Problem Score 1 /25 2 /16 3 /20 4 /24 5 /15 Total /100

Transcription

1 PHYS 4 Exa 3 Noveber 8, 6 Tie o Discussion Section: Nae: Instructions Clear your desk o everything but pens/pencils and erasers. Take o all caps, hats, visors, etc., and place the on the loor under your seat or the duration o the exa, along with all backpacks, bookbags, etc., and all electronic devices, including calculators (be sure phones are turned o). Do not open exa until so instructed. Write nae and discussion tie where indicated above; do not write anything in score table at right. Proble Score /5 /6 3 / 4 /4 5 /5 Total / For axiu credit, show your work; you ay also draw a diagra, give a brie discussion, or explain what you did (or would do). Be sure to enter the correct values, in SI units, into any inal orula, and give the units o the result (its nuerical value need not be calculated). You ay use the inoration given on the last page (only the sheet handed out with the exa); ore speciic inoration ay be given in an individual proble. The points listed add to. You have 5 inutes. The inoration sheet is the last page o the exa. You ay tear it o (i you do tear it o, do not turn it in with your exa).

2 . (5 points) The conducting bar is pushed along the conducting rails through the agnetic ield at a constant speed o v =. /s. The only resistance in the circuit is the bulb, which has R = 5. Ω. (a) (5 points) What is the direction o the induced current, clockwise or counterclockwise? (b) ( points) Find the agnitude o the induced current. (c) ( points) Find the agnitude o, and state the direction o, the external orce that ust be applied to keep the bar oving at constant speed.

3 . (6 points) For the ollowing, just give answers unless an explanation is asked or. (a) (4 points) A current-carrying wire is pulled away ro a conducting loop in the direction shown. Is the current induced in the loop clockwise, counterclockwise, or zero? (b) (4 points) The history plot shown here gives the displaceent at a certain point as a wave passes, traveling to the right (positive x-direction). Sketch a snapshot o this wave as a unction o position, taken at any tie (the scale doesn t atter; just sketch the shape o the wave). (c) (4 points) A standing sound wave in a tube with one end closed and one end open has a requency o 3 Hz. You are told that this noral ode is the third haronic. What is the requency o the next higher haronic that is also a noral ode o this tube? (d) (4 points) White light passes through a diraction grating and ors rainbow patterns to either side o a central white spot on a screen. For each rainbow (circle the correct stateent; i you re not sure, you ay get partial credit or a brie explanation): i. the red side is on the right, the violet side on the let. ii. the red side is on the let, the violet side on the right. iii. the red side is closest to the central white spot. iv. the violet side is closest to the central white spot.

4 3. ( points) The oscillations o an LC circuit drive a speaker so that it eits a sound wave o the sae requency as the circuit oscillations, 686 Hz. (a) ( points) I C =.5 μf, what is the value o the inductance L? (b) ( points) Suppose there is a second speaker identical to the irst. When you carry one speaker toward the other (stationary) one, you hear a beat requency o 4 Hz. What is your speed?

5 4. (4 points) A thin, transparent soap il has an index o reraction n =.33 = 4/3. It is suspended in air, so there is air (n = ) on both sides o the il. Light norally incident on the il (propagating in a direction perpendicular to the suraces o the il) has a wavelength o 3 n, inside the il. (a) ( points) What is the requency o this light? (b) (4 points) Suppose the thickness o the il is 5 n. Do the light waves relected ro the two sides o the il interere constructively or destructively? Careully explain your answer, or (or partial credit) explain how you would go about deciding on an answer.

6 5. (5 points) Light o wavelength 5 n illuinates a single slit and a double slit, and the intensity patterns are viewed on a screen at a distance o c ro the slits. (a) (5 points) Identiy each pattern by writing single slit or double slit below each igure. (b) ( points) Choose one o the two patterns, and state which one you have chosen. I you choose the single slit, ind the slit width. I you choose the double slit, ind the slit separation.

7 Inoration or Exa K = = 8.99 N /C ε = 8.85 C /N (or F/) 4 πε 9 3 e =.6 C e = 9. kg 7 7 μ = 4π T A =.67 kg / 8 c = = 3. /s v sound in air = 343 /s ε μ C Q ΔV C ε A = d = ( ) U p C = C ΔVC, and ΔV ρl I =, and R = P = IE, and R A t /τ Q( t) = Q e, where = RC B r ds r = μ P = I τ I through μ I μ NI Blong wire = B = = μ ni πd L F = ILB E = vlb r r dφ Φ = B d A E = dt area o loop Φ L = I U L = LI, and u B B μ I ( t) t /τ = I e, where = L / R ΔV L = L di dt = Q t) Q cos( ωt) ( u E R = Δ = ε E ( V ) =, where ω = / LC τ D ( x, t) = asin( ( kx ω t) + φ ) π π ω k =, ω = = π v = λ =, ω = vk λ T k ± = (oving source) ± = ( ± v o / v) (oving observer) v / v = s ± v / c rel ± (light) vrel / c v v = =, =, 3, 5, λ 4L v v = =, =,, 3, λ L Δφ A = a cos Δr π (constructive) Δφ = π + Δφ = beat = od = λ ( + ) π (destructive) d sin θ = λ, =, ±, ±, ± 3,... a sin θ p = pλ, p = ±, ±, ± 3,....λ sinθ = D Δφ I = CA = 4Ca cos = 4I R R Δ φ cos