Organ Pipes: Wave Reflection Explained

[sadhu]

I want to know that what exactly causes the wave to get reflected in an open tube when there is nothing sort of a reflecting medium.

 

[pam]

The sound wave is really a pressure wave, with standing waves of the form
p=cos kx or sin kx. The boundary condition at the x=0 end of an open pipe is that p=0,
giving sin kx. At the x=0 end of a closed pipe, the BC is dp/dx=0 (or p is a maximum),
gilving cos kx.

 

[sir-pinski]

The phenomenon of wave reflection in open tubes, such as organ pipes, can be explained by the principle of boundary conditions. This principle states that when a wave encounters a change in the medium it is traveling through, such as a change in density or rigidity, it will experience a change in its behavior. In the case of an open tube, the boundary condition is the sudden change in air pressure at the end of the tube.

When a wave travels through the open tube, it causes the air particles inside the tube to vibrate back and forth. As the wave reaches the open end of the tube, it encounters a sudden drop in air pressure. This change in pressure acts as a boundary condition, causing the wave to be reflected back towards the source.

This reflection occurs because the sudden drop in air pressure creates a change in the density and rigidity of the medium. The air particles at the open end of the tube are now free to vibrate more easily, which allows the wave to be reflected back towards the source with minimal loss of energy.

In addition, the length of the tube also plays a role in the reflection of the wave. If the length of the tube is an exact multiple of the wavelength of the wave, the reflected wave will interfere constructively with the original wave, resulting in a stronger vibration and a louder sound. This is why organ pipes are often designed to be a specific length in order to produce the desired pitch and volume.

In summary, the reflection of waves in open tubes, like organ pipes, is a result of the change in air pressure at the open end of the tube acting as a boundary condition. This phenomenon can be further enhanced by the length of the tube, resulting in the production of music and sound.