should not be installed.
Please submit a PuMA QC Info on all vehicles indicating which of the above has repaired the vehicle.
If all of the above procedures have not repaired the vehicle, please submit a PuMA case to the Drivetrain Group and wait for a response.
WARRANTY INFORMATION
Covered under the terms of the BMW New Vehicle Limited Warranty.
Refer to KSD for proper defect code and labor allowance for work performed.
Here is the OEM information from Mini about your belt:
Serpentine Belt 11287518250 $29.34

Sorry, they don't provide instructions for changing it, though. But it's an automatic tensioner, so easy to do. Labor time requirement is 0.6 hours (36 minutes), but usually done in 0.4 hours (24 minutes).

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It could be a lot of things, but usually it is a worn belt. It's not hard to replace on most vehicles, but you probably should talk to someone with mechanic experience and have him/her listen to it. 
Is the whistle constant? 
Does it get louder when you press the gas, will it go away when you take your foot off? 
Does it only happen on the highway or at high speeds? 
Does the sound stay with you the entire time that you are driving? 

Lets check a couple things first. 
I'm assuming it's not your window. 
I'll also assume its not your belts because that is a pretty clear sound, very loud, more of a squeal than a whistle. 

90% of the time a whistle is a vacuum leak. If the car/truck/ van or whatever is running rough, using more fuel than normal there is a good chance its a leak. 

Turn the engine on and open the hood, try to follow the whistle. Hopefully you can hear it. If not there are two ways to check this. One is safer but sounds horrible, but it isn't. The other is something you need to do while the engine is cold. 

Option one. 
Take a small propane torch with the torch end cut off at the section where flange section meets the area where the propane flows out from the little holes. Some will unscrew to adapt other tips. Take a 1 ft section of vacuum line and connect that to the nozzle. Once the engine is running, turn the propane on 1/4 open and run the hose along the manifold, pcv valves plugs and what have you. Don't worry about blowing up, there will be no propane resting around the engine while the car is running, the fan will blow it away. 

While running the hose, listen for idle change, when t he cars rpms go up, you have found the leak. Replace or repair. 

The second option 
Same idea, but with brake cleaner. This option is a little more dangerous than the first. 

Spray around the same areas of the intake, hoses and whatnot. Small shots will do, don't use a constant stream. ALWAYS HAVE A FIRE EXTINGUISHER WHILE USING THE BRAKE CLEANER. 
Whistling sound means a vacuum leak, if it is more like a metallic squeal the brakes may be the problem. Brake pads have a wear indicator that start squeaking when it is time to replace the pads. If brakes were installed without putting the proper amount of grease on the back of the pads they will make a "singing sound". This happens as the to surfaces rub together causing vibrations, like drawing the bow across the strings of a musical instrument.

This will help.

Thanks.