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Physics AP-B: Waves

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?”. Waves Overview. Types Speed Traveling (“harmonic”) Superposition

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Physics AP-B: Waves

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  1. 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?”

  2. Waves Overview • Types • Speed • Traveling (“harmonic”) • Superposition • Standing 05

  3. 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 Types of Waves slinky demo 8

  4. 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 “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.” 12

  5. 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 Slinky stretches more, so it has a smaller mass/length m. Slinky-spring demo 17

  6. Wavelength  Amplitude A A 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 y x 20

  7. 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 f = v / l 22

  8. +2 3p/4 p/4 p / 2 t -2 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 25

  9. correct 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 = v T 26

  10. 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

  11. 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

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

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

  14. Reflection • 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 Reflection/standing wave demo “I don't understand the picture with free boundary versus fixed boundary” 37

  15. Standing Waves Fixed Endpoints • Fundamental n=1 (2 nodes) • ln = 2L/n • fn = v/l =n v / (2L) 44

  16. L = l / 2 f = v / l tells us v if we know f (frequency) and l (wavelength) Standing Waves: 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 329.63 Hz, what is the mass of the string? 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) (329.63 s-1) = 428.5 m/s 48

  17. Summary • Wave Types • 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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