Musical Instruments

Many woodwind instruments consist of an air column enclosed inside of a hollow metal or wood tube. These tubes may be more than a meter in length and the metal ones often curve one or more times in order to conserve space.

If the end of the tube is uncovered such that the air at the end of the tube can freely vibrate when the sound wave reaches it, then the end is referred to as an open end.
If both ends of the tube are uncovered or open, the musical instrument is said to contain an open-end air column. If one end of the instrument has an open end and the other end is covered or closed the musical instrument is said to contain a closed-end air column.

These air columns make sounds due to the concept of resonance.

Open Pipes
A variety of instruments operate on the basis of open-end air columns such as
-flutes      -trombones       -saxophones       - oboes

The first resonant frequency for an open pipe occurs at 1/2 of a wavelength for a wave.
The peaks of the wave will be placed at the ends of the tube, this will create the loudest sound.

Second and Third Harmonics

The next resonant frequency will occur at one wavelength. At this point the peaks of the wave still occur at the open ends of the tube creating the loudest sound
The third frequency at which resonance occurs is at 1 1/2 wavelengths

Closed pipes

The first resonant frequency for an open pipe occurs at 1/4 of a wavelength for a wave.
The peaks of the wave will be placed at the ends of the tube, this will create the loudest sound.

Third and Fifth Harmonics

The next resonant frequency will occur at 3/4 wavelength. At this point the peaks of the wave still occur at the open ends of the tube creating the loudest sound
The third frequency at which resonance occurs is at 1 1/4 wavelengths