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Notes on Waves

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Waves are ENERGY! Travel through medium (Electromagnetic waves can travel through vacuum.) Medium doesn’t move, only energy travels

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Two Types of Waves Transverse – oscillates perpendicular to the direction of travel Longitudinal – oscillates parallel to the direction of travel (AKA Compressional)

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Properties of Transverse Waves Crest – the high point of the wave Trough – the low point of the wave Wavelength – the distance from crest to crest, or trough to trough. Amplitude – the height of the wave, from midpoint (equillibrium) to crest, or midpoint to trough Notes on Waves

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There are 2 ½ waves in the above wave train.

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Examples of Transverse Waves Water waves; wave on a string; electromagnetic waves (e.g. radio waves, television signals, infrared waves, visible light, ultraviolet radiation, microwaves, x-rays); S-waves (earthquakes)

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These waves must travel through a medium Compression – regions where the molecules in the medium are bunched together Rarefaction – regions where the molecules in the medium are spread apart Wavelength – the distance from compression to compression Amplitude – the distance that any one molecule is pushed away from equillibrium Properties of Longitudinal Waves Notes on Waves

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Examples of Longitudinal Waves Waves through a slinky, sound waves, shock waves, P-waves (earthquakes)

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Earthquake Damage Vertical S-waves Lateral S-waves

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Period & Frequency Period – How long it takes for a single wave cycle; measured in seconds, minutes, hours, days, etc. (abbr.= T ) Frequency – The number of wave cycles in one second; measured in Hertz 1 Hz = 1 cycle/s (abbr. = f ) f = 1/T and T = 1/f Notes on Waves

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Example problem : An ocean wave has a period of 8 seconds. What is the frequency of that wave? Period & Frequency Notes on Waves f = 1/T = 1/ 8 seconds = 1/8 Hz = 0.125 Hz

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Wave Speed Waves travel at different speeds through different media. Notes on Waves Gases Materialv (m/s) Hydrogen (0°C)1286 Helium (0°C)972 Air (20°C)343 Air (0°C)331 Liquids at 25°C Materialv (m/s) Glycerol1904 Sea water1533 Water1493 Mercury1450 Solids Materialv (m/s) Diamond12000 Pyrex glass5640 Iron5130 Aluminum5100 Brass4700 Copper3560 Gold3240

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Wave Speed Notes on Waves

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Wave Speed Example problem A blue whale bellows in the deep ocean with a frequency of 15 Hz. If the wave has a length of 100.3 m, what is the speed of sound in the ocean? Notes on Waves

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o Reflection – when waves bounce off of a surface o Refraction – when waves change speed (and often direction) as they travel through different media. o Diffraction – when waves bend around corners o Interference – when waves interact with other waves Constructive Interference – when two (or more) waves meet to make a bigger wave Destructive Interference – when two (or more) waves meet to make a smaller wave Waves Behavior Notes on Waves

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Reflection – when waves bounce off of a surface Notes on Waves The angle of incidence equals the angle of reflection.

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Refraction – when waves change speed (and often direction) as they travel through different media. Notes on Waves

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Refraction In which medium does light travel faster? (glass rod appears bent)

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Speed of Light v is the speed of light in the new medium. c= 3.0 x 10 8 m/s As the index increases the speed decrease. Draw a graph for index vs. speed. n is the absolute index of refraction. This is a measure of optical density. n is defined as the ratio of the speed of light in a vacuum to the speed of light in a new medium.

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Relative Index of Refraction n is the relative index of refraction. If air is not used, then remember n rel = n 2 /n 1 What is the relative index when going from diamond into lucite? If n rel < 1 ; speeds up If n rel > 1 ; slows down

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Refraction V w = 2.26 x 10 8 m/s V g = 2.00 x 10 8 m/s Calculate the speed of light in water and glass. n (water) =1.33; n (glass) =1.50; n (air) =1.00

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Refraction When a wave slows down it bends closer to the normal. {less to more – toward} n2>n1 When a wave speed up it bends away from the normal. {BLA – Big ― › Little – Away} n2<n1 n 1 - from n 2 - into

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Refraction If light rays bend closer to the normal when slowing down, why does the glass rod seem to bend away form the normal?

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Apparent Depth Diverging rays enter your eyes. You “think” in Straight Lines. A virtual image appears to come from point y R – Real Depth A – Apparent Depth

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Apparent Depth If the chest is 20 m below the surface at what depth will the image appear? Assume n sea water = 1.34

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Snell’s Law n 1 sin θ 1 = n 2 sin θ 2 v 1 /v 2 = λ 1 / λ 2

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Example A monochromatic light ray f = 5.09 x 10 14 Hz is incident on medium X at 55˚. The absolute index of refraction for material X is 1.66 1. What is material X? 2. Determine the angle of refraction. 3. Determine the speed of light in medium X.

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Ex: Solution The index of 1.66 is Flint Glass To find the angle of refraction use Snell’s Law. θ 2 = 30˚ To find the speed use n=c/v. v = 1.8 x 10 8 m/s v = 1.8 x 10 8 m/s

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Diffraction – when waves bend around corners Notes on Waves

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Interference – when waves interact with other waves Constructive Interference – when two (or more) waves meet to make a bigger wave Destructive Interference – when two (or more) waves meet to make a smaller wave Notes on Waves Constructive Interference Destructive Interference

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Constructive and Destructive Interference

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Doppler Effect Notes on Waves. The frequency (and wavelength) of a wave changes depending upon how the observer of the waves is moving relative to the source of the waves

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Notes on Waves: Doppler Effect If the source is traveling towards the observer, the wavelength is smaller and the frequency is higher than if the observer and source had the same velocity. If the source is traveling away from the observer, the wavelength is larger and the frequency is lower than if the observer and source had the same velocity. YouTube Video

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Notes on Waves: Doppler Effect If the source is traveling towards the observer, the wavelength is smaller and the frequency is higher than if the observer and source had the same velocity. If the source is traveling away from the observer, the wavelength is larger and the frequency is lower than if the observer and source had the same velocity. Speed of Sound in air = 343 m/s

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Notes on Waves: Doppler Effect Remember that the Doppler Effect applies to ALL waves, including electromagnetic waves (light!). When applied to light the Doppler effect is referred to as either a Red Shift or a Blue Shift. It is by studying this data from surrounding stars and galaxies, that we know that the universe is expanding. Most stars and galaxies exhibit a Red Shift.

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Speed of sound in dry air @ 20˚C = 343 m/s = 1,126 ft/s = 768 mph Speed of light in a vacuum ~ 3.0 x 10 8 m/s = 186,282 mph Notes on Waves Good Numbers to Know:

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