The frequency of vibrations is measured by the number of vibrations per what?

Hertz, abbreviated "Hz". The unit of Hz is "per second".

this is measured in hertz

Same as any other frequency: in Hertz, or some multiple, like kilohertz.

Hertz.

This is called the frequency f. It measures the number of occurrences of a repeating event, in this case sound waves, per unit of time.