Announcements 10/12/11 Prayer Term projects: Proposals due a week from Saturday, ed to me with your proposal in body of . Groups of 2 are encouraged. Groups of 3 with permission. Just send one per group, but CC your partners on the . Syllabus: “The term project is an opportunity for you to propose and conduct a simple experiment or to theoretically, mathematically, or computationally investigate an aspect of the course in more depth.” Guidelines: “At least 15 hours of work per person (not including time spent at the hardware store, etc.)” Some ideas to get you thinking: Some actual projects: htm htm

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: calculator: log 10 (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 equals 100? ln(100) = ? (“ln” = log e = log … ) Translation: e to what number =100? (4.605…) Ambiguity: “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)?

Thought Question A +3 dB increase is just about a factor of  2 in intensity. How many dB represents a factor of  4 increase in intensity? a. a.+4 b. b.+6 c. c.+8 d. d.+9 e. e.+10 What if you need to solve for I?

Other Power and Intensity Scales Power or Intensity sound a. a.dB β = 10 log(I/I 0 )I 0 = W/m 2 microwaves/rf a. a.dBm β = 10 log(P/P 0 )P 0 = 1 mW electronics/electrical circuits a. a.dB β = 10 log(P 2 /P 1 )(ratio only)

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 dBm: β = 10 log(P/P 0 ) P 0 = 1 mW

Thought Question How much power is 33 dBm? a. a.1003 mW b. b.1006 mW c. c.1100 mW d. d.2000 mW e. e.3000 mW

Thought Question You have a 1 volt amplitude sine wave. You want to go up 3 dB in power. How many volts do you need? (Recall: Power ~ amplitude 2 ; true for voltages, sound, and light waves as well as waves on a string) a. a.1 V b. b.  2 V c. c.  3 V d. d.2 V e. e.3 V

Doppler Effect Demo: Doppler Speaker What happens if the source is moving? What happens if the observer is moving? Key point: Frequency is _______________when the source and observer approach each other, ______________ when they go away from each other Stokes Come, Come, Ye Saints recording a. a. (0:32)

The Pie Factory v belt Spacing between pies = ? a. a.  = v/f v s source speed v o observer speed v speed of sound (v belt ) If observer moves toward source (pie maker), she would measure the same ___________ but the pies are coming at her at a faster ________ If source moves toward observer, the __________ shrinks, but the pie _______ doesn’t change wavelength speed f = v new / old wavelength speed f = v old / new new =(v belt -v s )/f s

Doppler, cont. Combine both effects: What does  mean? Stokes Flash video a. a. (1:50)

Distant light source a.Traveling toward you b.Traveling away from you See HW 19.4 for equation

Astronomy Edwin Hubble, 1929: Distance to galaxies is proportional to their speed a. a.Distance measured through Cepheid variable star observations, “standard candle” b. b.How did he measure speed? – – Doppler shift of spectral lines! That’s now a standard technique for today’s astronomers when they want to measure distance to far away objects… just measure Doppler shift. Hubble’s Law and the Big Bang a. a.(Yes, it’s OK for LDS to believe in the Big Bang…)

Sonic Boom (2:47) (2:53) Happens with all types of waves whenever the sources is traveling faster than the speed of the wave… …so, what is “sonic boom” of water waves?

θ Sonic boom manifested by condensation of water in air Sonic Boom sin  = v sound /v source = 1/“Mach number”

Sonic boom of bullet in flight (holographic interferometry?) Sonic Boom How fast is the bullet traveling? a.Mach # = 1/sin 

Interference Path length a. a.Constructive b. b.Destructive Video: Two outdoor speakers (1:16) Demo: Moire pattern transparencies Demo: Hearing test Demo: 2-speaker interference Ripple Tank image: wikipedia