The reason the relay humms or buzzes is that the pole faces on the relay are not aligning properly. This could be a result of the relay being out in the weather and developing a coat of rust on it. If the relay stops the noise when given a tap on its side then that is the cause.
The other cause could be from a broken shorted turn. The use of laminations in an ac relay reduces the heating due to eddy currents. In addition, a copper strap or ring (called a shorted turn) is placed near the end of the pole piece of an ac relay to reduce chatter during operation. Because the ac is going through a peak, dropping to zero, going through a peak in the opposite direction, and then dropping to zero again during each complete cycle, the coil tends to release the armature each time the current drops to zero and attracts the armature each time it reaches a peak. The shorted turn acts as the secondary of a transformer, the primary of which is the relay operating coil. The current in the shorted turn is out of phase with the current of the operating coil because the copper ring has low-inductive reactance. Thus, when the operating coil flux is zero, the flux produced by the shorted coil is different from zero, and the tendency of the relay to chatter is reduced.
