Name: Closed Organ Pipe
Uploaded: 2019-07-19
Duration: 3 min 44 s
Description: An organ pipe is closed at one end and open at the other end. Bottle, whistle, etc., are examples of a closed organ pipe. Let's learn about its different mod...

Question

Explain graphically the formation of stationary waves as a result of reflection of a progressive wave from an open end.

Accepted Answer

A pipe which is open at both ends is called open-ended pipe.

Consider a pipe of length $l$ , open at both ends lying along $x$ -axis, with the ends at $x = 0$ and $x = l$ when air is flown at $x = l$ , a longitudinal wave travels along the pipe towards $x = 0$ and is reflected wave.

A stationary wave is formed along with the length of pipe with antinodes at both open ends.

The three modes of vibration ar shown in fig. $1$ .

First mode of vibration is also known as fundamental mode.

In fig. $1 a$ , two antinodes are formed at two ends and a node is formed in between $l = \frac{λ_{1}}{2}$

$∵$ distance between a node and antinode $= \frac{λ}{4}$

Or, $λ_{1} = 2 l$

Frequency of this node of viberation $n_{1} = \frac{ϑ}{λ_{1}}$

This is the lowest frequency of viberation and is called the fundamental frequency. It is also called first harmonic.

$II$ mode of vibration is shown in fig. $1 (b)$

In this mode, two additional nodes are formed.

$\frac{4 λ_{2}}{4} = l$ or $l = λ_{2}$

$n_{2} = \frac{ϑ}{λ_{2}} = \frac{ϑ}{l} = \frac{2 ϑ}{2 l} = 2 h_{1}$

This node produced is called first overtone or second harmonic of the open pipe.

$III$ mode of vibration is shown in fig. $1 (c)$ .

Let $λ_{3}$ , the wavelength of the standing waves in the pipe corresponding

$l = \frac{3 λ_{3}}{2}$ or $λ_{3} = \frac{2 l}{3}$

$ϑ = n_{3} λ_{3} = n_{3} = \frac{ϑ}{\frac{2 l}{3}} = \frac{3 ϑ}{2 l} = 3 h_{1}$

Sound note produced in this pipe is called second overtone or third harmonic. In an open pipe, all odd and even harmonic are formed.

Explain graphically the formation of stationary waves as a result of reflection of a progressive wave from an open end.

Important Questions on Superposition of Waves-2 : Stationary (Standing) Waves : Vibration of Air Columns

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