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.

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.

Demo Reflection at a boundary

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.

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

Mathematica 0.7 seconds1.3 seconds 0.1 seconds

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 Note: frequencies are infinitely close together

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)

On Wikipedia Example where v phase > v group

Not yet on Wikipedia Example where v phase is negative!

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

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

Speed of sound Speed of sound… a. a.in gases: ~ m/s (343 m/s for air at 20  C) b. b.in liquids: ~ m/s c. c.in solids: ~ 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)

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?

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

Decibels Threshold of hearing0 dB 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

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.2 b. b.4 c. c.6 d. d.8 e. e.9

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: (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 … ) 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)?

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