Name: Wave Motion:Transverse and Longitudinal Waves
Uploaded: 2019-07-19
Duration: 3 min 47 s
Description: Waves transfer energy from one place to another. There are two types of wave motions depending upon the movement of the particles about their axes. Watch the...

Question

Explain the modes of vibration of an air column in an open pipe.

Accepted Answer

An open pipe has anti nodes at both ends. The wavelength of the wave is given by $λ = \frac{2 L}{n}$ .

Where $L$ = length of pipe $n$ = integer for mode no.

First normal mode of vibration:

In this mode there will be two anti nodes and one node corresponding to $n = 1$ .

$λ_{1} = \frac{2 L}{1} or L = \frac{λ_{1}}{2}$ and frequency $ν = \frac{v}{λ_{1}} = \frac{v}{2 L}$ .

This is the lowest (fundamental frequency) or first harmonic

Second normal mode of vibration:

In this case there will be three anti nodes and two nodes and the wavelength is corresponding to $n$ $= 2$ , the wave length is given by:

$λ_{2} = \frac{2 L}{2} = L frequency = ν_{2} = \frac{2 v}{2 L} = 2 ν_{1}$ .

This is double of the fundamental and called second harmonic or first overtone.

Third normal mode of vibration:

In this case there will be $4$ anti nodes and $3$ nodes. The wavelength is given by,

$λ_{3} = \frac{2 L}{3} or L = \frac{3 λ_{3}}{2} and frequency = ν_{3} = \frac{v}{λ_{3}} = \frac{3 v}{2 L} or 3 ν_{1}$ .

This is third harmonic or second overtone.

Explain the modes of vibration of an air column in an open pipe.

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