The early stages of a motor failure exhibits the famous 60 cycle hum. 120 volts is supplied to the motor; if any of the windings begin to short; there is not enough induction, the rotor of the motor stalls and eventually locks (locked rotor amps) draws excessive current and trips the internal/external overload on the motor. Before this occurs, if a winding in the motor is shorting, you will hear a buzzing noise which is the 60 cycle frequency of the 120 volt supply indicating (perhaps) a failing motor.

Source: New dryer works great, but fills house with a hum noise