1. Announcements 10/11/10 Prayer Exams… not graded all the way yet, hopefully by tomorrow. Matt Allen, Jake Peery: Are you present? See me ASAP. HW notes: a. a.As said in email: must turn in actual printouts when problem says, “Use a computer program such as Mathematica…” b. b.As said in later email: if can’t get printer to work, can send plots to grader via email (Chris’s email address is on class website) c. c.As said in still later email: “how to print” instructions given, so try those before sending plots to Chris by email.

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

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

4. Wikipedia Example where v phase > v group http://en.wikipedia.org/wiki/Group_velocity

5. 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? a. a.Much less than 80% b. b.A little less than 80% c. c.About 80% d. d.More than 80% e. e.It depends on the color of the rope.

6. Demo Reflection at a boundary

7. Reading Quiz Sound waves are typically fastest in: a. a.solids b. b.liquids c. c.gases

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

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

10. Intensity Intensity: power/area a. a.Spherical Waves b. b.Non-spherical waves? Question: you measure the sound intensity produced by a spherically-emitting speaker to be 10 W/m 2 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?

11. Reading Quiz How do we calculate the sound level in decibels? a. a.β = 10 log( I / Io ) b. b.β = 10 ( I / Io ) c. c.β = 10 ( I - Io ) d. d.β = 10 e ( I / Io ) e. e.β = e 10 ( I / Io ) add 10 to    10 to I

12. Decibels Threshold of hearing0 dB10 -12 W/m 2 Whisper30 dB10 -9 W/m 2 Vacuum cleaner70 dB10 -5 W/m 2 Rock Concert120 dB1 W/m 2 Nearby jet airplane150 dB1000 W/m 2

13. 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? a. a.4 b. b.6 c. c.9 d. d.12 e. e.None of the above

14. Logarithm Review Log 10 (x) is the inverse of 10 y → if x = 10 y then y = log 10 (x) a. a.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(a n ) = n log(a) log 10 (100) = ? Translation: 10 to what number equals 100? ln(100) = ? (“ln” = log e = log 2.71828… ) Translation: e to what number =100? (4.605…) If the problem just says log(100)…could be either log 10 or ln Question: log 10 (1,000,000) = ? Question: If log(3) = 0.477, what is log(300)?

15. Power and Intensity Scales Power or Intensity dBβ = 10 log(I/I0)I 0 = 10 -12 W/m 2 dBWβ = 10 log(P/P0)P 0 = 1 W dBmβ = 10 log(P/P0)P 0 = 1 mW What if you need to solve for I?

16. Thought Question How much power is 0 dBm? a. a.0 mW b. b.1 mW c. c.10 mW d. d.-10 mW e. e.I have no idea!

17. Thought Question How much power is 30 dBm? a. a.1 mW b. b.3 mW c. c.30 mW d. d.100 mW e. e.1000 mW

18. Thought Question How much power is 33 dBm? a. a.1002 mW b. b.1003 mW c. c.1100 mW d. d.2000 mW e. e.3000 mW