If you notice the whistling sound in your appliance coming from the vicinity of the freezer compartment, the most common reason for it will be the evaporator fan. Like any electric fan, it's powered by a motor. The fan might make a variety of noises that include squealing, chirping, whistling and even moaning. This is usually because the lubrication is gone or the bearings are worn out. You'll need to have the evaporator fan replaced entirely since the fan motor cannot be lubricated.
The evaporator fan can cause a mild whistling sound while working normally. This fan draws air over the cooling coils and forces air to circulate throughout the refrigerator. The forced air moves through the various orifices in the freezer and fresh food compartments. In some models this air causes a whistling sound as it passes through the openings throughout the refrigerator. This is a normal noise and nothing to be concerned about.
Newer refrigerators are likely equipped with high-efficiency compressors, which run much faster than older compressors. They get the job done more quickly with less energy, but can also make a different noise than old compressors. These high-efficiency units may produce a high-pitched whine or hum. Some consider this whining sound to be a whistle. Unfortunately, if this noise is bothersome, you’ll have to live with it as long as you have the refrigerator, as it's the normal operating sound of your particular refrigerator.
If the whistling sound in your refrigerator is coming from the rear of the unit, the condenser fan may be the culprit. The condenser fan motor can squeal or whistle if the motor bearings are worn out, which requires replacing the fan motor. If the fan has gotten dirty from dust or lint, it could also be affecting the movement of the fan and cause different sounds such as whistling or humming.