1 department of textile the open university of sri lanka
TRANSCRIPT
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 2
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
Objectives
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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 1800 out of phase with each other they will
cancel.
When two waves are in phase with each other they add together.
(a.) Constructive Interference (b.) Destructive Interference
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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.Wave will not moveThis is a combination of two
waves which move in opposite directions
Stores energyConsists of nodes and
antinodes
Traveling waves.The wave will moveThis consists of one wave
which moves in one direction
Transmits energyAll particles are vibrating
(a.) Standing wave (b.) Travelling wave 10
Standing waves in stringsWhen a wave is propagating along a string its linear mass density can be written as follows.
Here ,m =Mass of the string
L=Length of the string
=Linear mass density
T= Tension of the stringVelocity depends on both tension and linear density.
Lm
TV
mTLV
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Standing waves in strings.
LfLm
T2
The fundamental vibration mode of a stretched string is seen in the figure.The wavelength is twice the length of the string.Hence
Also in a string
T=Tension of the stringL=Length of the string
Lm
TV
LfVL
fVL
222
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LmT
Lf
2
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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
Pipes with one open end. Pipes with two open ends.
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.
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