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. As said in email: must turn in actual printouts when problem says, “Use a computer program such as Mathematica…”

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. As said in still later email: “how to print” instructions given, so try those before sending plots to Chris by email.

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 spectrum

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)

Wikipedia Example where vphase > vgroup

http://en.wikipedia.org/wiki/Group_velocity

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

Demo Reflection at a boundary

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

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?

Thought Question

How much power is 0 dBm?a. 0 mWb. 1 mWc. 10 mWd. -10 mWe. I have no idea!

Thought Question

How much power is 30 dBm?a. 1 mWb. 3 mWc. 30 mWd. 100 mWe. 1000 mW

Thought Question

How much power is 33 dBm?a. 1002 mWb. 1003 mWc. 1100 mWd. 2000 mWe. 3000 mW