A-Level Course Notes: PHYSICS

A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves

SECTION IV Oscillations and Waves

CIE A-Level [AS and A2] ______

Course Notes

DIPONT Educational Resource - Science 1 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves Syllabus Details______

DIPONT Educational Resource - Science 2 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves 14. Oscillations [A2]______

Content 14.1 Simple harmonic motion 14.2 Energy in simple harmonic motion 14.3 Damped and forced oscillations: resonance

Learning outcomes______

Candidates should be able to: (a) describe simple examples of free oscillations

Pendulum

Spring

(b) investigate the motion of an oscillator using experimental and graphical methods

Output x

Motion Sensor Time /s

DIPONT Educational Resource - Science 3 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves

(c) understand and use the terms amplitude, period, frequency, angular frequency and phase difference and express the period in terms of both frequency and angular frequency x

, t T n T=1/f e m e c a l p

s A i D Time /s

In Phase positions Mean position x

, t  n e m e c a l p

s A i D Position /m

One complete oscillation

Term Symbol Definition Displacement x The instantaneous distance of the moving object from its mean position Amplitude A Maximum displacement from the mean position Period T Time for one complete oscillation in seconds Frequency F The number of oscillations that take place in 1 second Angular  The frequency expressed in radians per second frequency Phase  Measure of how in “step” different particles are. difference 180o = completely out of phase 0o = completely in phase

T= 2p / w f= 1/ T

(d) recognise and use the equation a = –ω 2x as the defining equation of simple harmonic motion

Simple Harmonic Motion: Any vibration for which the restoring force is directly proportional to the negative of the displacement.

F -x

F = ma therefore….. a a  -x a = -2x

a = acceleration x  = angular frequency x = displacement  = 2 / T

T = Period

This formula is given at the start of the test paper

(e) recall and use x = x0sinωt as a solution to the equation a = –ω 2x 2 2 (f) recognise and use v = v0cos ωt, v = ± ω sqrt(x0 -x ) (g) describe, with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion

x x 0 t n e m e c a

l T /2 T p s i Time D v v0 y t i c o l e

V T /4 3T /4 Time a

n o i t a r e l e c c

A Time

Time x = x0sin(t) x = x0cos(t)

v = v0cos(t) v = v0sin(t)

x = displacement x0 = maximum displacement (Amplitude) v = velocity v0 = maximum velocity  = angular frequency

2 2 v = ±   (x0 – x )

These formula are given at the start of the test paper

(h) describe the interchange between kinetic and potential energy during simple harmonic motion

Pendulum

2 2 2 2 Ek = ½ mv = ½ m (x0 – x )

2 2 Ep = ½ m x

2 2 2 2 2 ET = Ek + Ep = ½ m (x0 – x ) +½ m x

2 2 ET = ½ m x0

(i) describe practical examples of damped oscillations with particular reference to the effects of the degree of damping and the importance of critical damping in cases such as a car suspension system

Damping = a frictional force (dissipative force) that always acts in the opposite direction to the direction of motion of the oscillating particle. x

, t n e m e c a l Light damping p s i D Time /s x

, t n e m e c a l Over damping p s i D Time /s Critical damping

Light damping (under damped) = resistive force is small, time period id not effected and the oscillation continues for a number of cycles. Heavy damping (over damping) = large resistive force which can completely prevent the oscillation. Particle may take a long time to return to zero displacement. Critical damping = intermediate resistive force which gives the fastest return to zero displacement without any overshoot.

Situation Oscillation Damping Car suspension Car oscillates due to spring Critical damping needed to stop like connection to wheels oscillation as quickly as possible to avoid motion sickness – hydraulic in nature Tall buildings During earthquakes Large weight hung at the top of the building to supply a counter oscillation

(j) describe practical examples of forced oscillations and resonance

Natural frequency: The frequency at which an object will vibrate freely when set in motion. Forced oscillation: Oscillations produced by an external force which has its own particular frequency. Resonance occurs when a system is subject to an oscillating force at exactly the same frequency as the natural frequency of oscillation of the system

(k) describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system, and understand qualitatively the factors that determine the frequency response and sharpness of the resonance

Resonance n o i t a l l i c s

o Light damping

e d u t i l p m A

Heavy damping

Natural Driving frequency frequency

(l) show an appreciation that there are some circumstances in which resonance is useful and other circumstances in which resonance should be avoided.

Example Description

Quartz oscillator Quartz crystals can be made to oscillate using electric fields. The natural frequency of the quartz oscillation can then be use to generate an oscillating voltage which can be used as an internal clock of electronic devices Microwave generator The oscillating electric field in a microwave causes water molecules with KE energy, and so raises the temperature Vibrations in machinery Moving parts in engines provide a regular driving force. If the driving force is at the natural frequency of other parts in the machinery, they will resonate.

SEE PHET SIM

DIPONT Educational Resource - Science 9 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves 15. Waves [AS]______

Content 15.1 Progressive waves 15.2 Transverse and longitudinal waves 15.3 Polarisation 15.4 Determination of speed, frequency and wavelength 15.5 Electromagnetic spectrum

Candidates should be able to: (a) describe what is meant by wave motion as illustrated by vibration in ropes, springs and ripple tanks Water Surface Oscillation or Rope

Energy Transfer Forced oscillation Spring or Air Oscillation

Forced Energy Transfer oscillation

SEE PHET SIM

(b) show an understanding of and use the terms displacement, amplitude, phase difference, period, frequency, wavelength and speed

Term Symbol Definition Displacement x The change that has taken place as a result of the wave passing that point Amplitude A Maximum displacement from the mean position Period T Time for one complete oscillation in seconds Frequency F The number of oscillations that take place in 1 second Wavelength  Shortest distance between two points in phase with one another. Wave speed v The speed at which wave fronts pass a stationary observer

(c) deduce, from the definitions of speed, frequency and wavelength, the equation v = fλ (d) recall and use the equation v = fλ

distance v = time

 v = T=1/f T

v = velocity f = frequency v = f  = wavelength

(e) show an understanding that energy is transferred due to a progressive wave (f) recall and use the relationship intensity proportional to (amplitude)2

Intensity I The power per unit area received by an observer. I 

(g) compare transverse and longitudinal waves

Transverse Waves Oscillations perpendicular to direction of energy transfer

Energy transfer

Longitudinal Waves Oscillations parallel to direction of energy transfer

Energy transfer

Transverse Waves Longitudinal Waves

Water ripples Sound waves Earthquakes Earthquakes Light waves Compression waves down a spring Waves on a stretched rope

SEE PHET SIM

(h) analyse and interpret graphical representations of transverse and longitudinal waves x

, t T n T=1/f e m e c a l p

s A i D Time /s

In Phase positions Mean position x

, t  n e m e c a l p

s A i D Position /m

One complete oscillation

(i) show an understanding that polarisation is a phenomenon associated with transverse waves

Wave nature of Electromagnetic Waves E

Direction of motion of wave

• E = Electric Field • B = Magnetic Field • E and B oscillate at 90 degrees each other • The direction of motion of the wave is perpendicular to both B and E

Polarized Light

Direction of electric field Un-polarized Light oscillation

(j) determine the frequency of sound using a calibrated c.r.o.

KEY CONTROLS…. •Time base: Time taken for beam to pass through one horizontal division [Sec/div] •Vertical amplifier gain: The vertical scale control [Volts/div]

 Input the sound signal via a microphone into the Y-input  Adjust the time base control until at least one complete cycle is visible on the screen  Measure the separation between two points in phase and determine the time period from comparison to the Time base setting

(k) determine the wavelength of sound using stationary waves

e = end correction

For the first position:

l/4 = L1 + e L2 For the second position: L1 3l/4 = L2 + e

Combining the two equations:

l/2 = L2 - L1

Substituting into c = lf:

c = 2f (L2 - L1)

(l) state that all electromagnetic waves travel with the same speed in free space and recall the orders of magnitude of the wavelengths of the principal radiations from radio waves to γ-rays.

Electromagnetic waves travel with the same speed in free space. Wavelength

3 x 104 m 3 m 3 x 10-4 m 3 x 10-8 m 3 x 10-12 m

Infrared Gamma rays Radio waves Ultraviolet

Microwaves X-rays

104 Hz 108 Hz 1012 Hz 1016 Hz 1020 Hz

Frequency 7.5 x 10-7 m 4 x 10-7 m

4 x 1014 Hz 7.5 x 1014 Hz Visible Light

DIPONT Educational Resource - Science 15 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves 16. Superposition [AS]______

Content 16.1 Stationary waves 16.2 Diffraction 16.3 Interference 16.4 Two-source interference patterns 16.5 Diffraction grating

Candidates should be able to: (a) explain and use the principle of superposition in simple applications

When two waves meet they interfere. The Principle of Superposition…

“The overall disturbance at any point and at any time where the waves meet is the vector sum of the disturbance that would have been produced by each of the individual waves”

Time /s Time /s + +

Time /s Time /s

Destructive Interference Constructive Interference

Time /s Time /s

(b) show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns

MICROWAVES Microwave Metal source Reflector

Detector

STRETCHED STRING String Vibrator pulley

masses

DIPONT Educational Resource - Science 17 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves c) explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes

l l Fundamental 0 = 2l 1st Harmonic f0 Node Node Anti-node

| 2nd Harmonic l = l | Node Node f =2f0 Node Anti-node Anti-node

|| 3rd Harmonic l = 2/3l || Node Node Node Node f =3f0 Anti-node Anti-node Anti-node

RESONANCE FREQUENCIES - Pipe Open at Both End

Anti-node Anti-node Anti-node Node Node Anti-node Node Node Anti-node l Anti-node Node Node Anti-node Anti-node Anti-node

Fundamental 2nd Harmonic 3rd Harmonic 1st Harmonic

l l | l || 0= 2l = l = 2/3l | || f =2f f =3f0 f 0 0

RESONANCE FREQUENCIES - Pipe Open at One End

Anti-node Anti-node Anti-node Node Node Anti-node l Anti-node Node Anti-node

Node Node Node

Fundamental 2nd Harmonic 3rd Harmonic 1st Harmonic

l l | l || 0= 4l = 4/3l = 4/5l | || f =3f f =5f0 f 0 0

(d) explain the meaning of the term diffraction

Geometric Shadow

Geometric Geometric Shadow Shadow

 The bending of waves around an obstruction  As the size of the aperture or the object decreases the effects of diffraction increase

 The wavelength needs to be similar to the size of the aperture for diffraction to be noticeable (e) show an understanding of experiments that demonstrate diffraction including the diffraction of water waves in a ripple tank with both a wide gap and a narrow gap

 Diffraction can be illustrated on a ripple tank as shown above

SEE PHET SIM

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

INTERFERENCE: Overlapping of waves CONSTRUCTIVE – Two waves in phase DESTRUCTIVE – Two waves 180o out of phase

COHERENCE: Having a constant phase relationship

Two coherent wave sources

Two incoherent wave sources

(g) show an understanding of experiments that demonstrate two-source interference using water, light and microwaves

Two-source interference – water waves or sound waves

Interference pattern y t i s n e t n I

Constructive interference

Destructive interference

Source 1 Source 2 Constructive interference – Regions where waves are in phase

Destructive interference - Regions where the waves are out of phase

Young’s Double Slit Experiment - Light

Interference pattern Region of superposition y t i s n e t n I

Double slit

Source slit

Monochromatic light source

(h) show an understanding of the conditions required if two-source interference fringes are to be observed

To observe two-source interference you need…

. Two coherent sources  Have the same frequency  Constant phase relationship between the two sources  Roughly the same amplitude

(i) recall and solve problems using the equation λ = ax/D for double-slit interference using light

a l= ax / D l S 2 D

(j) recall and solve problems using the formula d sinθ = nλ and describe the use of a diffraction grating to determine the wavelength of light (the structure and use of the spectrometer are not included).

d  For Constructive Interference d sin n Path difference = d sin

Using the diffraction grating to measure wavelengths

 The angle at which constructive interference occurs is wavelength dependent  If the position of the maxima for a diffraction grating are accurately measured the wavelength can be calculated

Adding more slits (a diffraction grating) has the following effect on the interference pattern…  Condition of constructive interference will NOT change  The principle maxima have the same separation  The principle maxima become sharper  The pattern increases in intensity

2 Slits

4 Slits

50 Slits

DIPONT Educational Resource - Science 25 A-Level Course Notes: PHYSICS SECTION IV: Oscillations and Waves Background Reading______

PHYSICS, Giancoli 6th edition, Chapter 13-14 Useful Websites______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

Constants______

[These are given on each test paper]

DIPONT Educational Resource - Science 26