Waves Intro Chapter 25

Vocabulary Wave Medium Pulse Vibratory disturbance that propagates (moves) through a medium Medium Material through which a wave propagates Pulse Single disturbance

Waves Waves transfer energy from one place to another, not mass

Wave Types Two main types Transverse Longitudinal Motion of the disturbance is perpendicular to the direction of the wave propagation Longitudinal Motion of the disturbance is parallel to the direction of the wave propagation

Transverse Waves Motion of the disturbance is perpendicular to the direction of the wave propagation Example: Light TRANSVERSE WAVES

Longitudinal Waves Motion of the disturbance is parallel to the direction of the wave propagation Example: Sound LONGITUDINAL WAVES

Surface Waves Combination of transverse and longitudinal waves Example: Water

Water Waves (surface)

Wave Characteristics Amplitude, A (m) Wavelength, λ (m) Period, T (s) Displacement away from equilibrium point Wavelength, λ (m) Length of 1 wave cycle Period, T (s) Amount of time for 1 wave cycle

Wave Characteristics (cont) Crest λ (m) A T (s) Trough

Wave Characteristics (cont) Frequency, f (Hz or s-1) Number of cycles per second Inverse of period Speed, v (m/s) How fast wave is traveling Related to frequency (period) and wavelength

Equations f = frequency (Hz) T = period (s) v = speed (m/s) λ = wavelength (m)

Light Light is also called electromagnetic radiation Light is a combination of fluctuating electric fields and magnetic fields that are perpendicular to each other

Electromagnetic Spectrum

Electromagnetic Spectrum R Radiowave M Microwave I Infrared V Visible U Ultraviolet X X-Rays G Gamma C Cosmic Wavelength Decreases Frequency Increases Energy Increases

Light (cont) Transverse Wave Travels through vacuum Color is based on frequency Green Light = 5.6 x 1014 Hz Speed of light in a vacuum (air also) c = 3 x 108 m/s

Sound Longitudinal Wave Needs a material (medium) to move Pitch is based on frequency Concert A = 440 Hz Speed of Sound in air is dependent on Temp v = 331 m/s at STP

Wave Speed Waves must follow the kinematic equation The speed of waves depends upon the material that the wave travels through

Wave Speed Sound can not travel in a vacuum, light can Light travels fastest in a vacuum, slower in all other materials Sound travels faster in more dense materials

Phase Difference Two points are considered “in phase” when they are at the same point in a wave cycle The amount of “in or out of phase” is measured in degrees

Phase Difference Examples What point is in phase with A? B and D are how far out of phase? Name two other points in phase with each other.

Wave Motion Waves propagate in all directions without barriers

Wave Fronts Line that represents waves that are all in phase, usually crests

Principle of Superposition When two waves meet, they combine together briefly, then go their separate ways Crest + crest = bigger amplitude Trough + trough = bigger amplitude Crest + trough = lower amplitude

Interference Constructive Interference Destructive Interference When 2 waves interfere with resultant wave having larger amplitude Destructive Interference When 2 waves interfere with resultant wave having smaller amplitude

Simulation Examples http://www.surendranath.org/Applets/Waves/TWave02/TW02.html

Interference Example Two point sources (green dots) What do the red dots represent? What do the blue dots represent?

Sound Beats Interference produced when two sounds interact Frequency of beats is equal to difference of frequencies of two sounds Concept used to tune pianos Demo

Doppler Effect Change in frequency due to moving wave source or observer Example

Doppler Effect When distance between source and observer is decreasing, frequency increases Blue Shift When distance between source and observer is increasing, frequency decreases Red Shift

Sonic Boom When moving object exceed the speed of sound, air builds up into a shock wave

Sonic Boom

Standing Waves Occurs when two waves traveling in opposite directions in the same medium, with the same amplitude and same frequency Resultant wave appears to be standing still Demo

Nodes and Antinodes Nodes Antinodes Points of maximum destructive interference Antinodes Points of maximum constructive interference

Nodes and Antinodes

Nodes and Antinodes

Video YouTube Video How does this work?

Resonance Natural Frequency Resonance Particular frequency that every elastic body will vibrate at if disturbed Resonance Vibration of a body at its natural frequency because of the action of a vibrating source of the same frequency

Real Life Microwaves produce waves that have the same frequency as the vibrational frequency of water molecules UV rays have the same frequency as certain chemicals in human skin, causing sun burns Google – Tacoma Narrows Bridge

Sound Chapter 26

Vocabulary Wave Medium Pulse Vibratory disturbance that propagates (moves) through a medium Medium Material through which a wave propagates Pulse Single disturbance

Waves Waves transfer energy from one place to another, not mass Sound must have a medium to travel through Sound can not travel in a vacuum No Sound is space

Longitudinal Waves Motion of the disturbance is parallel to the direction of the wave propagation Example: Sound LONGITUDINAL WAVES

Longitudinal Waves Compression – area of compacting molecules Rarefaction – area of low pressure between compressions LONGITUDINAL WAVES

Wave Characteristics Amplitude, A (m) Wavelength, λ (m) Period, T (s) Displacement away from equilibrium point Wavelength, λ (m) Length of 1 wave cycle Period, T (s) Amount of time for 1 wave cycle

Wave Characteristics (cont) Crest λ (m) A T (s) Trough

Wave Characteristics (cont) Frequency, f (Hz or s-1) Number of cycles per second Inverse of period Pitch is based on frequency Concert A = 440 Hz Human Hearing ranges from 20-20,000 Hz

Equations f = frequency (Hz) T = period (s) v = speed (m/s) λ = wavelength (m)

Speed of Sound The speed of sound depends upon the material that it travels through Sound travels faster in more dense materials Speed of Sound in air is dependent on Temp v = 331.5 m/s at STP

Echo Reflection of sound bouncing off an object Radar and Sonar use this concept Remember: time to hear echo is for double distance (there and back again)

Doppler Effect Apparent change in frequency due to moving wave source or observer When distance between source and observer is decreasing, frequency increases Blue Shift When distance between source and observer is increasing, frequency decreases Red Shift Example

Interference When two waves meet, they combine together briefly, then go their separate ways Constructive Interference When 2 waves interfere with resultant wave having larger amplitude Destructive Interference When 2 waves interfere with resultant wave having smaller amplitude

Sound Beats Interference produced when two sounds interact Frequency of beats is equal to difference of frequencies of two sounds Concept used to tune pianos Demo

Standing Waves Occurs when two waves traveling in opposite directions in the same medium, with the same amplitude and same frequency Nodes Points of maximum destructive interference Antinodes Points of maximum constructive interference

Nodes and Antinodes

Nodes and Antinodes

Resonance Natural Frequency Resonance Particular frequency that every elastic body will vibrate at if disturbed Resonance Vibration of a body at its natural frequency because of the action of a vibrating source of the same frequency

Harmonics Fundamental Frequency(1st Harmonic) Lowest frequency possible 2nd Harmonic 2x frequency of 1st Harmonic (Octave higher)

Closed Pipe Harmonics 1st Harmonic L = 1/4 3rd Harmonic L = ¾  5th Harmonic L = 1 1/4   = 4/5L

Open Pipe Harmonics 1st Harmonic L = ½ =2L 2nd Harmonic L =  3rd Harmonic L = 1 ½  =2/3L

Light and Color Chapters 27 & 28

Review Wavelength Frequency Period Amplitude Length of one wave cycle Number of cycles per second Period Amount of time for one cycle Amplitude Displacement away from equilibrium point

Wave Characteristics (cont) Crest λ (m) A T (s) Trough

Equations f = frequency (Hz) T = period (s) v = speed (m/s) λ = wavelength (m)

Transverse Waves Motion of the disturbance is perpendicular to the direction of the wave propagation Example: Light TRANSVERSE WAVES

Light Light is also called electromagnetic radiation Light is a combination of fluctuating electric fields and magnetic fields that are perpendicular to each other

Light (cont) Transverse Wave Travels through vacuum Color is based on frequency Green Light = 5.6 x 1014 Hz Speed of light in a vacuum (air also) c = 3 x 108 m/s

Light How long does the light from the sun take to each Earth? 500s ~8min

Electromagnetic Spectrum

Electromagnetic Spectrum R Radiowave M Microwave I Infrared V Visible U Ultraviolet X X-Rays G Gamma C Cosmic Wavelength Decreases Frequency Increases Energy Increases

Light Light Year Distance light travels in one year 9.46x1015m

Color Color of light is based on frequency Color Addition (Light) All colors added together produces white light Color Subtraction (Art) All colors “added” together produce black

Primary Colors Red, Green, Blue Red + Blue =Magenta Red + Green = Yellow Blue + Green = Cyan Secondary Colors

Complementary Colors Two Colors that when added together produce white Blue + Yellow Green + Magenta Red + Cyan

Polarization Process by which non-polarized light is transformed into polarized light Doesn’t work for sound Polarized Light has the wave vibrations occurring in a single plane

Polarization Non-polarized light has wave vibrations in all directions

Reflection Chapter 29

Reflection When a wave encounters a new medium or barrier some of the wave is bounced back (reflected), and some is transmitted (refracted) Simulation

Law of Reflection Angle of Incidence = Angle of Reflection θi = θr Always measured from Normal(Perpendicular) θi θr

Types of Reflection Regular Reflection Diffuse Reflection Reflection of light from a smooth surface Diffuse Reflection Reflection of light from a rough surface

Image Types Real – Light rays actually travel to that location Virtual – Light appears to be at that location Upright – image is right side up compared to object Inverted – image is upside down as compared to object

Plane (flat) Mirror Mirror The light we see appears to originate from the other side of the mirror

Curved Mirrors Concave Mirrors Convex Mirrors Can produce real or virtual images Rear View Mirrors on Cars Convex Mirrors Always produce virtual images Image is always smaller

Curved Mirrors Portion of a circle Center of Curvature (C) is located at the center of the Circle Focal Length (focal point) (f) is located halfway between the center of curvature and the mirror along the optical axis C f

Concave Mirrors Drawing Ray Diagrams Any ray entering through the center of curvature will, after interaction with the optical device (mirror), leave (or appear to leave) through the center of curvature C f

Concave Mirrors Drawing Ray Diagrams Any ray entering parallel to the optical axis will, after interaction with the optical device (mirror), leave (or appear to leave) through the focal point C f

Concave Mirrors Drawing Ray Diagrams Any ray entering through the focal point will, after interaction with the optical device (mirror), leave (or appear to leave) parallel to the optical axis C f

Concave Mirrors C f

Convex Mirrors Same Rays as concave C f

Mirror Simulation Simulation

Mirrors Object distance, do Image distance, di Where the object is located Image distance, di Where the image is located Negative distance is located “inside” mirror, opposite side

Mirrors Object size, So Image size, Si Negative means inverted

Mirror Equations M = Magnification

Review Law of Reflection Angle of Incidence = Angle of Reflection θi = θr

Distance Positive distance is in front of mirror Object distance, do=o Where the object is located, distance from mirror Image distance, di=i Where the image is located, distance from mirror Positive distance is in front of mirror Negative distance is located “inside” mirror, opposite side, behind mirror

Size Object size, So Image size, Si Magnification, M Is image bigger or smaller Negative means inverted

Images All real images Virtual Images have a (+)di Have a (–)di Inverted, (-)M Virtual Images Have a (–)di Upright, (+)M

Principle Rays for Curved Mirrors In parallel, out through focal point (f) In through Focal point (f), out parallel In through Center of Curvature (C), out through Center of Curvature (C) Incident at center of mirror, reflected at same angle out from center of mirror

Refraction Chapters 29

Question Imagine running down the road how fast are you going? Imagine running in thick mud Thicker Material How fast are you going? Speed decreases How long is your stride? Wavelength decreases

Refraction Changing of speed when wave enters new material (frequency remains constant) Speed decreases in more dense material Wavelength decreases Speed increases in less dense material Wavelength increases

Refraction Example Freqair=Freqwater because the color remains the same Since the wavelength changes, the velocity must change proportionately Air Water

Index of Refraction (n) Measure of the optical density of a material Table in the Reference Tables

Refraction When a wave enters a new medium, it changes speed. When a wave enters a new medium, it changes direction

Refraction

Refraction Simulation

Snell’s Law n1 sin θ1 = n2 sin θ2 Air Water θi θr

Snell’s Law When a wave enters a more dense material, the wave will bend TOWARDS the normal When a wave enters a less dense material, the wave will bend AWAY from the normal

Example n1 sin θ1 = n2 sin θ2 θr= 58.7° Air Water n = 1.00 n = 1.33 40°

Dispersion Spreading of light into its color components Index of refraction is based on frequency of light Index varies for different frequencies

Dispersion

Dispersion

Rainbows

Example θi= 47° θr= 76.6° θi= 48° θr= 81.3° Air Water n = 1.00 n = 1.33 θi= 47° θr= 76.6° θi= 48° θr= 81.3° θi= 49° θr= ? Is there a problem? θr=?

Critical Angle, θc At a certain incident angle the refracted ray will be at 90°. Total Internal Reflection At angles greater than the Critical Angle, the ray is reflected back into the material. θi Air Water n = 1.00 n = 1.33 θr

Critical Angle n1 sin θC = n2 sin θ2 sin θ2 = 1 n1 sin θC = n2

Total Internal Reflection For angles larger than the critical angle, all of the light is reflected inward Fiber Optic Cable

Lenses Chapter 30

Vocabulary Object distance, o Image distance, i Distance object is from optical device Image distance, i Distance image is from optical device

Vocabulary Object size, So Size of object Image size, Si Size of image

Vocabulary Real Image Image formed by actual intersection of light rays Image can be projected on a screen

Vocabulary Virtual Image (imaginary) Light rays do not travel to that location, only appear to travel there Image can NOT be projected on screen

Lenses Equation

Lenses Converging Lenses Diverging Lenses Biconvex f=(+) Biconcave

Converging Lens Rays Ray that is initially parallel to central axis will refract through far focal point Ray that is initially through near focal point will refract parallel to central axis Ray that passes through center of lens pass without refraction

Converging Lens

Converging Lens Example f = 10 cm i= ? o = 20 cm i= 20 cm M = 1

Diverging Lens Rays Ray that is initially parallel will refract as if coming from near focal point Ray that is initially through far focal point will refract as if coming from parallel Ray that passes through center will continue on

Diverging Lens

Diverging Lens Example o = 25 cm f = -10 cm i = ? i = -7.14 cm M = 0.3

Example Applet

How the Eye works Light enters the eye through the cornea Outer layer covering the eye (n=1.38) Travels through the aqueous humor fluid between cornea and lens Travels through the pupil Empty black space created by the Iris (colored part)

How the Eye works Refracted through the lens Travels through vitreous humor Fluid inside of the eye Image is on the retina Back of eye with light receptors Optic nerve transmits information to Occipital lobe of the brain where the image is interpreted

How the Eye works

Eye problems Nearsightedness (Myopia) Farsightedness (Hyperopia) Image is focused in front of the retina Farsightedness (Hyperopia) Image is focused behind the retina Astigmatism Irregular curvature of lens or cornea

Lenses in Combination Image from the first lens becomes the object for the second lens Microscope Telescope Galilean (refracting) Keplerian (refracting) Newtonian (reflecting)

Lenses in Combination

Lenses in Combination do1 = 25 cm f2 = 8 cm di2 = 12 cm f1 = 10 cm

Aberrations Distortions in an image Combining lenses can minimize the aberrations

Aberrations Spherical Aberrations Results when light passes through the edges of a lens (mirrors also)

Aberrations Chromatic Aberrations Different speeds of light for different colors

Diffraction Chapters 31

Wave Motion Waves propagate in all directions without barriers

Wave Fronts Line that represents waves that are all in phase, usually crests

Huygens Principle Every point on a propagating wave front serves as a source of a spherical secondary wavelet The corresponding spherical wavelets produce further wave fronts Basis for Diffraction, Reflection, Refraction

Huygens Principle

Huygens Principle

Huygens Principle First proposed explanation that light is a wave Newton later proposed that light is a particle

Diffraction Bending of waves around an obstacle or the edges of an opening Example: You can often hear people in the hallway without seeing them Shadows

Sound Diffraction

Diffraction

Diffraction

Diffraction Causes interference patterns a certain distance away from the source Bright and dark spots for light Loud and dead spots for sound Amount of diffraction is a measure of distance between consecutive bright spots

Young’s Double Slit Experiment Proof that light acts like a wave Light shining through 2 slit opening Bright and dark lines on screen

Diffraction Equation x = amount of diffraction λ = wavelength L = distance from opening to screen d = distance between slits d<<L

Examples Applet Laser Pointer

Path Difference

Path Difference For Maximum Constructive Interference the path difference is nλ For Maximum Destructive Interference, the path difference is (n +1/2)λ