# Open-Ended Air Columns: Natural Freq of Cylinder?

• Tam Le
In summary, the natural frequency of an open-ended air column is related to both the air column and the hollowed cylinder containing it. The frequency is for the container and the column together as a system, as the surrounding air does not have a natural frequency in this context. However, the cylinder itself has natural frequencies related to waves propagating in the solid material of the walls. As one advances in understanding, a more complete picture will be introduced, where the tube is treated as rigid and one-dimensional in the beginning, and later other shapes will be dealt with.
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.

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.

Tam Le
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.

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.

## 1. What is an open-ended air column?

An open-ended air column is a tube or cylinder that is open on one end and closed on the other end. This setup allows for the propagation of sound waves through the column.

## 2. How does an open-ended air column produce sound?

When a sound wave enters the open end of the column, it travels down the length of the column until it reaches the closed end. The sound wave then reflects off the closed end and travels back up the column, resulting in a standing wave pattern. This standing wave produces the sound that we hear.

## 3. What is the natural frequency of an open-ended air column?

The natural frequency of an open-ended air column is determined by the length of the column and the speed of sound in the medium. It can be calculated using the formula f = v/2L, where f is the natural frequency, v is the speed of sound, and L is the length of the column.

## 4. How does the length of the column affect its natural frequency?

The shorter the column, the higher the natural frequency will be. This is because a shorter column will have a shorter wavelength, resulting in more oscillations per unit time.

## 5. How can the natural frequency of an open-ended air column be changed?

The natural frequency of an open-ended air column can be changed by altering the length of the column or the speed of sound in the medium. It can also be affected by the material and shape of the column. Additionally, adding objects or obstructions to the column can change its natural frequency by altering the standing wave pattern.

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