section 4. oscillations and waves course notes

8/18/2019 Section 4. Oscillations and Waves Course Notes

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A-Level Course Notes: PHYSICS

SECTION IV: Oscillations and Waves

SECTION IV

Oscillations and Waves

CIE A-Level [AS and A2]

________________________

Course Notes

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Syllabus etails______________________






!"# Oscillations [A2]_________________________

Content

!"#! Si$%le &a'$onic $otion!"#2 Ene'(y in si$%le &a'$onic $otion

!"#) a$%ed and *o'ced oscillations+ 'esonance

Lea'nin( outco$es_____________________________________

Candidates s&ould be able to+

(a) desc'ibe si$%le e,a$%les o* *'ee oscillations

(b) investi(ate t&e $otion o* an oscillato' usin( e,%e'i$ental and ('a%&ical $et&ods






(c) unde'stand and use t&e te'$s a$%litude %e'iod *'e.uency an(ula' *'e.uency

and %&ase di**e'ence and e,%'ess t&e %e'iod in te'$s o* bot& *'e.uency and an(ula'

*'e.uency

Te'$ Sy$bol e*initionis%lace$ent x The instantaneous distance of the moving object

from its mean position

A$%litude A Maximum displacement from the mean position

/e'iod T Time for one complete oscillation in seconds

0'e.uency F The number of oscillations that take place in 1

second

An(ula'

*'e.uencyω The frequenc expressed in radians per second

/&ase

di**e'enceφ Measure of ho! in "step# different particles are$

1%&o ' completel out of phase

&o ' completel in phase

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(d) 'eco(nise and use t&e e.uation a 1 ω 2 x as t&e de*inin( e.uation o* si$%le

&a'$onic $otion

Si$%le 3a'$onic 4otion+ )n vibration for !hich the restoring force is directl

proportional to the negative of the displacement$

* ∝ +x

* ' ma therefore,$$

a ∝ +x

a ' accelerationω ' angular frequenc

x ' displacement

T ' -eriod

T&is *o'$ula is (iven at t&e sta't o* t&e test %a%e'

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(e) 'ecall and use x 1 x 5sinωt as a solution to t&e e.uation a 1 ω 2 x

(f) 'eco(nise and use v 1 v5cos ωt v 1 6 ω sqrt /x&2+x2 0

(g) desc'ibe 7it& ('a%&ical illust'ations t&e c&an(es in dis%lace$ent velocity and

accele'ation du'in( si$%le &a'$onic $otion

x ' displacement x& ' maximum displacement /)mplitude0

v ' velocit v& ' maximum velocit

ω ' angular frequenc

T&ese *o'$ula a'e (iven at t&e sta't o* t&e test %a%e'

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(h) desc'ibe t&e inte'c&an(e bet7een 8inetic and %otential ene'(y du'in( si$%le

&a'$onic $otion

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(i) desc'ibe %'actical e,a$%les o* da$%ed oscillations 7it& %a'ticula' 'e*e'ence to

t&e e**ects o* t&e de('ee o* da$%in( and t&e i$%o'tance o* c'itical da$%in( in cases

suc& as a ca' sus%ension syste$

a$%in( ' a frictional force /dissipative force0 that al!as acts in the opposite

direction to the direction of motion of the oscillating particle$

Li(&t da$%in( 9unde' da$%ed: ' resistive force is small time period id not

effected and the oscillation continues for a number of ccles$

3eavy da$%in( 9ove' da$%in(: ' large resistive force !hich can completel prevent the oscillation$ -article ma take a long time to return to 4ero

displacement$

C'itical da$%in( ' intermediate resistive force !hich gives the fastest return to

4ero displacement !ithout an overshoot$

Situation Oscillation a$%in(

Car suspension Car oscillates due to springlike connection to !heels

Critical damping needed to stoposcillation as quickl as possible to

avoid motion sickness 5 hdraulic

in nature

Tall buildings 6uring earthquakes 7arge !eight hung at the top of the

building to suppl a counter

oscillation

(j) desc'ibe %'actical e,a$%les o* *o'ced oscillations and 'esonance

Natu'al *'e.uency+ The frequenc at !hich an object !ill vibrate freel !hen set

in motion$

0o'ced oscillation+ 8scillations produced b an external force !hich has its o!n

particular frequenc$

;esonance occurs !hen a sstem is subject to an oscillating force at exactl the

same frequenc as the natural frequenc of oscillation of the sstem

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(k) desc'ibe ('a%&ically &o7 t&e a$%litude o* a *o'ced oscillation c&an(es 7it&

*'e.uency nea' to t&e natu'al *'e.uency o* t&e syste$ and unde'stand .ualitatively

t&e *acto's t&at dete'$ine t&e *'e.uency 'es%onse and s&a'%ness o* t&e 'esonance

(l) s&o7 an a%%'eciation t&at t&e'e a'e so$e ci'cu$stances in 7&ic& 'esonance is

use*ul and ot&e' ci'cu$stances in 7&ic& 'esonance s&ould be avoided#

E,a$%le esc'i%tion

9uart4 oscillator 9uart4 crstals can be made to oscillate using electricfields$ The natural frequenc of the quart4 oscillation

can then be use to generate an oscillating voltage !hich

can be used as an internal clock of electronic devices

Micro!ave generator The oscillating electric field in a micro!ave causes

!ater molecules !ith :; energ and so raises the

temperature

<ibrations in machiner Moving parts in engines provide a regular driving

force$ =f the driving force is at the natural frequenc of

other parts in the machiner the !ill resonate$

>;; -?;T >=M

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!<# Waves [AS]______________________________

Content

!<#! /'o('essive 7aves!<#2 T'ansve'se and lon(itudinal 7aves

!<#) /ola'isation

!<#" ete'$ination o* s%eed *'e.uency and

7avelen(t&

!<#< Elect'o$a(netic s%ect'u$

Lea'nin( outco$es_____________________________________

Candidates s&ould be able to+

(a) desc'ibe 7&at is $eant by 7ave $otion as illust'ated by vib'ation in 'o%es

s%'in(s and 'i%%le tan8s

>;; -?;T >=M

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(b) s&o7 an unde'standin( o* and use t&e te'$s dis%lace$ent a$%litude

%&ase di**e'ence %e'iod *'e.uency 7avelen(t& and s%eed

Te'$ Sy$bol e*inition

is%lace$ent x The change that has taken place as a result of

the !ave passing that pointA$%litude A Maximum displacement from the mean position

/e'iod T Time for one complete oscillation in seconds

0'e.uency F The number of oscillations that take place in 1

second

Wavelen(t& λ >hortest distance bet!een t!o points in phase

!ith one another$

Wave s%eed v The speed at !hich !ave fronts pass a

stationar observer

(c) deduce *'o$ t&e de*initions o* s%eed *'e.uency and 7avelen(t& t&e e.uation

v 1 f = (d) 'ecall and use t&e e.uation v 1 f =

(e) s&o7 an unde'standin( t&at ene'(y is t'ans*e''ed due to a %'o('essive 7ave

(f) 'ecall and use t&e 'elations&i% intensity %'o%o'tional to 9amplitude:2

Intensity I The po!er per unit area received b an

observer$ = ∝ Α2






(g) co$%a'e t'ansve'se and lon(itudinal 7aves

T'ansve'se Waves Lon(itudinal Waves

Aater ripples >ound !aves

;arthquakes ;arthquakes

7ight !aves Compression !aves do!n a spring

Aaves on a stretched rope

>;; -?;T >=M






(h) analyse and inte'%'et ('a%&ical 'e%'esentations o* t'ansve'se and lon(itudinal

7aves

(i) s&o7 an unde'standin( t&at %ola'isation is a %&eno$enon associated 7it&

t'ansve'se 7aves






(j) dete'$ine t&e *'e.uency o* sound usin( a calib'ated c#'#o#

• =nput the sound signal via a microphone into the B+input

• )djust the time base control until at least one complete ccle is visible on the

screen

• Measure the separation bet!een t!o points in phase and determine the time

period from comparison to the Time base setting

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(k) dete'$ine t&e 7avelen(t& o* sound usin( stationa'y 7aves

(l) state t&at all elect'o$a(netic 7aves t'avel 7it& t&e sa$e s%eed in *'ee s%ace and

'ecall t&e o'de's o* $a(nitude o* t&e 7avelen(t&s o* t&e %'inci%al 'adiations *'o$

'adio 7aves to >-'ays#

Elect'o$a(netic 7aves t'avel 7it& t&e sa$e s%eed in *'ee s%ace#

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!?# Su%e'%osition [AS]_______________________

Content

!?#! Stationa'y 7aves!?#2 i**'action

!?#) Inte'*e'ence

!?#" T7o-sou'ce inte'*e'ence %atte'ns

!?#< i**'action ('atin(

Lea'nin( outco$es_____________________________________

Candidates s&ould be able to+(a) e,%lain and use t&e %'inci%le o* su%e'%osition in si$%le a%%lications

Ahen t!o !aves meet the interfere$

T&e /'inci%le o* Su%e'%osition@

"The overall disturbance at an point and at an time !here the !aves meet is the

vector sum of the disturbance that !ould have been produced b each of the

individual !aves#






(b) s&o7 an unde'standin( o* e,%e'i$ents t&at de$onst'ate stationa'y 7aves usin(

$ic'o7aves st'etc&ed st'in(s and ai' colu$ns

4IC;OWAVES

ST;ETC3E ST;IN






c) e,%lain t&e *o'$ation o* a stationa'y 7ave usin( a ('a%&ical $et&od and identi*y

nodes and antinodes

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(d) e,%lain t&e $eanin( o* t&e te'$ di**'action

Ceometric >hado!

Ceometric

>hado!

Ceometric

>hado!

• The bending of !aves around an obstruction

• )s the si4e of the aperture or the object decreases the effects of diffraction

increase

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• The !avelength needs to be similar to the si4e of the aperture for

diffraction to be noticeable(e) s&o7 an unde'standin( o* e,%e'i$ents t&at de$onst'ate di**'action includin(

t&e di**'action o* 7ate' 7aves in a 'i%%le tan8 7it& bot& a 7ide (a% and a na''o7

(a%

• i**'action can be illust'ated on a 'i%%le tan8 as s&o7n above

>;; -?;T >=M

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(f) s&o7 an unde'standin( o* t&e te'$s inte'*e'ence and co&e'ence

INTE;0E;ENCE+ 8verlapping of !aves

C8N>TDECT=<; 5 T!o !aves in phase6;>TDECT=<; 5 T!o !aves 1%&o out of phase

CO3E;ENCEF ?aving a constant phase relationship

(g) s&o7 an unde'standin( o* e,%e'i$ents t&at de$onst'ate t7o-sou'ce inte'*e'ence

usin( 7ate' li(&t and $ic'o7aves






(h) s&o7 an unde'standin( o* t&e conditions 'e.ui'ed i* t7o-sou'ce inte'*e'ence

*'in(es a'e to be obse'ved

To observe t!o+source interference ou need,

T!o coherent sources

• ?ave the same frequenc

• Constant phase relationship bet!een the t!o sources

• Doughl the same amplitude






(i) 'ecall and solve %'oble$s usin( t&e e.uation = 1 a,B *o' double-slit

inte'*e'ence usin( li(&t

(j) 'ecall and solve %'oble$s usin( t&e *o'$ula d sin 1 n= and desc'ibe t&e use o* a

di**'action ('atin( to dete'$ine t&e 7avelen(t& o* li(&t 9t&e st'uctu'e and use o* t&e

s%ect'o$ete' a'e not included:#

θd

-ath difference

' d sinθ

*or Constructive =nterference

d sinθ = nλ

θd

-ath difference

' d sinθ

*or Constructive =nterference

d sinθ = nλ

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Esing the diffraction grating to measure !avelengths

The angle at !hich constructive interference occurs is !avelength

dependent

=f the position of the maxima for a diffraction grating are accuratel

measured the !avelength can be calculated

)dding more slits /a diffraction grating0 has the follo!ing effect on the interference

pattern,

Condition of constructive interference !ill N8T change

The principle maxima have the same separation

The principle maxima become sharper

The pattern increases in intensit

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Dac8('ound ;eadin(_________________

-?B>=C> iancoli th edition Chapter 13+1(

se*ul Websites______________________

&tt%+BB%&et#colo'ado#eduBenBsi$ulationsBcate(o'yBne7

&tt%+BB777#s-cool#co#u8BalevelB%&ysics#&t$l

&tt%+BB777#%&ysicsclass'oo$#co$B$$ediaBinde,#c*$

&tt%+BB777#%&ys#&a7aii#eduBFtebBGavaBntnuGavaBinde,#&t$l

&tt%+BB777#colo'ado#eduB%&ysicsB2555Binde,#%l

Constants___________________________ [T&ese a'e (iven on eac& test %a%e']

http://phet.colorado.edu/en/simulations/category/new

http://www.s-cool.co.uk/alevel/physics.html

http://www.physicsclassroom.com/mmedia/index.cfm

http://www.phys.hawaii.edu/~teb/java/ntnujava/index.html

http://www.colorado.edu/physics/2000/index.pl

http://phet.colorado.edu/en/simulations/category/new

http://www.s-cool.co.uk/alevel/physics.html

http://www.physicsclassroom.com/mmedia/index.cfm

http://www.phys.hawaii.edu/~teb/java/ntnujava/index.html

http://www.colorado.edu/physics/2000/index.pl

section 4. oscillations and waves course notes

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