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Waves

Waves. Physics 202 Professor Lee Carkner Lecture 6. Suppose you are watching Jupiter’s moon Io in a telescope. Where will Io appear to be moving fastest across the sky?. When it is furthest away from Jupiter When it is closest to Jupiter

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Waves

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  1. Waves Physics 202 Professor Lee Carkner Lecture 6

  2. Suppose you are watching Jupiter’s moon Io in a telescope. Where will Io appear to be moving fastest across the sky? • When it is furthest away from Jupiter • When it is closest to Jupiter • When it is half the maximum distance away from Jupiter • The speed is the same everywhere • We can’t tell without more information

  3. Which of the following would increase the rate at which a damped system loses energy the most? • Doubling b • Doubling m • Halving b • Halving m • a and d only

  4. Imagine a swing with a resonance at a period of T. What other period will also produce resonance? • 1/10 T • ¼ T • ½ T • 2 T • 2.5 T

  5. PAL #5 Damped SHM • What is r if vmax = 13600 m/s and T = 3.6 days? • vmax = wxm so xm = vmax/w • w = 2p/T = 2p/(3.6)(24)(60)(60) = 2.02 X 10-5 rad/sec • xm = • What is mass of planet? • Gravitational force = centripetal force • GMm/r2 = mv2/r • M = v2r/G =

  6. Test Next Friday • About 15 multiple choice • Mostly concept questions • About 4 problems • Like PALs or homework • Bring calculator and pencil • Formulas and constants provided (but not labeled) • Worth 15% of grade

  7. What is a Wave? • Example: transmitting energy, • A sound wave can also transmit energy but the original packet of air undergoes no net displacement

  8. Transverse and Longitudinal • Transverse waves are waves where the oscillations are perpendicular to the direction of travel • Examples: • Longitudinal waves are waves where the oscillations are parallel to the direction of travel • Examples: • Sometimes called pressure waves

  9. Transverse Wave

  10. Longitudinal Wave

  11. Waves and Medium • The wave has a net displacement but the medium does not • This only holds true for mechanical waves • Photons, electrons and other particles can travel as a wave with no medium (see Chapter 33)

  12. Wave Properties • The y position is a function of both time and x position and can be represented as: y(x,t) = ym sin (kx-wt) • Where: • k = angular wave number

  13. Wavelength and Number • One wavelength must include a maximum and a minimum and cross the x-axis twice k=2p/l

  14. Period and Frequency • Frequency is the number of oscillations (wavelengths) per second (f=1/T) w=2p/T • The quantity (kx-wt) is called the phase of the wave

  15. Speed of a Wave y(x,t) = ym sin (kx-wt) • But we want to know how fast the waveform moves along the x axis: v=dx/dt • If we wish to discuss the wave form (not the medium) then y = constant and: • e.g. the peak of the wave is when (kx-wt) = p/2 • we want to know how fast the peak moves

  16. Wave Speed

  17. Velocity • We can take the derivative of this expression w.r.t time (t): • Since w = 2pf and k = 2p/l v = w/k = 2pfl/2p v = lf • Thus, the speed of the wave is the number of wavelengths per second times the length of each • i.e.

  18. Next Time • Read: 16.6-16.10 • Homework: Ch 16, P: 12, 15, 18, 24

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