1. Open and Closed Pipes
Sound

2. Open Tube Instruments
Many woodwind instruments consist of an air column enclosed inside of a hollow metal tube. These tubes metal may be more than a meter in length and 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. A variety of instruments operate on the basis of open-end air columns such as
flute
trombone
saxophone
oboe.

3. Open Pipes
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.

4. The Third and Fourth 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 1/4 wavelengths

5. Relationships for Open Pipes

6. Practice Problem
The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm

7. 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.

8. The 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

9. Relationships for Closed Pipes

10. Practice Problem
The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of a closed-end air column which has a length of 67.5 cm.