Waves By Neil Bronks Some definitions Crest 1

Waves By Neil Bronks

Some definitions… Crest 1) Amplitude – this is height of the wave. Trough 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)

Some definitions… Transverse waves are when the displacement is at right angles to the direction of the wave… e. g. Light Longitudinal waves are when the displacement is parallel to the direction of the wave… e. g. Sound

Transverse waves are when the oscillation is at 90 o 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 Equation The 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 Remember Frequency – this is how many waves pass by a point every second and is measured in Hertz (Hz) Using this formula we can convert any wavelength to a frequency.

Some example wave equation questions 1) A water wave has a frequency of 2 Hz and a wavelength of 0. 3 m. How fast is it moving? 0. 6 m/s 2) A water wave travels through a pond with a speed of 1 m/s and a frequency of 5 Hz. What is the wavelength of the waves? 0. 2 m 3) The speed of sound is 330 m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound? 0. 5 m 4) Purple light has a wavelength of around 6 x 10 -7 m and a frequency of 5 x 1014 Hz. What is the speed of purple light? 3 x 108 m/s

Refraction through a glass block: Wave slows down and bends towards the normal due to entering a more dense medium Wave slows down but is not bent, due to entering along the normal Wave speeds up and bends away from the normal due to entering a less dense medium

Refraction 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 diagrams 1) Reflection 2) Refraction 3) Refraction 4) Diffraction

H/W Higher 2008 Q 9

Diffraction is when waves spread out from the edge of an obstacle or through a gap. More diffraction if the size of the gap is similar to the wavelength More diffraction if wavelength is increased (or frequency decreased) Sound bends better around corners

Finding the Critical Angle… 1) Ray gets refracted 3) Ray still gets refracted (just!) THE CRITICAL ANGLE 2) Ray still gets refracted 4) Ray gets internally reflected

Uses of Total Internal Reflection Optical 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 reflection 1) Endoscopes (a medical device used to see inside the body): 2) Binoculars and periscopes (using “reflecting prisms”)

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

Other uses of ultrasound 1) Echo sounding The ultrasound is reflected from the sea floor. 2) Breaking down kidney stones Ultrasonic 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 Each type of radiation shown in the electromagnetic spectrum has a different wavelength and a different frequency: High frequency, short wavelength Gamma rays X-rays Low frequency, long wavelength Ultra violet Visible light Infra red Microwaves Radio/TV γ 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). 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 100 years • 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 work Microwaves 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 ( ) rays X-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 1 Wave 2 Resultant wave

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/W Higher 2002 Q 7

White Light Interference

Diffraction only works when wavelength is about same as gap

Proving the wave nature of Light To get two n=1 n=0 n=1 Constructive Interference coherent sources (same frequency and phase) we use one source and two slits. The interference patterns prove light is a wave.

Internet Example

Equation for n=1 d • d = 1/(N x 1000) (Grating Const lines/mm) n=1 So one wavelength difference Constructive Interference

Equation • sin = /d • d sin = d • When more than one wavelength difference • d sin = n Goes to first spot on screen - constructive interference

For the n d th n dot • 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=3 n=1 n=2 n=0 n=2 n=3 3 wavelengths difference in path

MEASUREMENT OF THE WAVELENGTH OF MONOCHROMATIC LIGHT Metre stick Laser θ Diffraction grating D Tan θ = x/D n = 2 n = 1 x n = 0 n = 1 n = 2

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 Q 7

Polarization of Light Normally 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

Polarisation Transverse waves are plane-polarised if the vibrations stay in one plane of oscilation only. Longitudinal waves cannot be polarised.

Polarizing Filters Polarisation is the taking a transverse wave that oscillates in all perpendicular planes and filtering it so it oscillates in only one perpendicular plane. Hydrocarbons that absorb light that is in it’s plane of orientation.

Uses of polarisation • Finding faults/stress points in clear plastic model • Sending 2 signals of same frequency

Stationary Waves No net transfer of energy

Stationary Waves Caused by two waves of the same amplitude and frequency traveling in opposite directions meet the waves combine to form a stationary wave We draw this as the two extremes n A

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

Real Standing Waves Strings /2 Closed Tubes /4 Open Tubes /2

MEASUREMENT OF THE SPEED OF SOUND IN AIR Vibrating Tuning fork λ = 4(l 1 + 0. 3 d) A l 1 N Graduated cylinder Tube Water

Method 1. 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) l 1 with a metre stick.

• An end correction factor has to be added to the length e = 0. 3 d, where d is the average internal diameter of the tube (measured using a vernier callipers). • Hence λ = 4(l 1 + 0. 3 d) • • c = f c = 4 f(l 1 + 0. 3 d). • 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 ½ 1. 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=length T=tension =mass/unit length

INVESTIGATION OF THE VARIATION OF FUNDAMENTAL FREQUENCY OF A STRETCHED STRING WITH LENGTH Vibrating Tuning Fork Paper rider l Sonometer Bridge

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 length f

INVESTIGATION OF THE VARIATION OF THE FUNDAMENTAL FREQUENCY OF A STRETCHED STRING WITH TENSION Vibrating Tuning Fork Paper rider Pulley Sonometer Bridge 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

Musical Notes Music waves have a regular shape where noise is irregular Three 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 cars Wave crests

Red Shift of Stars (Doppler in Light) The Sun Moved to longer wavelengths proving the star is moving away from us Oh Bugger!

Example. A train emits a whistle at 700 Hz what is the apparent frequency if it is traveling towards you at 30 m/s? (c=340 m/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 Q 7

Tuning Forks - Both prongs vibrate and create sound

Summary - Sound as a Wave Interference 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.

L O U D S O F T

Sound Intensity • Amount of sound energy passing through 1 m 2 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 10 W. What is its intensity at 2 m away? Area of Sphere = 4 r 2 = 4 x 3. 142 x 4 = 50. 2 m 2 If we look in the log book the units of Sound intensity is W/m 2 this gives us the calculation. Sound Intensity Level=10 W/50. 2 m 2 =0. 2 W/M 2

Sound Intensity Level • This is to measure the very large range of energy levels the ear can respond to, measured in decibels (d. B). This is an exponential scale so if the energy doubles the level goes up by e d. B. • Home CD player 75 d. B tops but a good rock band maybe 110 d. B. • Health and safety tell us that if you stay in an environment above 85 d. B 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 d. B (decibels). • The measure of a ratio of two sound intensities is • where J 1 and J 0 are the intensities. • The sound intensity level is given the letter "LJ" and is measured in "d. B". Decibels (d. B) are dimensionless.

• If J 0 is the standard reference sound intensity, where • (W = watt), then instead of "d. B" we use "d. B SIL". (SIL = sound intensity level). • We also have d. BA, 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 1 k. Hz.

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/m 2 rising to 208 W/m 2 is an increase of 3 d. B • . 312 W/m 2 rising to 1248 W/m 2 is an increase of 6 d. B (ie 70 d. B to 76 d. B)

High Tension Voltage +- X-Rays • Electrons jump from the surface of a hot metal cathode – • Thermionic Emission Accelerated by high voltage they smash into tungsten target anode to produce x-rays Most of the electron energy is lost as heat. -about 90% X-rays very penetrating, fog film, not effected by fields.

Photons • Bohr first suggested a model for the atom based on many orbits at different energy levels E 2 E 1

Photons • If the electron in E 1 is excited it can only jump to E 2 E 1

Photons • Then the electron falls back. The gap is fixed so the energy it gives out is always the same E 2 E 1

Photons • So Max Planck said all energy must come in these packets called photons. • He came up with a formula for the frequency E 2 –E 1 = h. f E 2 E 1 Where f=frequency h= Planck’s constant

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 e e e Polished Sodium Metal • Electrons emitted • This is The PHOTOELECTRIC EFFECT

We can prove this with the experiment below

A negatively 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 Electron Energy Newtonian Physics could not explain this Frequency of light

Einstein’s Law So 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 Electron Energy f 0=Threshold Frequency of light Energy of incident photon = h. f 0+ KE of electron Work Function, Energy to release Electron Energy left over turned into velocity

Primary and secondary colours • A secondary colour is 2 primary colours mixed • Complimentary are that combine to make white 125

Class Challenge • • Why is the book red What is absorbed and what reflected It I shone red light on it… If I shone green light……

Reflection Wave bouncing off a solid object Refraction Waves changing speed and direction due to change in density of medium Diffraction spreading of a wave around an obstacle or on the emergent side of a slit. Interference Polarisation Two coherent waves meeting combined wave at any point is the algebraic sum of the two waves Echo Frequency stays the same Better with long wavelength Sound round corners Spreading from slit Proves things are waves Constructive and destructive Reduces transverse Difference waves to one plane between transverse of oscillation and longitudinal Hear people across a lake Snow sunglasses

H/W gets serious • • Higher 2008 Q 9 Higher 2002 Q 7 2005 HL Q 7 2003 Q 7 HL