Air filters trap particles that flow through your ductwork from your furnace, before they can escape into the house. While there are many qualities and types of air filters, they all need to be cleaned or replaced at regular intervals. If an air filter becomes loose, crooked or too full of debris, the air flowing through it can make a whistling sound. Replacing or readjusting your vent can often fix this problem.
Air vents can also become clogged with debris. This occurs with both supply vents bring air to the furnace and ductwork vents throughout the house, but may be more common with supply vents because of their exposure to outdoor conditions. If these vents become clogged, they will create whistling noises as the furnace tries to draw the amount of air it needs to function properly.
Gas flow refers to how easily gas flows from the main line into gas furnaces. If you have a natural gas furnace, over time trace amounts of contaminants in the gas may cause it to make a whistling noise as it flows through the line to your furnace and exits into the firebox. While this does not necessarily mean you have a gas leak, it does impair the efficiency of the furnace and should be repaired as soon as possible.
Burners can encounter sediment, corrosion from condensation and blockages from dirt. When the primary burners try to activate, they can create noises that signal problems, including a whistling noise. If your burners are whistling and your furnace is not heating as fast as it used to, it could be a sign of a damaged burner.