2.3 Stationary Waves

7/24/2019 2.3 Stationary Waves

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Stationary Waves

Stationary waves are produced bysuperposition of two progressive waves ofequal amplitude and frequency, travellingwith the same speed in opposite directions.

http://www2.biglobe.ne.jp/norimari/science/!ava"d/e#wave$.html


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%roduction of Stationary Waves

& stationary wave would be set up bycausing the string to oscillate rapidly at aparticular frequency.

'f the signal frequency is increasedfurther, overtone patterns appear.


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%roperties of a stationary wave()*

Stationary waves have nodes where there is nodisplacement at any time.

'n between the nodes are positions calledantinodes, where the displacement has

ma+imum amplitude.

A vibrating loop

N A N A N

VibratorVibrator


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%roperties of a stationary wave(2*

he waveform in a stationary wave does notmove through medium- energy is not carriedaway from the source.

he amplitude of a stationary wave varies fromero at a node to ma+imum at an antinode,and depends on position along the wave.


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Vibrations of particles in astationary wave

&t t 0, all particles are at restbecause the particles reach theirma+imum displacements.

&t t 1,%articles a, e, and iare at rest

because they are the nodes.%articles b, cand dare movingdownward.

hey vibrate in phase but withdierent amplitude.

%articles f, gand hare movingupward.hey vibrate in phase but withdierent amplitude.

t= 0

t= T

t= T

t= T

t= T

a

bc

d

e

f g

hii

ab c d

ef g h

ii


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%roperties of a stationary wave(2*

&ll particles between two adjacent nodes(within one vibrating loop* are in phase.

Video

). Stationary waves (string*

2. Stationary waves (sound*


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3odes of vibration of strings

Picture of Standing Wave Name Structure

1st armonic

or

!undamental

1 Antinode

" Nodes

"nd armonic

or

1st #vertone

" Antinodes$ Nodes

$rd armonic

or

"nd #vertone

$Antinodes

% Nodes

%t& armonicor

$rd #vertone

%Antinodes

' Nodes

't& armonic

or

%t& #vertone

'Antinodes

( Nodes

) = *1

f1= v+")

) = *"f"= v+)

) = 1*$

f3= $v+")

) = "*%f%= "v+)

) = "*'

f5= 'v+")

http://id.mind.net/ona/mstm/physics/waves/standingWaves/standingWaves)/StandingWave

4


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using sound waves andmicrowaves

3oving the detector along the line between the wavesource and the re5ector enables alternating points ofhighand lowsignal intensity to be found. hese arethe antinodesand nodesof the stationary waves.

he distance between successive nodes or antinodescan be measured, and corresponds to half thewavelength 6.

'f the frequency fof the source is 7nown, the speed ofthe two progressive waves which produce the

stationary wave can be obtained.8e5ector

9etectorWave source


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8esonant requencies of a;ibrating String

rom the e+periment, we


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fundamental frequency of avibrating string

he frequency of vibration depends on the mass per unit length of the string, the tension in the string and, the length of the string.

he fundamental frequency is given by

T

Lfo

"

1= where T tension

mass per unit length L length of string


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;ibrations in &ir >olumn

When a loudspea7er producing sound is placednear the end of a hollow tube, the tuberesonates with sound at certain frequencies.

Stationary waves are set up inside the tubebecause of the superposition of the incidentwave and the re5ected wave travelling inopposite directions.

http://www.walter#fendt.de/ph))e/stlwaves.htm
http://www.walter-fendt.de/ph11e/stlwaves.htmhttp://www.walter-fendt.de/ph11e/stlwaves.htm


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fundamental frequency of avibrating air column

he natural frequency of a windinstrument is dependent uponhe type of the air column,he length of the air column of the

instrument.

?pen tube >losed tube


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Name

tube

Picture of Standing Wave Structure1st armonic

or

!undamental

" Antinodes

1 Node

"nd armonic

or1st #vertone

$ Antinodes

" Nodes

$rd armonic

or

"nd #vertone

% Antinodes

$ Nodes

%t& armonicor

$rd #vertone

' Antinodes

% Nodes

't& armonic

or

%t& #vertone

( Antinodes

' Nodes

) = *1

f1= v/")

) = *"

f2= v+)

) = 1*$

f$= $v+")

) = "*%

f%="v+)

) = "*'

f'= 'v+")


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o es o v ra on or a c osetube

Picture of Standing Wave Name Structure

1st armonic

or

!undamental

1 Antinode

1 Node

$rd armonic

or1st #vertone

" Antinodes

" Nodes

't& armonic

or

"nd #vertone

$ Antinodes

$ Nodes

,t& armonicor

$rd #vertone

% Antinodes% Nodes

-t& armonic

or

%t& #vertone

' Antinodes

' Nodes

) = *1

f1 = v+%)

) = .*$

f3 =$v/%)

) = 1*'f5 ='v+%)

) = 1.*,f7= ,v+%)

) = "*-f

-=-v+%)


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he quality of sound (imbre*

he quality of sound is determined by thefollowing factors: he particular harmonics present in addition to

the fundamental vibration, he relative amplitude of each harmonic, he transient sounds produced when the

vibration is started.

)stovertone undamental2ndovertone

=rdovertone

resultant

http://surendranath.tripod.com/@armonics/@armonics.html


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>hladniAs %late

>hladniAs plate is an e+ample ofresonance in a plate.

here are a number of frequencies at

which the plate resonate. "ach gives adierent pattern.

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2.3 Stationary Waves