When a wave reflects off of something, it can interefere with its own reflection. The interference is alternately constructive or destructive as the two waves move past each other. This creates a standing wave.

Certain points along the standing wave never move. These points are called nodes. The points that move the most are called antinodes.

Along any length, only waves with certain frequencies can create standing waves. This is because the distance from one node to the next must always be some fraction of the total length (one half, one third, etc.).

The different standing waves corresponding to different fractions are called harmonics. The first three harmonics are shown on the right.

Sounds are waves moving though the air (see October 20). Notes are just standing waves of a specific frequency. On a piano these notes are organized into an assending scale.

The musical scale used today was first discovered by the Greek mathematician Pythagoras in the 6th century BC. While playing the lyre, he noticed that he could create the different harmonics by placing his finger at fractional points on the string. Where he placed his finger corresponded to the nodes of each harmonic.

So if notes are just waves of different frequencies, why do all the different instruments sound different when they play the same notes?

Actually an instrument always plays several frequencies at once. The most dominant frequency is that of the note, but many others are played as well. These are determined by the shape of the instrument. This spectrum of frequencies is called the instruments timbre.

Many instruments create notes by vibrating strings, which in turn cause the air to vibrate with the frequency of the note. Vioins, guitar, and piano all use strings to make music.

When a string is plucked, the wave reflects off of the bridge and a standing wave is created.

When air in a cylindrical instrument, like trumpets or flutes, vibrates it creates standing waves that can resonate at different frequencies. This vibration is usually caused by the players lips or a reed.

Waves created in a cylinder open at both ends, like a flute.

Waves created in cylinders with one closed end, like those of a pipe organ.