Final answer:
Physical vibrations in transformers occur at twice the frequency of the AC power due to magnetostriction, where the iron core material alternately expands and contracts in response to the time-varying magnetic field produced by the AC. This effect causes the core to vibrate at double the AC frequency.
Step-by-step explanation:
The physical vibrations in transformers at twice the frequency of the AC power involved are due to the phenomenon called magnetostriction, which is closely associated with the core material of the transformer. As the AC current flows through the primary coil of the transformer, it creates a time-varying magnetic field. This alternating magnetic field causes the magnetic domains within the iron core to realign with each phase of the AC cycle, which results in the physical expansion and contraction of the core material. Because the AC current alternates, this process happens twice per cycle, leading to vibrations at double the frequency of the AC power. This recurring process of magnetostriction is an inherent physical response of the ferromagnetic material in the core to the magnetic field produced by the AC.