superposition notes 2013_student version

7/24/2019 Superposition Notes 2013_Student Version

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RAFFLES INSTITUTIONYEAR 5-6 PHYSICS DEPARTMENT

Chapter11 Superposition

Sy!"us Content Stationary waves Diffraction Interference Two-source interference patterns Diffraction grating

Le!rnin# Out$o%es(a) explain and use the principle of superposition in simple applications.

(b) show an understanding of experiments which demonstrate stationary

waves using microwaves stretched strings and air columns.

(c) explain the formation of a stationary wave using a graphical method andidentify nodes and antinodes.

(d) explain the meaning of the term diffraction.

(e) show an understanding of experiments which demonstrate diffractionincluding the diffraction of water waves in a ripple tan! with both a wide gapand a narrow gap.

(f) show an understanding of the terms interference and coherence.

(g) show an understanding of experiments which demonstrate two-source

interference using water light and microwaves.(h) show an understanding of the conditions re"uired if two-source interference

fringes are to be observed.

(i) recall and solve problems using the e"uation # $ ax%D for double-slitinterference using light.

(&) recall and solve problems by using the formula dsin' $ n# and describe theuse of a diffraction grating to determine the wavelength of light. (Thestructure and use of the spectrometer is not re"uired.)

&


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&&'& Intro(u$tion

Prin$ipe o)Superposition

wave is a continuous and periodic disturbance that travels through space.or mechanical waves li!e sound and water waves the disturbance refers to

the displacement of the particles of the media from their e"uilibrium position.or electromagnetic waves the disturbance refers to the varying electric andmagnetic field.

*hat happens when two waves of the same !ind (e.g. sound waves from twodifferent sources) meet at a point in space+ The answer to this "uestion isprovided by the Principle of Superposition which states that

when two waves of the same kind meet at a point in space, the resultantdisplacement at that point is given by the vector sum of thedisplacements due to each of the waves at that point.

This is illustrated below,

*

+

=

+

=

+

=

Fi#' &' *hen two waves meet the resultant disturbance is vector sum of thedisturbance of disturbance due to each of the waves.


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&&'* St!tion!ry +!,es

+!t is ! St!tion!ry+!,e

Imagine two similar waves of exactly the same amplitude same frequencyandsame wavelengthmoving toward each other as shown in ig. .

They eventually meet each other and start to overlap. *e then have a situationin which the superposition of the two waves is observed along the line of

propagation. The principle of superposition applies at each point and at aparticular instant of time we may get a resultant waveform such as ig. ,

.

Fi#' *

Fi#' .' Superposition of two waves displaced by /apart.

NA

*ave moving tothe right

*ave moving tothe left

0esultantwave

t t$ 0,


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Properties o) !St!tion!ry +!,e

Fi#' /!' #r!pi$! represent!tionof a stationarywave (where the maximum displacement is drawn

on a displacement-distance graph)

Fi#' /"' The waveform (displacement-positiongraph) of a stationary wave at e"ual time interval

of 12T .

The resultant waveform has the following features,

1. The wave profile does not propagate. s such the resultant wave is!nown as a st!tion!ry 0!,e or st!n(in# 0!,e.

. 3very particle of the wave merely oscillates about their respectivee"uilibrium positions with the s!%e )re1uen$y but (i))erent!%pitu(es. The fre"uency is the same as that of the two componentwaves.

. n!ntino(eis a point in a standing wave where the amplitude is themaximum. 4articles at the antinodes vibrate with the greatest

amplitude. These are labeled 56 on ig. . The amplitude of oscillationat the antinodes is double that of the component waves.

7. no(eis a point in a standing wave where the amplitude is 8ero. Theyare labeled 596 on ig. .

:. *ithin two consecutive nodes every particle oscillates in p!se i.e.they reach their respective maxima minima and e"uilibrium positions atthe same instant. 9ote that these particles do not have the sameamplitude.

2. Distance between two ad&acent nodes (or antinodes) is ;.

out of phase with eachother.

=. In physics and engineering the en,eope )un$tionof a rapidly varyingsignal is a smooth curve outlining its extremes in amplitude.

?. Draw in displacement axis and position axis so that studentsunderstand meaning of such graphs.

/


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Co%p!rin#St!tion!ry +!,es!n( Pro#ressi,e+!,es

*e may compare a stationary wave with a progressive wave as follows,

E2!%pe & (@?>%41%1)

4rogressive waves of fre"uency >> A8 are superimposed toproduce a system of stationary waves in which ad&acent nodesare 1.: m apart. *hat is the speed of the progressive waves+

Soutions

5

Property Pro#ressi,e +!,e St!tion!ry +!,e

*aveform The disturbancepropagates across space.

The disturbance does notpropagate across space.

3nergy Transports energy Does not transport energy

mplitude 3very point oscillates withthe same amplitude.

mplitude varies from > at thenodes to at the antinodes.

4hase ll particles within onewavelength have differentphases.

4hase of all particles between ad&acent nodes is the same.4articles in ad&acent segments

have a phase difference of rad.


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&&'. St!tion!ry +!,es in Strin#s !n( Pipes

St!tion!ry +!,es inStret$e( Strin#s

Stationary waves of various fre"uencies can be set up in a stretched wire bypluc!ing the wire at different points along the wire.

The fre"uency of sound waves produced is e"ual to the fre"uency of thestationary transverse wave on the string. This is how music is produced instring instruments.

*hen a stationary wave is set-up on a string or in a tube several modes ofvibration of the stationary wave are possible. The stationary wave with thelowest fre"uency is said to be vibrating with the )un(!%ent! )re1uen$y.Aigher modes of vibration are !nown as the o,ertones.

The following steps can be used to derive the fre"uency of the different modes

of vibration of a stationary wave in general.

Step 1 Select the %o(e o) ,i"r!tionof the stationary wave

Step Draw the #r!pi$! represent!tionof the stationary wave

Step Derive 0!,een#tof stationary wave in term of length Lof the string (or tube)

Step 7 Bsing f v = where vis the speed of the progressive waves obtain the)re1uen$yof the stationary wave in terms of vand L.

St!tion!ry +!,es on ! Strin#

Codes ofibration

Eraphical0epresentation

*avelength re"uencylso !nown

asF

undamentalmode%fre"uency

1

1

1

L

L

=

=

1

vf

L= 1stharmonic

1stovertone

-

-

L

L

=

=

--

vf

L

=

* ndharmonic

6


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ndovertone

.

.

L

L

=

=

.-

vf

L

=

. rdharmonic

(nG 1)th

overtone

n

n

L n

L

n

=

=

-

n

vf

L

=

n nthharmonic

Note3

t the fixed ends there must be nodes (since the string cannot vibrate atthese points).

E2!%pe * (9?:%4%(b))In order to investigate stationary waves on a stretched string astudent set up the apparatus shown in ig. : below.

Fi#' 5

(i) 3xplain why it is necessary to ad&ust either the length ofthe string or the fre"uency of the vibrator in order to obtainobservable stationary waves on the string.

(ii) *hat is meant by a node+ 3xplain why a node mustexist at the pulley.

Soutions (i) Since the tension of the string is fixed the velocity of thewave on the string is fixed. Stationary waves will only be

formed (i.e. resonance occurs) when the length of thestring is e"ual to certain fixed multiples of half-wavelengthof the wave. Aence it is necessary to ad&ust the length ofthe string to fit multiples of half-wavelength or ad&ust thefre"uency (and thus wavelength) to fit the length of thestring.

(ii) node is a point on the stationary wave where the particleis always at rest. node must exist at the pulley as thepulley and hence the string is fixed in position.

9ote, The end of the string which is attached to the oscillator

can also be considered as a node as the amplitude ofvibrations is considered small compared to the antinode.

4

mechanical oscillator

pulley

weights


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E2!%pe . (@=%4%1)

taut wire is clamped at two points 1.> m apart. It is pluc!ednear one end. *hich are the three longest wavelengths presenton the vibrating wire+

Soutions

St!tion!ry +!,es inAir Cou%ns orPipes

It is also possible to set up stationary sound waves in air columns or pipes. pipe is termed closedif one end of the pipe is closed while the other is openand termed opened if bothends of the pipe are open.

`

Cose( Pipes *hen a sound wave is sent into a closed pipe the wave propagates to the endof the pipe and is reflected. The reflected wave superposes with the incidentwave and a stationary wave is formed. displacement nodeis formed at theclosed end of the pipe while a displacement antinode is formed at the openend,

St!tion!ry +!,es in Cose( Tu"es

Codes ofibration Eraphical0epresentation *avelength re"uency lso !nownasF

7

Fi#' 6! closed pipe " open pipe

Fi#' 4

L

Eraphical representation of astationary wave in closed pipe

rrows indicate the amplitudeof vibration of air molecules ofthe stationary wave


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undamentalfre"uency

1

1

17

7

L

L

=

=

17

vf

L= 1stharmonic

1stovertone

.

.

7

7

L

L

=

=

.7

vf

L

=

. rdharmonic

ndovertone

:

:

:7

7

:

L

L

=

=

:7

vf

L

=

5 :thharmonic

(nG 1)th

overtone( )

( )

- 1

- 1

- 17

7

- 1

n

n

L n

L

n

=

=

( )- 17

n

vf

L

=

n* - &(nG 1)th

harmonic

Open Pipes *hen a sound wave is sent propagating in a open pipe the stationary waves formedwill have displacement antinodes at both ends as shown in ig. =.

St!tion!ry +!,es in Open Tu"es

Codes ofibration

Eraphical0epresentation

*avelength re"uencylso !nown

asF

undamentalfre"uency

1

1

1

L

L

=

=

1

vf

L= 1stharmonic

1stovertone

-

-

L

L

=

=

--

vf

L

=

* ndharmonic

ndovertone

.

.

L

L

=

=

.-

vf

L

=

. rdharmonic

8

Fi#' 7


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(nG 1)th

overtone

n

n

L n

L

n

=

=

-

n

vf

L

=

n nthharmonic

En( Corre$tion The antinode at the open ends of the pipes are actually located slightly outsidethe pipe as shown in ig. ?. This results in a small end correction to beincluded in the calculation of the wavelength.

E2!%pe / (9. m long is open at one end and closed at the

other. The speed of sound in air is > m s1. ssuming that end

corrections are negligible calculate

(a) the fre"uencies of the fundamental and the first overtone

(b) the length of a pipe which is open at both ends and whichhas a fundamental fre"uency e"ual to the difference ofthose calculated in (a).

Soutions

&9

c

Fi#' 8


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E2!%pe 5 source of sound of fre"uency :> A8 is used with a resonancetube closed at one end to measure the speed of sound in air.Strong resonance is first obtained at tube lengths of >.> m andthen >.?2 m. ind

(a) the speed of the sound and

(b) the end correction of the tube.

Soutions

&&'/ Di))r!$tion

+!t is Di))r!$tion: Diffraction refers to the bending or spreading of waves when they travel

through an aperture or when they pass round an obstacle . It is a phenomenonof waves.

Due to the effects of diffraction waves bend from a straight path and enter aregion that would otherwise be shadowed.

or example when you are in a room you can hear someone in the corridorthrough the open door even if you cannot see them. *hy+

narrow aperture wide aperture

Fi#' &9

Diffraction depends on the relative value of the wavelength and the si8e ofaperture.

&&


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Eenerally (i))r!$tion is pronoun$e( 0en te 0!,een#t o) te 0!,e iste s!%e or(er o) %!#nitu(e !s te 0i(t o) te !perture or o"st!$e.

This is the reason why under normal circumstances we never observe anydiffraction of light because the holes and apertures that we come acrosseveryday are much bigger than the wavelengths of light.

&&'5 Inter)eren$e

Coeren$e Sources are said to be $oerentif they have a $onst!nt p!se (i))eren$e.

This implies that the sources must have the same fre"uency or wavelength.elocities of the waves are assumed to be identical.

3xamples of coherent sources These are not coherent sources

diffracted laser beams through twoslits incident by a single laser beam

two lasers

two spea!ers fed by same source two filament lamps

Inter)eren$e Interference is the superpositionof two or more $oerent 0!,es to give a

resultant wave whose resultant amplitude is given by the prin$ipe o)superposition.

*hen two waves interfere they can give rise to $onstru$ti,e inter)eren$eand (estru$ti,e inter)eren$e.

Constru$ti,eInter)eren$e

Honstructive interference ta!es placewhen two waves arrived at the samepoint in p!se (i.e. their phasedifference is 8ero). %!2i%u% is

obtained.

&*

Fi#' &&' 0ipple tan! images of water waves emerging from an opening. s thewavelength is increased from (a) to (c) the effect of diffraction becomes moreand more pronounced.

$! "

Fi#' &*


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A common misconception:onstructive !nterference occurs onlywhen wave crests meet wave crests orwave troughs meet wave troughs.

!t should be: onstructive interferenceoccurs whenever two waves meet inphase.

Destru$ti,eInter)eren$e

Destructive interference ta!es placewhen two waves arrived at the same

point with a p!se (i))eren$e o) r!(.

%ini%u%is obtained.

A common misconception:

"estructive interference occurs onlywhen wave crests meet wave troughs.

!t should be: "estructive interference

occurs whenever two waves meet rad

out of phase

&&'6 T0o-sour$e Inter)eren$e

Con(itions )oro"ser,!"einter)eren$e

1. The waves (or sources) must be $oerent.. The waves must have approximately the s!%e !%pitu(e.. The waves must be unpo!rise( or po!rise( in the same plane (for

transverse waves).7. The waves must inter)ere to give regions of %!2i%! (constructive

interference) and %ini%!(destructive interference).

Te Rippe T!n;E2peri%ent

Two ball-ended dippers attached to a mechanical oscillator (and hence arecoherent sources) send out two sets of circular ripples at S 1and S. Thesewaves interfere when they overlap as shown in ig. 17.

y the principle of superposition $onstru$ti,e inter)eren$eta!es place alongthe !nti-no(! ines when the two waves are in p!se.

In between anti-nodal lines are the no(! inesalong which the waves arrive

e2!$ty r!( out o) p!se. Destru$ti,e inter)eren$eoccurs.

&.

Fi#' &/

Fi#' &.


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P!t Di))eren$e P!t (i))eren$e is te (i))eren$e in te (ist!n$es t!t e!$ 0!,e tr!,es)ro% its sour$e to te point 0ere te t0o 0!,es %eet'

*e can also loo! at path difference to analyse whether two waves meet inphase or out of phase and hence whether constructive or destructiveinterference results.

Honsider wave sources S1and Sand points 4 J K where the two waves meet,

&/

Fi#' &5! Fi#' &5"


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t point 4 the two waves meet in phase (i.e. constructive interference)

4ath difference #$ S4 G S14 $ >

t point K the two waves also meet in phase (i.e. constructive interference)

4ath difference #$ SK G S1K $

Aence in general for $onstru$ti,e inter)eren$eto occur

4ath difference x< n (where n is an integer)

*hen the two sources are in phase the nthorder maximum (or bright fringe)

occurs at positions where the path difference is n.

9ow consider wave sources S1and Sand points 0 J T where the two wavesmeet,

t point 0 the two waves meet out of phase (i.e. destructive interference)

4ath difference #$ S4 G S14 $ ;

t point T the two waves also meet out of phase (i.e. destructiveinterference)

4ath difference #$ SK G S1K $ 1;

Aence in general for (estru$ti,e inter)eren$eto occur

4ath difference x< n + = (where n is an integer)

9ote that the above scenarios happened when the two waves sources aregenerating the waves in phase.

>uestion3*hat happens at 4 K 0 and T if the two sources are rad out-of-

phase+

Ans0er3

*aves arrive at 4 J K rad out-of-phase destructive interference at 4 J K*aves arrive at 0 J T in phase constructive interference at 0 J T

&5

Fi#' &6! Fi#' &6"


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P!t Di))eren$eSu%%!ry

In summary the following table can be used to determine whether constructiveor destructive interference occurs at a certain point where the two waves meet.

$. Determine whether the two sources are in phase or out of phase.

%. Determine the path difference in terms of .

&. Bse the table to chec! whether constructive or destructive interferenceoccurs.

sources in phase sources rad out of phase

Honstructive Interference

(maxima) x< n x< n + =)

Destructive Interference

(minima) x< n + =) x< n

E2!%pe 6 (9==%41%=)Two wave generators S1 and S produce water waves of

wavelength m. They are placed 7 m apart in a water tan! and adetector 4 is placed on the water surface m from S 1as shown inthe diagram.

*hen operated alone eachgenerator produces a wave at4 which has an amplitude .*hen the generators areoperating together and inphase what is the resultantamplitude at 4+

Soution

&&'4 Youn#?s Dou"e Sit E2peri%ent

Set up setup for viewing the two source interference pattern with light is the Loung6sdouble slit experiment. The experimental setup is shown below.

t points of constructive interference (maxima) bright fringes are observed.t points of destructive interference (minima) dar! fringes are observed.

&6

m

7mS

1S

4

Fi#' &4

diffracted light acts as acoherent light source for the

double slits


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E1u!tions Met us now try to derive an e"uation for the fringe separation i.e. the spacingbetween two successive bright (or dar!) fringes.

9otations, #n$distance of nthbright fringe from central fringe

a$ slit separation "$ distance between slits and screen

Honsider at 4 where nthorder bright fringe (maximum) is obtained.

If a '' " the rays from S1and Sare almost parallel and ?>o.

path difference - 1 -S 4 S 4 S sin n# a = = (ig. 1=a)

Since the waves passing through slits 1S and -S are in phase for constructive

interference

sinn

a n = where n$ > 1 F

sin nn

a

=

rom NI4 (ig. 1=b)

tan nn#

" =

&4

Fi#' &7! Fi#' &7"

n


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or small n (O 1>o)

sin tann n

n#n

a "

Aence constructive interference ta!es place at these positions

n

n "#

a

= where n$ > 1 F

Spacing between successive bright fringes

1

( 1)n n

n " n " "# # #

a a a

= = =

Frin#e sep!r!tion "#

a

=

IntensityDistri"ution o)Inter)eren$eFrin#es

T!;e note The formula

"#

a

= is applicable only if

a '' "(assumed that rays are parallel)

O 1>o(assumed that sin tan )

or interference of light the typical values for slit width P >. mmw slitseparation P >.: mma slit-screen distance P 1 m" wavelength of light

P :>> mm .

The purpose of the single slit is to ensure waves exiting from the double slitsare coherent. The single slit acts li!e a point source of light.

If two coherent sources are used and they have a phase difference of radthe conditions for constructive and destructive interference would beinterchanged.

&7

Fi#' &8

pd

pdpd

pd pd


19/27


E2!%pe 4 In a Loung6s double-slit experiment the separation betweenthe first and the fifth bright fringe is .: mm when thewavelength used is 2> nm. If the distance from the slit to thescreen is >.=> m calculate the separation of the two slits.

Soution

E2!%pe 7 student sets up the apparatus shown below in order toobserve two-source interference fringes.

(a) State a suitable separation for the two slits in the doubleslit.

(b) State and explain what change if any occurs in theseparation of the fringes and in the contrast betweenbright and dar! fringes observed on the screen wheneach of the following changes is made separately.

(i) increasing the intensity of the red light incident on thedouble slit.

(ii) increasing the distance between the double slit andthe screen.

(iii) reducing the intensity of light incident on one of thedouble slit.

Soution (a) >.: mm(b) (i) The contrast is improved because the bright fringes

become brighter.

(ii) The fringe separation increases (use#$ "(a)

(iii) Hontrast decreases because the dar! fringes are notcompletely dar!.

&8

red

light

double slit screen


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&&'7 Di))r!$tion @r!tin#

Di))r!$tion @r!tin# diffraction grating consists of a large number of fine e"ually spaced lines (orslits) of e"ual width. diffraction grating typically consists of 1> lines to 1>>>lines per mm.

*hen a narrow beam of monochromatic light is incident on a diffraction grating

sharp maxima are obtained at various angular positions n as shown in ig.

>b.

E1u!tion Honsider a narrow beam of monochromatic light incident on a diffraction

grating of ) lines per metre. t angular position ofn

where nthorder bright

fringe (maxima) is obtained. The path difference between ad&acent slits (ig.>a) is

sin n# *+ d = = where1

slit separationd)

= =

Since the waves passing through all the slits are in phase for constructiveinterference

*9

Fi#' *9! Fi#' *9"


21/27


sin nd n = where n$ > 1 F

T!;e Note 1. Since )is typically >> to 1>>> per mm d is of the order of 1>2m. Since dis very small in fact only a few times more than the wavelength of visible

light (about >.7 1>2to >.2m) the angle of diffraction of even thefirst order (n $ 1)is "uite big.

. rom sin nn

d

= we see that the larger the value of n the larger the value

of . Since nO ?>sin 1

1

n

n

d

dn

> lines per mm illuminated normally with light ofwavelength 2 nm+

Soution

*&


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E2!%pe && Describe with the aid of a labelled diagram the appearance ofthe 1stGorder spectra when white light of wavelength from =>nm (violet) to nm (red) is incident normally on a diffractiongrating of :>> lines per mm.

SoutionSlit separation

.

21 1> .> 1> m:>>

d

= =

or violet light

?

1 2

1

=> 1>sin >.1?.> 1>

11.>

,

,

d

= = =

=

or red light?

1 2

1

1>sin >.?

.> 1>

.>

-

-

d

= = =

=

9ote that the longer wavelength deviates the most from thecentral fringe which remains white as all colours fall on it.

grating

1storder spectrumred

red

violet

violet

11.>

.>

**


23/27


Appen(i2 A St!tion!ry +!,es A M!te%!ti$! Appro!$ Option!

n analytical treatment of the production of stationary waves from the superpositionof two progressive waves having the same fre"uency and amplitude is given below.The two progressive waves may be represented by the e"uations

1

-sin

#y a t

=

and --

sin #

y a t

= +

where 1y and -y are travelling toward the right and left respectively.

Bsing the principle of superposition of waves the resultant wave can be representedby the e"uation

1 -

sin sin

sin cos

sin cos

cos

y y y

# #a t a t

#a t

#a t

A t

= +

= + +

=

=

=

where

sin#

A a

= is the amplitude of the resultant stationary wave for a point at a

distance#from a reference point.

t the nodes the amplitude is always 8ero and

>

>

#

#

=

=

K

K

t the antinodes the amplitude is maximum and e"uals a. This occurs when

*.


24/27


:

:

7 7 7

#

#

=

=

K

K

*e find that the distance between two successive nodes or antinodes is always

.

Appen(i2 B Me!surin# spee( o) soun( in !ir

The speed of sound in air can be measured either using a cathode-ray oscilloscopeor a resonance tube.

sing athode/-ay scilloscope

1. small microphone connected to a H0N is positioned between a reflectingboard and a loudspea!er.

. Sound wave of constant fre"uency travels from the spea!er towards the

reflecting board. Interference between the incident and reflected sound wavesproduces a stationary wave when a steady sinusoidal signal is shown in theH0N.

. s the microphone moves towards the spea!er the amplitude of the waveformon the H0N increases to a maximum (pressure antinode) at position and thenanother maximum at .

7. Since the distance between two successive pressure antinodes (displacement

nodes) is ;and the fre"uency fcan be determined from the H0N the speed of

the sound can be calculated using

-v f fL= =

sing -esonance Tube with Tuning 1ork

*/

L$

L%


25/27


1. tuning for! of fre"uency fis struc! and held over the top of atube filled with water.

. The water level is lowered gradually until the note is at its

loudest as shown in (a). 9ote the length of the air column 1L .

The air column is said to be resonating with the fre"uency of

the tuning for!.

. 0epeat the above steps while lowering the water level furtheruntil a second wea!er resonance is heard in (b). 9ote the new

length -L .

7. s shown in the diagram

1- - 1

L L=

:. Since the fre"uency fof the tuning for! is !nown speed ofsound in air can be calculated using

( )- 1v f f L L

= = Appen(i2 C isu!iin# ! Lon#itu(in! St!tion!ry +!,e Use)u

The following diagram shows the actual position of the particles in a longitudinalstationary wave. Dar! regions represent areas of %!2i%u% $o%pression(i#est pressure) while light regions represents areas of %!2i%u%r!re)!$tion(o0est pressure).

9otice that both the maximum compressions and maximum rarefactions occur at thenodes. This means that the (isp!$e%ent no(esare also the pressure !ntino(es

and vice versa.

*5

t2>

t 2 T%=

t 2 T%7

t 2 T%=

t 2 T%

t 2


26/27


Appen(i2 D Deter%in!tion o) 0!,een#t o) i#t usin# (i))r!$tion #r!tin#

parallel beam of monochromatic light after emerging from the collimator is incidentnormally on the diffraction grating. s a result bright fringes are produced at variousangular positions.

The telescope is first rotated such that the nthorder bright fringe is at the centre of the

crosswire in the telescope and its angular position 1 is noted. It is then positioned on

the opposite side of the normal to the grating and its angular position 2 is noted.

The angular position of the nthorder bright fringe is

( )- 11

n

=

Aence

sinn

d

n

=

*6


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Appen(i2 E Ho0 Do Mi$ropones +or;:

Cicrophones are a type of transducer- a device which converts energy from oneform to another. Cicrophones convert acoustical energy (sound waves) into electrical

energy (the audio signal).

Different types of microphone have different ways of converting energy but they allshare one thing in common, The diaphragm. This is a thin piece of material (such asaluminium) which vibrates when it is struc! by sound waves. In a typical hand-heldmic li!e the one below the diaphragm is located in the head of the microphone.

*hen the diaphragm vibrates it causes other components in the microphone tovibrate. These vibrations are converted into an electrical current which becomes theaudio signal.

Include ppendix on single-slit interference pattern in order to understand thatactual intensity of double-slit and diffraction grating is not constant but falls offaccording to single-slit envelope.

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superposition notes 2013_student version

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