Open-Ended Air Columns: Natural Freq of Cylinder?

[Tam Le]

When we calculate the natural frequency of an open-ended air column, is the natural frequency we calculated pertaining to the air column or the hollowed cylinder containing the air column?

I imagine that the natural frequency belongs to the hollowed cylinder, for the natural frequency of the air column should be the same as the natural frequency of the surrounding air.

 

[Simon Bridge]

The frequency is for the container and the column together as a system.
Without the container you don't have the refection you need for standing waves to form and without the air there is no medium for the waves.

Note: the surrounding air does not have a natural frequency in this context because it supports traveling waves by default.

 

[nasu]

What Simon said.
It is the frequency of the air column, with the boundary conditions imposed by the cylinder.

However, the cylinder itself has natural frequencies that are related to waves propagating in the solid material of the walls. If you hit the cylinder, you may excite both air waves and the flexural waves in the cylinder.

 

[Tam Le]

Thank you, Simon Bridge and nasu, for improving my understanding.

 

[Simon Bridge]

No worries.
When you start to learn this stuff you are only given the simplest pictures - as you advance you will be introduced to a more complete picture.
In the beginning the tube is treated as rigid and one dimensional for eg. Later you'll deal with other shapes.