announcements 2/16/11 prayer exams… hopefully graded by friday extra time on lab 3: now due tues...
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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. Much less than 80%b. A little less than 80%c. About 80%d. More than 80%e. It depends on the color of the rope.
2 1
1 2
R
I
A v vr
v vA
2
1 2
2T
I
A vt
v vA
2R r 1T R
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. 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 seconds 1.3 seconds
0.1 seconds
Time Evolution of Time Evolution of DispersiveDispersive Pulse PulseCredit: 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 spectrumNote: frequencies are infinitely close together
Phase and Group VelocityPhase and Group Velocity
evaluatedat
velocity of "envelope"ave
gk
dv
dk
velocity of "wiggles"pv k
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 vphase > vgroup
http://en.wikipedia.org/wiki/Group_velocity
Not yet on Wikipedia Example where vphase is negative!
Reading Quiz Sound waves are typically fastest in:
a. solidsb. liquidsc. gases
Sound Waves What type of wave? What is waving? Demo: Sound in a vacuum Demo: tuning fork Demo: Singing rod Sinusoidal?
a. Demo: musical disk
Speed of sound Speed of sound…
a. in gases: ~300-1200 m/s (343 m/s for air at 20C)
b. in liquids: ~1000-1900 m/sc. in solids: ~2000-6000 m/s
General form: v = sqrt(xxx/yyy)a. What are “xxx” and “yyy”?
Speed of sound in aira. Dependence on Temperature (eqn in
book)
Intensity Intensity: power/area
a. Spherical Wavesb. 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?
Reading Quiz How do we calculate the sound level in
decibels?a. β = 10 log( I / Io )b. β = 10 ( I / Io )c. β = 10 ( I - Io )d. β = 10 e( I / Io )
e. β = e10 ( I / Io )
add 10 to 10 to I
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
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. 2b. 4c. 6d. 8e. 9
Logarithm Review Log10(x) is the inverse of 10y
→ if x = 10y then y = log10(x)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(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)?
Power and Intensity Scales
Power or Intensity
dB β = 10 log(I/I0) I0 = 10-12 W/m2
dBWβ = 10 log(P/P0) P0 = 1 W
dBmβ = 10 log(P/P0) P0 = 1 mW
What if you need to solve for I?