# The Physics of Sound: Pitch

The number of times the string naturally vibrates back and forth in a given unit of time is called the fundamental frequency of the string. This vibration is perceived by our ears/brains as the pitch of the note.

The more often the string vibrates back & forth, the higher the pitch; the less often the string vibrates back & forth, the lower the pitch. The number of times the string vibrates back and forth per unit time is called its frequency.  The usual way to measure frequency is in cycles per second, also named Hertz (Hz).  So, “100 Hz” is the same as “100 cycles per second.”

By the way, concert pitch (the standard tuning for ensemble instruments) defines middle A as 440 Hz. In other words, the A above middle C is tuned such that it vibrates back and forth 440 times per second.

The pitch (frequency that the string vibrates back & forth) depends on three things:

• the length of the string.
• the weight of the string.
• the amount of force (tension) used to stretch the string.

## Effect of String Length on Pitch

All else being equal, the shorter the string, the higher the pitch and vice versa.

This short string…

vibrates faster & sounds higher in pitch than this long string…

## Effect of String Weight on Pitch

All else being equal, the lighter the string, the higher the pitch and vice versa.

This light string…

vibrates faster & sounds higher in pitch that this heavy string…

## Effect of String Tension on Pitch

All else being equal, the tighter the string is stretched, the higher the pitch and vice versa.

This string, with more tension,…

vibrates faster & sounds higher in pitch that this string, with less tension…

Try it Yourself: You can try all the above yourself by simply stretching rubber bands of various lengths and thicknesses between your fingers and plucking away, noticing the effect that length, weight, and tension have on the pitch.