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Introduction to Waves and Wave Motion

This lecture provides an overview of waves and wave motion, covering topics such as superposition, overtones, transverse and longitudinal waves, harmonics, wavelength, amplitude, period, velocity, and standing waves. The lecture also includes practice problems to reinforce understanding.

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Introduction to Waves and Wave Motion

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  1. Exam 3 Physics 101: Lecture 21 Waves • Today’s lecture will cover Textbook Chapter 11

  2. Preflight 5 Which concepts did you find the most difficult when preparing for this lecture? Superposition and interference Waves and wave motion in general are difficult for me to grasp… Overtones…

  3. Waves Overview • Types • Speed • Harmonic • Superposition • Standing 05

  4. Transverse: The medium oscillates perpendicular to the direction the wave is moving. • Water (more or less) • Slinky demo • Longitudinal: The medium oscillates in the same direction as the wave is moving • Sound • Slinky demo Types of Waves “Understanding all the different kinds of waves.” “I have a hard time visualizing what a period is.” 8

  5. correct 5m 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 totally guessing here, but I LOVE SLINKYS!! 5 m/s isn't the distance one coil moves, its how fast the wave moves 12

  6. Velocity of Waves Act 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 Slinky stretches more, so it has a smaller mass/length m. 17

  7. Wavelength  Amplitude A A Harmonic Waves “the weird/new symbols get me confused i never know what they represent “ 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 y x 20

  8. 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 22

  9. +2 3p/4 p/4 p / 2 t -2 Harmonic 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 = 1.58 25

  10. correct Preflight 1+2 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 26

  11. 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

  12. H H Makes water molecules wiggle O ACT Solution • Recall that v = lf. 1 GHz = 109 cycles/sec The speed of light is c = 3x108 m/s 30

  13. Visible f = 10 GHz “water hole” Absorption coefficientof water as a functionof frequency. 31

  14. Interference and Superposition • When two waves overlap, the amplitudes add. • Constructive: increases amplitude • Destructive: decreases amplitude 34

  15. Reflection Act • 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 I don't understand the picture with free boundary versus fixed boundary 37

  16. Standing Waves Fixed Endpoints • Fundamental n=1 (2 nodes) • ln = 2L/n • fn = n v / (2L) I did not really understand what the point or meaning of the fundamental frequency was. 44

  17. L = l / 2 f1= fundamental frequency (lowest possible) f = v / l tells us v if we know f (frequency) and l (wavelength) Standing Waves: 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 329.63 Hz, what is the mass of the string? v2 = T / m m = T / v2 m= T L / v2 = 82 (0.65) / (428.5)2 = 2.9 x 10-4 kg v = l f = 2 (0.65 m) (329.63 s-1) = 428.5 m/s 48

  18. Summary • Wave Types • Transverse (eg pulse on string, water) • Longitudinal (sound, slinky) • Harmonic • 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

  19. Practice Problems Chapter 11, probs 1, 9, 13, 15, 17, 21, 25, 29, 31, 33, 49, 57, 61, 65 (hard!), 77 (hard!)

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