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Physics AP-B: Waves “Waves seem to really confuse me, particularly what the variables refer to in the equations” “Pretty much the entire chapter is baffling. How do you plan on getting this all into one lecture?” 1

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**Waves Overview Types Speed Traveling (“harmonic”) Superposition**

Standing 05

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Types of Waves Transverse: The medium oscillates perpendicular to the direction the wave is moving. Water Longitudinal: The medium oscillates in the same direction as the wave is moving Sound Stadium wave here, for fun. slinky demo 8

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Slinky Preflight 3 Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the slinky move through a distance of five meters in one second? 1. Yes 2. No “It wouldn't make sense for one coil to move 5 meters … We're measuring the velocity of a wave traveling along the slinky, not the velocity of the slinky.” correct 5m 12

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Velocity of Waves Act Slinky demo A spring and slinky are attached and stretched. Compare the speed of the wave pulse in the slinky with the speed of the wave pulse in the spring. A) vslinky > vspring B) vslinky = vspring C) vslinky < vspring Long Spring and slinky equal length (8 feet each) speeds up a LOT in slinky because mu is small and T is same. Slinky stretches more, so it has a smaller mass/length m. Slinky-spring demo 17

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**Traveling (“harmonic”) Waves**

“you can explain the formula for y=Acos(wt-kx) and y=Asin(wt-kx) are these two the same or am i missing something here?” y(x,t) = A cos(wt–kx) Wavelength: The distance between identical points on the wave. Amplitude: The maximum displacement A of a point on the wave. Angular Frequency w: w = 2 p f Wave Number k: k = 2 p / l Recall: f = v / l Add stuff here Wavelength y Amplitude A A x 20

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**Period and Velocity f = v / l**

Period: The time T for a point on the wave to undergo one complete oscillation. Speed: The wave moves one wavelength in one period T so its speed is v = / T. f = v / l 22

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**Traveling Waves Exercise**

y(x,t) = A cos(wt –kx) Label axis and tic marks if the graph shows a snapshot of the wave y(x,t) = 2 cos(4t –2x) at x=0. Recall: T = 2 p /w T = 2 p / w = 2 p/ 4 = p/2 = 1.58 t +2 -2 Students make plot at x=0, give them line, they mark tics p / 2 p/4 3p/4 25

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Preflight 1+2 Suppose a traveling wave moves through some medium. If the period of the wave is increased, what happens to the wavelength of the wave assuming the speed of the wave remains the same? 1. The wavelength increases 2. The wavelength remains the same 3. The wavelength decreases correct = v T 26

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ACT The wavelength of microwaves generated by a microwave oven is about 3 cm. At what frequency do these waves cause the water molecules in your burrito to vibrate ? (a) 1 GHz (b) 10 GHz (c) 100 GHz 1 GHz = 109 cycles/sec The speed of light is c = 3x108 m/s 29

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**ACT Solution Recall that v = lf. H Makes water molecules wiggle O**

1 GHz = 109 cycles/sec The speed of light is c = 3x108 m/s 30

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**Absorption coefficient of water as a function of frequency.**

Visible Absorption coefficient of water as a function of frequency. f = 10 GHz “water window” 31

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**Interference and Superposition**

When two waves overlap, the amplitudes add. Constructive: increases amplitude Destructive: decreases amplitude Do this with springs 34

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**Reflection/standing wave demo**

A slinky is connected to a wall at one end. A pulse travels to the right, hits the wall and is reflected back to the left. The reflected wave is A) Inverted B) Upright Fixed boundary reflected wave inverted Free boundary reflected wave upright Use large spring as demo here Reflection/standing wave demo “I don't understand the picture with free boundary versus fixed boundary” 37

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**Standing Waves Fixed Endpoints**

Fundamental n=1 (2 nodes) ln = 2L/n fn = v/l =n v / (2L) Two people with large spring, can produce all of these as demo. 44

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**Standing Waves: v2 = T / m v = l f m = T / v2**

L = l / 2 f1 = fundamental frequency (lowest possible) A guitar’s E-string has a length of 65 cm and is stretched to a tension of 82N. If it vibrates with a fundamental frequency of Hz, what is the mass of the string? f = v / l tells us v if we know f (frequency) and l (wavelength) Calculate tension in guitar string given mass density and frequency. Ch 11 # 45 v2 = T / m m = T / v2 m= mL = T L / v2 = 82 (0.65) / (428.5)2 = 2.9 x 10-4 kg v = l f = 2 (0.65 m) ( s-1) = m/s 48

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**Summary Wave Types Traveling Superposition**

Transverse (eg pulse on string, water) Longitudinal (sound, slinky) Traveling y(x,t) = A cos(wt –kx) or A sin(wt – kx) Superposition Just add amplitudes Reflection (fixed point inverts wave) Standing Waves (fixed ends) ln = 2L/n fn = n v / 2L 50

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PHYSICS 231 INTRODUCTORY PHYSICS I

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