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.
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