Humming sound in a transformer

Q. What is the reason for a humming sound in a transformer?

The basic cause of transformer noise is magnetostriction: 

the expansion and contraction of the iron core (laminations) due to the magnetic effect of alternation current flowing through the transformer coils. This produces an audible hum. Magnetostriction may be partially controlled by the transformer design, but it cannot be totally eliminated.

Transformer noise cannot be eliminated. It can, however, be reduced through proper design and assembly, and/or masked through proper consideration of the installation.

Applying voltage to a transformer produces a magnetic flux, or magnetic lines of force in the core. The degree of flux determines the amount of magnetostriction and hence, the noise level.

Why not reduce the noise in the core by reducing the amount of flux? 

Transformer voltages are fixed by system requirements. The ratio of these voltages to the number of turns in the winding determines the amount of magnetization. This ratio of voltage to turns is determined mainly for economical soundness. Therefore the amount of flux at the normal voltage is fixed. This also fixes the level of noise and vibration. Also, increasing (or decreasing) magnetization does not affect the magnetostriction equivalently. In technical terms the relationship is not linear.