Question

How are stationary waves formed in closed pipes and open pipes? Explain the various modes of vibrations and obtain relation for their frequencies.

Answer 1

Hint:The above problem can be resolved using the concepts and the fundamentals of the organ pipes. The organ pipes are the special devices used to produce the sound, utilizing the phenomena of resonance. The organ pipes are of two types: the open mouth organ pipe and the close mouth organ pipe. These organ pipes have several applications, along with the various modes of vibration of sound waves.

Complete step by step answer:
The open pipes and the closed pipes are sound producing devices that are different from each other in terms of construction, but the purpose of both the devices is the same. The closed pipes are kept open from one end and closed on the other hand, similarly the open pipes are kept open from both the ends. These pipes are also known as the organ pipes and separately called as open mouth organ pipes and closed mouth organ pipes. The stationary waves in these pipes are formed by the reflection and the superimposition of the incident sound waves.
Let L be the length of the organ pipe and v be the velocity of sound.
The frequency of sound wave at first mode of vibration is,
\[\begin{array}{l}
v = 2L{f_1}\\
{f_1} = \dfrac{v}{{2L}}
\end{array}\]
Here, f is the frequency of the sound wave in first mode.
The frequency of sound wave at second mode of vibration is
\[\begin{array}{l}
v = L{f_2}\\
{f_2} = \dfrac{v}{L}
\end{array}\]
Similarly, for the third mode of vibration, the frequency of sound wave is,
\[\begin{array}{l}
v = \dfrac{2}{3}L{f_3}\\
{f_3} = \dfrac{{3v}}{{2L}}
\end{array}\]

Note:Try to understand the concept and fundamentals of working of open and closed mouth organ pipes. The sound waves incident from one of these pipes' ends gets reflected and undergoes resonance to produce the resultant wave at the exit.