What causes physical vibrations in transformers at twice the frequency of the ac power involved.

The vibration is caused by the expansion and contraction of transformer coils at twice the frequency of the alternating current.

Explanation.
The phenomenon is called magnetostriction.
The iron core in a transformer experiences magnetic fields that cause it to expand and contract due to the AC (alternating current).
The resulting vibration has a fundamental frequency that is twice that of the transformer.
The vibration produces an audible humming sound.