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Wave Basics

Wave Basics. Textbook Chapter 12. What is a wave ?. According to our text: A wave is a disturbance that travels away from its source. Examples: Sound waves (air moves back & forth) Stadium waves (people move up & down) Water waves (water moves up & down) Light waves (what moves ??).

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Wave Basics

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  1. Wave Basics • Textbook Chapter 12

  2. What is a wave ? • According to our text: • A wave is a disturbance that travels away from its source. • Examples: • Sound waves (air moves back & forth) • Stadium waves (people move up & down) • Water waves (water moves up & down) • Light waves (what moves ??) 05

  3. Transverse: The medium oscillates perpendicular to the direction the wave is moving. • Water (really circles) • Spring Lab • Longitudinal: The medium oscillates in the same direction as the wave is moving • Sound • Spring Lab Types of Waves 10

  4. Waves on a String 11

  5. v correct Conundrum I A rope of mass M and length L hangs from the ceiling with nothing attached to the bottom (see picture). Suppose you start a transverse wave at the bottom end of the rope by giggling (sic) it a bit. As this wave travels up the rope its speed will: 1. Increase 2. Decrease 3. Stay the same 14

  6. Conundrum II Tceiling • Several masses are hung from the ceiling as shown. Compare the tension in the rope connected to the ceiling, with the tension in the rope connecting the bottom mass. • Tceiling > Tbottom • Tceiling = Tbottom • Tceiling < Tbottom Tbottom Tceiling = 5 MG Tbottom = 1 MG 16

  7. Harmonic Waves Where waves can go y(x,t) = A cos(wt –kx) A = amplitude w = angular frequency k = wave number = 2p/l 18

  8. Wavelength  Amplitude A A Amplitude and Wavelength • Wavelength: The distance  between identical points on the wave. • Amplitude: The maximum displacement A of a point on the wave. 19

  9. 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. Period and Velocity 21

  10. +2 3p/4 p/4 p / 2 t -2 Harmonic Waves Remember y(x,t) = A cos(wt –kx) Recall: T = 2 p /w T = 2 p / w = 2 p/ 4 = 1.58 Y(x,t) = 2 cos(4t –2x) 24

  11. Wave Properties... • The speed of a wave is a constant that depends only on the medium, not on amplitude, wavelength or period (similar to SHM) and T are related ! = v T or = 2v / (sinceT = 2 / or  = v / f (since T = 1/ f )  • Recallf = cycles/sec or revolutions/sec  = 2f v =  / T 26

  12. correct Conundrum III Suppose a periodic 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 = v T 28

  13. correct Conundrum IV The speed of sound in air is a bit over 300 m/s, and the speed of light in air is about 300,000,000 m/s. Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of the frequency of the light wave to that of the sound wave? 1. About 1,000,000. 2. About 1,000. 2. About .000,001 f = v/ fL/fS = vL/vS = 1,000,000 fS = 100 Hz (~ really low G) fL = 100 MHz (FM radio) 29

  14. correct 5m Conundrum V 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 no single coil on the slinky will move anywhere near 5 meters. Rather many coils will move many smaller distances in shorter times to create the wave that has a speed of 5 meters per sec. 31

  15. Conundrum VI • 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 34

  16. H H Makes water molecules wiggle O Solution • Recall that v = lf. 1 GHz = 109 cycles/sec The speed of light is c = 3x108 m/s 35

  17. Visible f = 10 GHz “water hole” Absorption coefficientof water as a functionof frequency. 36

  18. Interference and Superposition • When too waves overlap, the amplitudes add. • Constructive Interference: increases amplitude • Destructive Interference: decreases amplitude 40

  19. Reflection at Boundary • When a wave travels from one boundary to another, reflection occurs. Some of the wave travels backwards from the boundary • Traveling from fast to slow inverted • Traveling from slow to fast upright 43

  20. Transmission at Boundary • Fast to slow • Wave amplitude decreases • Wave length decreases • Slow to fast • Wave amplitude decreases • Wave length increases

  21. Standing Waves • Fundamental n=1 • n = # Loops • Loop = ½ λ • ln = 2L/n • fn = n v / (2L) 45

  22. L = l / 2 f1= fundamental frequency (lowest possible) f = v / l tells us f if we know v and l L = l f2= first overtone Standing Waves: HW: String 48

  23. Summary • Wave Types • Transverse (i.e. pulse on string, water) • Longitudinal (sound, slinky) • Superposition • Just add amplitudes • Reflection (fast to slow gets inverted) • Transmission • Standing Waves • ln = 2L/n • fn = n v / 2L 50

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