People vary in their ability to detect the pitch of a sound. For example, in tuning a guitar, some are able to distinguish easily between two notes of similar pitch while others can not hear the difference.
What you measure is frequency, just counting the number of complete to-and-fro motions each second. One to-and-fro motion each second is 1 hertz (Hz). So the frequency of any vibration is the number of complete vibrations made each second.
You hear a high-frequency vibration high pitch, low frequency as low pitch. A whole spectrum of sounds from squeak to rumble.
For very high frequency kilohertz (kHz) are used: 1000 hertz = 1 kilohertz.
A good pair of headphones might have a range of 20 hertz to 20 kilohertz and so produce vibrations across our whole range of hearing.
In 1939 musicians moved to an agreement on the standard pitch. Middle C (called that because it is a note around the middle of the piano keyboard) is 256 hertz and concert A (the note the orchestra tunes to before the show begins) is 440 hertz.
The frequency doubles for every octave upwards.