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Announcements 2/16/11

Announcements 2/16/11. Prayer Exams… hopefully graded by Friday Extra time on Lab 3: now due Tues Feb 22. Monday Feb 21 is President’s Day holiday. Tues Feb 22 is a virtual Monday

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Announcements 2/16/11

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  1. Announcements 2/16/11 • Prayer • Exams… hopefully graded by Friday • Extra time on Lab 3: now due Tues Feb 22. • Monday Feb 21 is President’s Day holiday. • Tues Feb 22 is a virtual Monday • Remember in HW 17-5b to be very careful to track the correct peak when plotting it for t = 0.1 s and t = 0.5 s, and when calculating the velocity of the peak.

  2. Thought question • A wave at frequency ω traveling from a string to a rope. At the junction, 80% of the power is reflected. How much power would be reflected if the wave was going from the rope to the string instead? • Much less than 80% • A little less than 80% • About 80% • More than 80% • It depends on the color of the rope.

  3. Demo • Reflection at a boundary

  4. Dispersion Summary • A dispersive medium: velocity is different for different frequencies • Any wave that isn’t 100% sinusoidal contains multiple frequencies. • To localize a wave in space or time, you need lots of frequencies… really an infinite number of frequencies spaced infinitely closely together.

  5. Two Different Velocities • What happens if a wave pulse is sent through a dispersive medium? Nondispersive? • Dispersive wave example: • s(x,t) = cos(x-4t) + cos(2 (x-5t)) • What is “v”? • What is v for w=4? What is v for w=10? • What does that wave look like as time progresses? (next slide)

  6. 0.1 seconds 0.7 seconds 1.3 seconds Mathematica

  7. Time Evolution of Dispersive Pulse Note: frequencies are infinitely close together Credit: Dr. Durfee Power spectrum Peak moves at about 13 m/s (on my office computer) How much energy is contained in each frequency component Wave moving in time

  8. Phase and Group Velocity Credit: Dr. Durfee Window is moving along with the peak of the pulse Can be different for each frequency component that makes up the wave 12.5 m/s, for dominant component A property of the wave as a whole (peak) 13 m/s

  9. On Wikipedia • Example where vphase > vgroup http://en.wikipedia.org/wiki/Group_velocity

  10. Not yet on Wikipedia • Example where vphase is negative!

  11. Reading Quiz • Sound waves are typically fastest in: • solids • liquids • gases

  12. Sound Waves • What type of wave? What is waving? • Demo: Sound in a vacuum • Demo: tuning fork • Demo: Singing rod • Sinusoidal? • Demo: musical disk

  13. Speed of sound • Speed of sound… • in gases: ~300-1200 m/s (343 m/s for air at 20C) • in liquids: ~1000-1900 m/s • in solids: ~2000-6000 m/s • General form: v = sqrt(xxx/yyy) • What are “xxx” and “yyy”? • Speed of sound in air • Dependence on Temperature (eqn in book)

  14. Intensity • Intensity: power/area • Spherical Waves • Non-spherical waves? • Question: you measure the sound intensity produced by a spherically-emitting speaker to be 10 W/m2 at a distance of 2 meters. What will be the intensity at 8 meters away? • Question: What is the total sound power (watts) being produced by the speaker?

  15. Reading Quiz • How do we calculate the sound level in decibels? • β = 10 log( I / Io ) • β = 10 ( I / Io ) • β = 10 ( I - Io ) • β = 10 e( I / Io ) • β = e10 ( I / Io ) add 10 to b 10 to I

  16. Decibels Threshold of hearing 0 dB 10-12 W/m2 Whisper 30 dB 10-9 W/m2 Vacuum cleaner 70 dB 10-5 W/m2 Rock Concert 120 dB 1 W/m2 Nearby jet airplane 150 dB 1000 W/m2

  17. Thought Question • A 3 dB increase in intensity is just about a factor of 2. How many dB represents a factor of 4 increase in intensity? • 2 • 4 • 6 • 8 • 9

  18. Logarithm Review • Log10(x) is the inverse of 10y → if x = 10y then y = log10(x) • I.e. “10 to the what equals 22?” answer: 1.3424 (log(22)) • Review of “Laws of Logs”: • 1. log(ab) = log(a) + log(b) • 2. log(an) = n log(a) • log10(100) = ? Translation: 10 to what number equals 100? • ln(100) = ? (“ln” = loge = log2.71828…) Translation: e to what number =100? (4.605…) • If the problem just says log(100)…could be either log10 or ln • Question: log10(1,000,000) = ? • Question: If log(3) = 0.477, what is log(300)?

  19. Power and Intensity Scales Power or Intensity • dB β = 10 log(I/I0) I0 = 10-12 W/m2 • dBW β = 10 log(P/P0) P0 = 1 W • dBm β = 10 log(P/P0) P0 = 1 mW What if you need to solve for I?

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