Vibrations of Sound in Closed Pipe and Open Pipe

Vibrations of the transverse waves in a closed pipe

A pipe that is open at one end and closed at other end is called as a closed pipe.

When a sound wave is passed, at the closed end it reflects back. There is a formation of node at the close the end and anti node at the open end. Different modes of vibration are possible and in each mode of the vibration different frequency is generated. These frequencies are called harmonics and they are in a systematic way. We can derive the equation for the ratios of the frequencies as shown below.

In a closed pipe, the first and second harmonics are having the ratios of frequencies 1:3. Basing on this concept we can derive the equation for the velocity of the sound using this to vibrations as shown below. We need to calculate the vibrating lengths at which a booming sound is heard. At that particular length of the air, the frequency of the tuning fork and the frequency of the air column are coinciding with each other. They are said to be in resonance and it together produces a large booming sound.

Different modes of vibration in open pipe

The pipe that is open at both the ends is called as open pipe. When it is exposed to a sound wave at both the ends there is a formation of anti node. Under different modes of vibration different frequencies are available and the ratio is derived as shown below.

Problem and solution

A pipe that is open at both the ends as a fundamental frequency n. When one by fourth of its length is immersed in water, what will be the fundamental frequency?

When the pipe is immersed in water it becomes a closed pipe. It will further have only three by fourth of the length is one by fourth is immersed in water.