How does a standing wave form in a tube?

When air is blown into a tube, the unsteady flow of air produces a sound wave. The sound wave is reflected at the other end of the tube. The incoming sound waves interfere with the reflected sound waves, producing standing waves. 

This is how wind instruments such as clarinets and flutes work. 

Tubes with closed ends

  • When air is blown into a tube with one closed end, the air at the closed end cannot vibrate, forming a node, a point of no displacement.
  • The air at the open end can vibrate freely, creating an antinode, a point of maximum displacement.
  • The simplest standing wave that can fit inside this tube has a node at the closed end and an antinode at the open end (ref to a). The wave will have a wavelength of 4\( l \), where \( l \) is the length of the tube. 
  • The wavelengths that can fit the tube follow the equation \( \frac{4}{x} l \), where x is 1, 3, 5, 7... . For example:
    4\( l \), \( \frac{4}{3} l \), \( \frac{4}{5} l \).
  • If a speaker is placed at the open end of the tube, a loud sound will be heard if the sound wave played by the speaker has a wavelength that fits the tube.
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Tubes with both ends open

  • When air is blown into a tube that is open at both ends, antinodes are formed at both ends.
  • In the simplest standing wave, there is a node in the middle and antinodes at both open ends.
  • The simplest standing wave has half the wavelength of the sound wave fitting within the tube. It has a wavelength of 2\( l \).
  • The wavelengths that can fit the tube follow the equation \( \frac{2}{x} l \), where x=1, 2, 3, 4...
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