The frequency of the vibrations is determined by the frequency of the AC current. The higher the frequency of the current, the higher the frequency of the vibrations and the higher the pitch of the sound.
The amplitude of the vibrations is determined by the strength of the current. The stronger the current, the greater the amplitude of the vibrations and the louder the sound.
In addition to the vibrations caused by the movement of the electrons, the AC current can also cause the wire to heat up. This is because the alternating current creates resistance in the wire, which causes the wire to lose energy in the form of heat. The amount of heat generated depends on the strength of the current and the resistance of the wire.
The vibrations and heat generated by the AC current can damage the wire if they are too strong. This is why it is important to use the correct gauge of wire for the intended application.