Waves

By Neil Bronks

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

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.Light

e.g.Sound

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

Refraction through a glass 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

H/WHigher 2008Q9

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 an obstacle or through a gap.

Sound bends better around corners

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 raises in temperature

Night Vision Camera• Of course we could just skip

forward 100years • Even a mobile phone camera will

show you an IR image.

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

brighteners fluoresces in UV light• As does Vaseline

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 more atmosphere more frequencies absorbed

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

Wave 2

Resultant wave

Wave 1

Coherent Waves

• Same Frequency• In Phase

Or Constant phase difference

Phase difference in measured in degrees of a circle

Coherent Waves

• Same Frequency• In Phase

Or Constant phase difference

Phase difference in measured in degrees of a circle

Interference is where 2 coherent waves meet. The resultant new wave is the

algebraic sum of the 2 waves at any point.

+ =

Constructive Interference

If 180 degrees out of phase.

+ =Destructive Interference

To Remember this we simplify it a little

H/WHigher 2002Q7

White Light Interference

http://upload.wikimedia.org/wikipedia/commons/5/52/Soap_bubbles-jurvetson.jpg

Diffraction only works when wavelength is about same as gap

To get two

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

Constructive Interference

n=0

n=1

n=1

Proving the wave nature of Light

The interference patterns prove light is a wave.

Internet Example

Equation for n=1

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

n=1

So one wavelength difference Constructive Interference

d

Equation

d

• When more than one wavelength difference

• d sin = n

• sin = /d• d sin =

Goes to first spot on screen - constructive interference

For the nth dot

d

n • sin = n/d• d sin = n

Goes to spot on screen that is constructive interference

• 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=0

n=1n=1

n=2n=2

n=3 n=3

3 wavelengths difference

in 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 nλ = dsinθ if d gets larger

then θ gets smaller

N d Error

H/W

• 2005 HL Q7

Polarization of LightNormally all e-m waves (Transverse)

oscillate in all perpendicular planes at once.

Polarization e-m wave vibrates in only one plane

Sound is a longitudinal wave and so can not be Polarised

PolarisationTransverse waves are plane-polarised if the vibrations stay in one plane only.Longitudinal waves cannot 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

nA

http://www.absorblearning.com/media/attachment.action?quick=8u&att=628

Real Standing Waves

Strings

Closed Tubes

Open Tubes

/2

/2

/4

MEASUREMENT OF THE SPEED OF SOUND IN AIR

N

Tuning fork

Tube

Water

l1Graduated cylinder

A

λ = 4(l1 + 0.3d)

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 λ = 4(l1 + 0.3d) • c = f• c = 4f(l1 + 0.3d). • 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.

This is the harmonics for a string this gives ½1.5

Violin Harmonics

Viola Harmonics

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

Stretched String

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

This is what gives the instrument its pleasant 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 shape where noise is

irregularThree Qualities – called the characteristics

1. Pitch - This is frequency of the wave.

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

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

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 of 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 carsWave crests

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 Hz

Where f= Source Frequency and f’=Apparent Frequency

C=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.

LOUD

SOFT

LOUD

LOUD

LOUD

SOFT

SOFT

SOFT

Sound Intensity• Amount of sound

energy passing through 1m2 every second (PERPENDICULAR)

• Units are just Watts/meter

As the sound gets further from source it spreads making the intensity decrease

Calculations• A speaker has an output of 10W.

What is its intensity at 2m away?

Area of Sphere = 4 r2

= 4x3.142x4 = 50.2 m2

If we look in the log book the units of Sound intensity is W/m2 this gives us the calculation.Sound Intensity Level=10W/50.2m2

=0.2 W/M2

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 "LJ" 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.

Limits 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.

Conversions

• Every increase of 3 decibels results in a doubling of intensity

• E.g. 104 W/m2 rising to 208 W/m2 is an increase of 3dB

• . 312 W/m2 rising to 1248 W/m2 is an increase of 6dB (ie 70dB to 76dB)

X-Rays• Electrons jump from the

surface of a hot metal –

• Thermionic 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

published scientist but the relativity stuff had not set the world alight.

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

The Problem• If you shine light on the surface of

metals electrons jump off

Polished Sodium Metal

e

e

e

e

e

• 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 Effect

The 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

could 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 combined 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

H/W gets serious

• Higher 2008 Q9• Higher 2002 Q7• 2005 HL Q7• 2003 Q 7 HL