If your furnace is in the basement, then any minor noises may go unnoticed. But if the furnace is in the living area then every noise will be heard. Typically, furnace noise issues fall into two categories; duct related or mechanical.
The vast majority of noise issues are duct related. Unfortunately, most duct systems are not sized properly and therefor can cause whistling noise or banging noise when the furnace starts or stops. Most homes don’t have enough cold air returns which results in a high static pressure. The problem can usually be resolved by adding more returns.
Mechanical noises from the furnace are easy to spot because they are very distinct and loud. They are almost always caused by the inducer motor or the blower motor. The inducer vents the flue gases into the chimney. Eventually the heat from the flue gases dries out the bearings and the motor makes a loud whirring sound. The only fix for this problem is to replace the motor.
The most common noise issue with blower motors is when the blower wheel makes contact with the blower housing. This creates a loud scratching noise. It is usually an easy fix by simply centering the wheel on the drive shaft and tightening the set screw. Most of these problems can be caught and corrected with regular HVAC maintenance inspections.