Waves

Classification of Waves• Waves can be classified as either

mechanical or electromagnetic.• Mechanical wave examples: water waves,

waves on a spring, sound waves and ultrasonic waves.

• Mechanical waves must have a medium to travel through and cannot travel in a vacuum.

• A mechanical wave passing through a medium is vibrations being passed on from molecule to molecule.

Classification of Waves

• Electromagnetic wave examples: radio waves, microwaves, infra-red waves, ‘visible’ light waves, ultraviolet waves, X-rays and gamma-rays.

• Electromagnetic waves can travel through a vacuum and do not need a medium to travel through.

• Electromagnetic waves travel fastest in a vacuum at a speed of 3 x 108 metres per second (speed of light).

Waves on a Spring• If you hold a number of coils together – called

a compression – let them go and the compression moves along the spring.

• After the compression passes a point on the spring, the coils in that part become stretched more than normal.

• This is called a rarefaction.

Waves Are a Means of Transferring Energy• When waves move along water or a rope, there

is no overall motion as the wave passes.• As the wave pulse passes a point, the medium

around the point is disturbed, but when the pulse has passed, the medium at that point is no longer moving.

• A Travelling Mechanical Wave is a disturbance carrying energy through a medium without any overall motion of that medium.

Electromagnetic Waves• When an electromagnetic wave passes

through a region of space, there is a rapidly changing electric and magnetic field in that region.

• By this means, energy gets transferred from one place to another by the wave (Heat energy).

• A travelling wave, either mechanical or electromagnetic, is a disturbance that travels out from the source producing it, transferring energy from the source to other places through which it passes.

Some definitions…

1) Amplitude – this is height of the wave.

2) Wavelength () – this is the distance between two corresponding points on the wave and is measured in metres:

3) Frequency – this is how many waves pass by a point every second and is measured in Hertz (Hz)

Crest

Trough

Longitudinal Wave

Some definitions…Transverse waves are when the displacement is at right angles to the direction of the wave…

Longitudinal waves are when the displacement is parallel to the direction of the wave…

e.g.Lighte.g.Light

e.g.Soune.g.Soundd

Transverse waves are when the oscillation is at 90o to the direction of propagation

Longitudinal waves are when the oscillation is parallel to the direction of propagation

“Seeing” a wave

1) Quiet sound, low frequency (i.e. high wavelength):

2) Quiet sound, high frequency (i.e. low wavelength):

3) Loud sound, low frequency:

4) Loud sound, high frequency:

The Wave EquationThe wave equation relates the speed of the wave to its frequency and wavelength:

Wave speed (v) = frequency (f) x wavelength ()

in m/s in Hz in m

V

f

f

Using this formula we can convert any wavelength to

a frequency.

Remember Frequency – this is how many waves pass by a point every second and is measured in Hertz (Hz)

1) A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving?

2) A water wave travels through a pond with a speed of 1m/s and a frequency of 5Hz. What is the wavelength of the waves?

3) The speed of sound is 330m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound?

4) Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light?

Some example wave equation questions

0.2m

0.5m

0.6m/s

3x108m/s

Reflection• Reflection is when a wave meets an

obstacle in its path, it bounces off that obstacle.

• This can be seen with a water wave, the reflection of light waves in a mirror and sound waves through an echo.

Reflection

Waves Changing Speed• Waves change speed when they go

from one medium to another.

• Their frequency remains the same.• The wavelength increases if the wave

speeds up and the wavelength decreases if the wave slows down.

Refraction through a glass Refraction through a glass block:block:

Wave slows down and bends towards the normal due to

entering a more dense medium

Wave speeds up and bends away from the normal due to

entering a less dense medium

Wave slows down but is not bent, due to

entering along the normal

RefractionRefraction is when waves ____ __ or slow down due to travelling in a different _________. A medium is something that waves will travel through.

In this case the light rays are slowed down by the water and are _____, causing the ruler to look odd. The two mediums in this example are ______ and _______.

Words – speed up, water, air, bent, medium

The wavelength also changes.

Internet Diagram

Wave diagrams1) Reflection

4) Diffraction3) Refraction

2) Refraction

Diffraction

More diffraction if the size of the gap is similar to the wavelength

More diffraction if wavelength is increased (or frequency decreased)

Diffraction is when waves spread out from the edge of a gap.

Sound bends better around corners

Interference of Waves• Interference is when two waves from

two sources meet and a new wave is produced.

• When waves arrive crest with crest and trough with trough, they are said to be in phase.

Interference of Waves

Finding the Critical Angle…

1) Ray gets refracted

4) Ray gets internally reflected3) Ray still gets refracted (just!)

2) Ray still gets refracted

THE CRITICAL ANGLE

Uses of Total Internal ReflectionOptical fibres:

An optical fibre is a long, thin, transparent rod made of glass or plastic. Light is internally reflected from one end to the other, making it possible to send large chunks of information

Optical fibres can be used for communications by sending e-m signals through the cable. The main advantage of this is a reduced signal loss. Also no magnetic interference.

It is important to coat the strand in a material of low n.

The light can not leak into the next strand.

Other uses of total internal reflection1) Endoscopes (a medical device used to see inside the body):

2) Binoculars and periscopes (using “reflecting prisms”)

How does ultrasound work?

Ultrasonic waves are partly _________ at the boundary as they pass from one _______ to another. The time taken for these reflections can be used to measure the _______ of the reflecting surface and this information is used to build up a __________ of the object.

Words – depth, reflected, picture, medium

Ultrasound is the region of sound above 20,000Hz – it can’t be heard by humans. It can be used in pre-natal scanning:How does it work?

Other uses of ultrasound1) Echo sounding

The ultrasound is reflected from the sea floor.

2) Breaking down kidney stonesUltrasonic waves break kidney stones into much smaller pieces

3) Cleaning (including teeth)Ultrasound causes dirt to vibrate dirt off without damaging the object

The electromagnetic spectrum

Gamma rays

X-rays Ultra violet Visible light

Infra red Microwaves

Radio/TV

Each type of radiation shown in the electromagnetic spectrum has a different wavelength and a different frequency:

Each of these types travels at the same speed through a vacuum and can be polarised. Different wavelengths are absorbed by different surfaces (e.g. infra red is absorbed very well by black surfaces). This absorption may heat the material up (like infra red and microwaves) or cause an alternating current (like in a TV Ariel).

High frequency, short wavelength

Low frequency,long wavelength

γ

The higher the frequency of the wave, the greater its energy. This makes X-rays dangerous and radio waves

safe

Detection

• Waves invisible to the eye have to be detected using special apparatus

• IR (Infra-Red) is a heat wave so a blackened thermometer bulb

Night Vision Camera

• Of course we could just skip forward 100years

UV Light

• Ever walked into a nightclub• White cloth washed in optical

brighteners glows in UV light

Gamma• Bubble chambers where the wave

leaves a trail of bubbles

How Microwaves and Infra-red workMicrowaves are absorbed by water molecules up to a depth of a few centimetres. The heat then reaches the centre of the food by conduction.

Infra-red waves are absorbed by the surface of the material and the energy is then passed to the centre of the food by conduction.

The higher the frequency of the wave, the greater its

energy

X-rays and gamma () raysX-rays are absorbed by ____ parts of the body, like ____. Unfortunately, over-exposure to x-rays will damage cells.

Gamma rays can be used to treat _______. A gamma ray source is placed outside the body and rotated around the outside of the tumour. Doing this can ___ the cancerous cells without the need for ______ but it may damage other cells and cause sickness.

Tracers can also be used – these are small amounts of ___________ material that can be put into a body to see how well an organ or ______ is working.

Words – radioactive, gland, cancer, hard, bones, kill, surgery

Sun is not Yellow

As the light is filtered through As the light is filtered through more atmosphere more more atmosphere more frequencies absorbedfrequencies absorbed

Sky appears blue as scattered blue light from sun appears Sky appears blue as scattered blue light from sun appears to be coming from lots of different directionsto be coming from lots of different directions

Wave 2

Resultant wave

Wave 1

Coherent Waves

• Same Frequency• In Phase

Or Constant Or Constant phase differencephase difference

Phase difference Phase difference in measured in in measured in degrees of a degrees of a circlecircle

Coherent Waves

• Same Frequency• In Phase

Or Constant Or Constant phase differencephase difference

Phase difference Phase difference in measured in in measured in degrees of a degrees of a circlecircle

Interference is where 2 coherent waves meet. The resultant is the algebraic sum of

the 2 waves at any point.

+ =

Constructive Constructive InterferenceInterference

If 180 degrees out of phase.

+ =Destructive Interference

To Remember this we simplify it a To Remember this we simplify it a littlelittle

White Light Interference

To get two

coherentcoherent sources (same frequency and phase) we use one source and two slits.

ConstructiveConstructive InterferenceInterference

n=0

n=1

n=1

Proving the wave nature of Light

The interference The interference patterns prove patterns prove light is a wave.light is a wave.

Internet Example

Equation

• d = 1/(N x1000) (Grating Const lines/mm)

n=1n=1

So one wavelength So one wavelength difference difference Constructive Constructive InterferenceInterference

dd

Equation

dd

• When more than one wavelength difference

• d sin = n

• sin = /d• d sin =

For the n=2 dot

dd

22

• When n wavelength differences

• d sin = n

• sin = 2/d• d sin = 2

• What we actually see on the screen is a series of bright lines called fringes where there is constructive interference. This an interference pattern

n=0n=0

n=1n=1n=1n=1

n=2n=2n=2n=2

n=3n=3 n=3n=3

3 3 wavelengths wavelengths difference difference

in pathin path

n = 2

n = 1

n = 2

n = 1

n = 0

x

D

Laser

Metre stick

Diffractiongrating

θ

Tan θ = x/D

MEASUREMENT OF THE WAVELENGTH OF MONOCHROMATIC LIGHT

1.    Set up the apparatus as shown.  Observe the interference pattern on the metre stick – a series of bright spots.2.    Calculate the mean distance x between the centre (n=1) bright spot and the first (n =1) bright spot on both sides of centre.3.    Measure the distance D from the grating to the metre stick.4.    Calculate θ.5.    Calculate the distance d between the slits, using d=1/N the grating number.Calculate the wavelength λ using nλ = dsinθ.

6. Repeat this procedure for different values of n and get the average value for λ

As As nλ = dsinθ if d gets larger if d gets larger

then then θθ gets smaller gets smaller

H/W

• 2005 HL Q7

Polarization of LightNormally all e-m waves (Transverse)

oscillate in all perpendicular planes at once.

Polarization leaves only one plane of oscillation

Sound is a longitudinal wave and so can Sound is a longitudinal wave and so can not be Polarisednot be Polarised

Polarizing Filters

Hydrocarbons that absorb light that is in it’s plane of orientation.

Polarisation is the taking a transverse wave that oscillates in all perpendicular planes and filtering it so it oscillates in only one perpendicular plane.

Standing WavesWhen two coherent waves of the same amplitude traveling in opposite directions meet the waves combine to form a stationary wave

We draw this as the two extremes

nnAA

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Real Standing Waves

Strings

Closed Tubes

Open Tubes

/2

/2

/4

MEASUREMENT OF THE SPEED MEASUREMENT OF THE SPEED OF SOUND IN AIROF SOUND IN AIR

N

Tuning fork

Tube

Water

l1Graduated cylinder

A

MEASUREMENT OF THE SPEED OF SOUND IN AIR

Tuning forkTuning fork

TubeTube

WaterWater

ll11 Graduated Graduated cylindercylinder

dd

λλ = 4( = 4(ll11 + 0.3 + 0.3dd))

Method1. Strike the highest frequency (512 Hz)

tuning fork and hold it in a horizontal position just above the mouth of the tube.

2. Slide the tube slowly up/down until the note heard from the tube is at its loudest; resonance is now occurring.

3. Measure the length of the air column (from the water level to the top of the tube) l1 with a metre stick.

• An end correction factor has to be added to the length e = 0.3d, where d is the average internal diameter of the tube (measured using a vernier callipers).

• Hence λλ = 4( = 4(ll11 + 0.3 + 0.3dd)) • c c = = ff• c c = 4= 4ff((ll11 + 0.3 + 0.3dd).). • Calculate a value of c for each tuning fork and

find an average value for the speed of sound.

Harmonics

Whole number multiples of the fundamental frequency that happen at the same time as the fundamental.

Violin Harmonics

Viola Harmonics

You can hear You can hear the the difference as difference as the two the two instruments instruments have have different different combinations combinations of harmonicsof harmonics

Stretched String

A low note on a Double A low note on a Double Bass contains all the Bass contains all the harmonics above it.harmonics above it.

This is what gives the This is what gives the instrument its pleasant instrument its pleasant timbre or quality.timbre or quality.

Formula for stretched string

L=lengthT=tension=mass/unit length

Tf

lf

1

T

lfrequency

2

1

INVESTIGATION OF THE VARIATION OF FUNDAMENTAL FREQUENCY OF A STRETCHED

STRING WITH LENGTH

Bridge

l

Paper rider

Sonometer

Tuning Fork

Place the bridges as far apart as possible.Strike the turning fork putting the end on the bridge and reduce the length until the maximum vibration is reached (the light paper rider should jump off the wire).Measure the length with a metre rule.Note the value of this frequency on the tuning fork.Repeat this procedure for different tuning forks and measure the corresponding lengths.

Plot a graph of frequency f

against inverse of lengthl

1

l

1

f

INVESTIGATION OF THE VARIATION OF THE FUNDAMENTAL FREQUENCY OF A STRETCHED STRING WITH TENSION

Bridge

l

Paper rider

Sonometer

Pulley

Weight

•Select a wire length l (e.g. 30 cm), by suitable placement of the bridges. Keep this length fixed throughout the experiment. •Strike the tuning fork and hold it on the bridge.•Increase the tension by adding weight slowly from lowest possible until resonance occurs. (Jumping paper)•Note tension from weight used (In Newtons) and frequency from the tuning fork.

Plot a graph of frequency f

against square root of the tension

f

T

Musical Notes

Music waves have a regular Music waves have a regular shape where noise is shape where noise is

irregularirregularThree Qualities – called the characteristics

1. Pitch - This is frequencyfrequency of the wave.

2. Loudness - this is the amplitudeamplitude of the wave.

3. Timbre or Quality - The wave shape that is mainly due its overtonesovertones.

Demo

• Oscilloscope and microphone

Resonance• Transfer of energy between two

objects with the same, or very similar, natural frequency.

Barton’s Pendulum

String

Resonance

• If we set the driver in motion

Resonance• The energy is transferred only to

the pendulum of the same length.

Barton’s Pendulum

Resonance

• And back again for a remarkably long time.

A Stationary Source

• The waves radiate out from the source

• The wavelength detected at A is the same as at B

A moving Source

• The waves still radiate out from the source

• The wavelength detected at A is the longer than that at B

Movement Movement of sourceof source

Doppler Effect

The apparent change in frequency due to the motion of the observer or the source• Hence the change in pitch as a car passes

• Used by the Gardai in to detect speeding cars

Red Shift of Stars (Doppler in Light)

The Sun

Oh Bugger!

Moved to longer wavelengths proving the star is moving away from us

Example.A train emits a whistle at 700Hz what is the apparent frequency if it is traveling towards you at 30m/s? (c=340m/s)

Using f’ = f.c/(c-v)

f’ = 700.340/(340-30)

= 767 HzWhere f= Source Frequency and f’=Apparent FrequencyWhere f= Source Frequency and f’=Apparent Frequency

C=Speed of Wave and v=Speed of ObjectC=Speed of Wave and v=Speed of Object

H/W

• 2003 HL Q7

Tuning Forks - Both prongs vibrate and create sound

Summary - Sound as a WaveInterference proves sound is a wave.

If we twist a tuning fork near our ear it goes loud and soft.

The two prongs of the fork are interfering with each other.

LLOOUUDD

SSOOFFTT

LLOOUUDD

LLOOUUDD

LLOOUUDD

SSOOFFTT

SSOOFFTT

SSOOFFTT

Sound Intensity Level• This is to measure the very large range of

energy levels the ear can respond to, measured in decibels (dB). This is an exponential scale so if the energy doubles the level goes up by e dB.

• Home CD player 75 dB tops but a good rock band maybe 110dB.

• Health and safety tell us that if you stay in an environment above 85dB for more than 8 hrs you do permanent and un-repairable damage to your ears. So Muse is right out.

Sound Intensity level

• Also called acoustic intensity level is a logarithmic measure of the sound intensity in comparison to the reference level of 0 dB (decibels).

• The measure of a ratio of two sound intensities is

• where J1 and J0 are the intensities.

• The sound intensity level is given the letter "L J" and is measured in "dB". Decibels (dB) are dimensionless.

• If J0 is the standard reference sound intensity, where

• (W = watt), then instead of "dB" we use "dB SIL". (SIL = sound intensity level).

• We also have dBA, which is adjusted to allow for the range of the human ear.

Acoustics• Use reflections and direct sound to

amplify sound in a concert hall.

To achieve a loud sound: * If necessary, reflectors and diffusers

may be used to provide beneficial supporting sound reflections

* The interior surfaces of the hall should be hard to ensure that sound energy is not absorbed and lost.

Threshold of Hearing

• The absolute threshold of hearing (ATH) is the minimum sound level of a pure tone that an average ear with normal hearing can hear in a noiseless environment at 1kHz.

Limit of Audibility• The top and bottom

values of the range are known as the limits of audibility.

• For the human ear, the lower limit is approximately 20 Hz and the upper limit is 20,000 Hz. In other words, our ears are supposed to be able to hear sound with frequencies that are greater than 20 Hz and less than 20,000 Hz.

• Different people have different ranges of audibility.

• People who are old cannot hear as well as those who are young. The ability of the ear drum to respond to sound decreases with age and the range of audibility becomes very much reduced as the lower limit rises and the upper limit falls.

X-RaysX-Rays• Electrons jump from the

surface of a hot metal –

• Thermionic EmissionThermionic Emission

Accelerated by high voltage they smash into tungsten

The electrons excite orbiting electrons to high energy orbits-see next few slides for details

These fall back emitting high frequency waves.

Most of the electron energy is lost as heat.-about 90%

X-rays very penetrating, fog film, not effected by fields.

High Tension Voltage

Photons

• Bohr first suggested a model for the atom based on many orbits at different energy levels

E1E2

Photons

• If the electron in E1 is excited it can only jump to E2.

E1E2

Photons

• Then the electron falls back. The gap is fixed so the energy it gives out is always the same

E1E2

Photons

• So Max Planck said all energy must come in these packets called photons.

• He came up with a formula for the frequency

E1E2

E2 –E1 = h.f

Where f=frequency

h= Planck’s constant

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Albert Einstein

• Uncle Albert was already a Uncle Albert was already a published scientist but the relativity published scientist but the relativity stuff had not set the world alight.stuff had not set the world alight.

• He set his career in real motion He set his career in real motion when he solved a problem and when he solved a problem and started the science of Quantum started the science of Quantum Mechanics that the old world Jew in Mechanics that the old world Jew in him could never come to terms him could never come to terms with.with.

The Problem• If you shine light on the surface of

metals electrons jump off

Polished Sodium MetalPolished Sodium Metal

ee

ee

ee

ee

ee

• Electrons emitted• This is The PHOTOELECTRIC EFFECT

We can prove this with the experiment below

A charged Zinc plate is attached to an Electroscope

When a U.V. lamp is shone on the plate the leaf collapses as all the electrons leave the surface of the zinc

The Photoelectric EffectThe Photoelectric EffectThe more intensity you gave it the more

electrical current was produced However something strange happened

when you looked at frequency

Frequency of light

Electron Energy Newtonian Physics Newtonian Physics

could not explain thiscould not explain this

Einstein’s LawSo we define the Photoelectric effect as:-

Electrons being ejected from the surface of a metal by incident light of a suitable frequency.

Uncle Albert used Plank’s theory that as energy came in packets

A small packet would not give the electron enough energy to leave

Low frequency light had too small a parcel of energy to get the electron free.

Energy of each photon = h.f

Photo-Electric Effect

Frequency of light

Electron Energy

f0=Threshold Frequency

Energy of incident photon =

h.f = h. f0+ KE of electron

Work Function,Energy to release Electron

Energy left over

turnedinto

velocity

Reflection Wave bouncing off a solid object Echo

Refraction

Waves changing speed and direction due to change in density of medium

Frequency stays the same

Hear people across a lake

Diffraction

spreading of a wave around an obstacle or on the emergent side of

a slit.

Better with long wavelength

Sound round cornersSpreading from slit

Interference

Two coherent waves meeting combine wave at any point is the algebraic sum of the two waves

Proves things are waves

Constructive and destructive

PolarisationReduces transverse waves to one plane of oscillation

Difference between transverse and longitudinal

Snow sunglasses