1 Department of TextileThe 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 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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Standing waves

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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

1

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

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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Author : Mr. L.S.A.Perera

Web Content Developer : B. Krishni Perera

Published by The Open University of Sri Lanka