Department of Textile
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The Open University
of Sri Lanka
Objectives
What is a wave?
 Principle of superposition
Introduction to standing waves
Conditions that apply for a standing wave
Difference between standing and travelling wave
Standing waves in strings
Standing waves in pipes
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Objectives
After completing this session you should be
able to
 explain what a wave is
 explain the Principle of superposition
 explain how standing waves are
formed
 draw the standing waves in closed
pipes, open pipes and strings
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What is a wave ?
Wave is a method of transmitting energy by
means of large number of oscillations.
Oscillations may be mechanical or
electromagnetic.
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Waves continue…
Have you ever seen a flag on a windy
day?
The wind creates waves in the flag.
Both the waves in a flag and the ocean
are waves that you can see.
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Principle of Superposition.
When two waves are in
phase with each other they
add together.
When two waves are 1800
out of phase with each other
they will cancel.
(a.) Constructive Interference
(b.) Destructive Interference
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Standing waves
 When two waves of the same frequency moving in opposite
directions super impose, produces a standing or stationary
wave.
 To get an idea about how to form a standing wave, let’s think
that a vibration is sent along a string. This may cause to form a
wave. This wave will reflect at the other end.
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Introduction cont.…
These incidents and reflected waves will superimpose with
each other and form a standing wave (Stationary wave).
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Conditions for a standing wave
 Both waves should be in the same
frequency
 The wave length of two waves
should be the same
 Amplitude must be equal or nearly
equal to each other
 Should travel in opposite directions
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Difference between Standing
and Traveling waves
Standing waves.
Traveling waves.
 Wave will not move
 This is a combination of two
waves which move in
opposite directions
 Stores energy
 Consists of nodes and
antinodes
 The wave will move
 This consists of one wave
which moves in one
direction
 Transmits energy
 All particles are vibrating
(a.) Standing wave
(b.) Travelling wave
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Standing waves in strings
When a wave is propagating along a string its linear mass
density can be written as follows.
Here ,
m =Mass of the string
  mL
L=Length of the string
V T

 =Linear mass density
V  TL m
T= Tension of the string
Velocity depends on both tension and linear density.
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Standing waves in strings.
The fundamental vibration mode of a stretched string is seen in
the figure.
The wavelength is twice the length of the string.
V  f
Hence L   2
  2L
Also in a string
V  f 2L
V
T
mL
T=Tension of the string
L=Length of the string
T
 f 2L
m L
f 
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1
T
2L m
L
Physics in a guitar string
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Standing waves in pipes
Many of the practical applications of
stationary waves are found in musical
instruments like the flute, trombone and
clarinet.
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Standing waves in pipes
As you know already standing waves are formed when two progressive waves of
the same medium are moving.
You can see that at the closed end of a tube there must be a node, because air
molecules couldn’t vibrate when they contact the wall . Open end should have a
antinode since it’s air particles are free to vibrations.
Pipes with two open ends.
Pipes with one open end.
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Published by The Open University of Sri Lanka
Author
: Mr. L.S.A.Perera
Web Content Developer : B. Krishni Perera
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