# Frequency

Any process that repeats on a regular basis has an associated frequency. The frequency is the number of repetitions, or cycles, that occur during a given time interval. The inverse of the frequency is called the period of the process.

Suppose you stand on a beach and watch the waves come in. You will notice that the waves arrive in a regular pattern, perhaps one every second. The frequency of that wave motion, then, is one wave per second. The period for the wave motion is the inverse of the frequency, or one second per wave.

All forms of wave motion have some frequency associated with them. That frequency is defined as the number of wave crests (or troughs) that pass a given point per second. Light waves, for example, have a frequency of about 4 × 10 14 to 7 × 10 14 cycles per second. By comparison, the frequency of X rays is about 10 18 cycles per second and that of radio waves is about 100 to 1,000 cycles per second.

## Harmonics

What makes a note from a musical instrument sound rich and pleasing to the ear? The answer is harmonics.

If you pluck a guitar string, the string vibrates in a very complex way. If you could actually watch that vibration in slow motion, you would see the whole string vibrating at once with a frequency known as the fundamental frequency. At the same time, however, the string would be vibrating in halves (the first overtone), in thirds (the second overtone), and in even smaller segments. The collection of overtones is known as the harmonics of the sound produced by the vibrating string.

The harmonics produced by a vibrating string depend on factors such as the place the string is plucked and how strongly it is pulled. The many different sounds produced from a single guitar string depend on the variety of harmonics that a player can produce from that string.

The frequency of some processes depends on other factors. For example, the frequency with which a string vibrates depends on factors such as the type of string used and its length. One way to change the frequency of a vibrating string is to change its length. The frequency of a vibrating string determines the pitch of the sound it produces. Thus, when a violinist plays on her instrument, she places her finger on different parts of the string in order to produce sounds of different pitches, or different notes.