{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

prelim1-sp05 - monster gomkws Physics 214 PRELIM I(March 8...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: monster gomkws Physics 214 PRELIM I (March 8, 2005 from 7:30-9:00 ) Name : Signature: Section # and TA: Please count your pages — they should be 13! Score: ° This examination is closed books and closed notes. NO calculators are permitted. A formulae sheet is provided. Use the provided space after each question for your answers. The first part consists of a few simple questions, and no partial credit will be given. Part II, III, IV are problems for which you have to show the work done arriving at the answer. Partial credit will be given for these answers. The perfect score of the exam is 100. The point value of the problem is given in the parenthesis next to the problem. ° Please put your name on each sheet. ' By signing this exam you certify to adhere to the Cornell academic integrity code. Part 1: Short answer questions (35 points —— 5 points each) You do not need to show work. No partial credit. 32 1 a2 FYOCJFV—ZFYUJ) (A) YOU) = f(X-Vt)g(X+Vt) B; D (B) y(x,t) = A [sin(x-vt)]3, where A is a constant (C) Y(X,t) = fix) g(X-VT) (D) y(x,t) = A elkom), where A is a complex number and k is a real number (E) none of the above 1. Which wave is a solution of the wave equation 2. A string has the wavevelocity v and displacement y(x,t). What is the acceleration of a segment on the string? 2 072 (A) V 33435,» E (E) none of the above. 3. An electric pulse with electric field E = (0,0,f(x-ct)) is propagating with wavespeed c in vacuum. In which direction is the pulse propagating? (A) +x direction (B) —x direction (C) +y direction (D) —y direction (E) +z direction (F) —2 direction 4. The general solution of the wave equation is y(x,t) = f(x+vt) + g(x-vt) on a string. What is the relationship between the function f and g given the initial condition that the string is flat at t=0? C (A) f(X,t) = -V g(X,t) (B) f(X,t) = g(X,t) (C) f(X,t) = ' g(X,t) (D) f(x,t) = l/g(x,t) (E) none of the above 5. The general solution of the wave equation is y(x,t) = f(x+vt) + g(x-vt) on a string. What is the relationship between the function f and g given the initial condition that the segment velocity is zero at t=0? E (A) f(Kat) = -V g(X,t) (B) fixat) = g(X,t) (C) f(XJ) = - g(xat) (D) f(x,t) = 1/g(x,t) (E) none of the above 6. A pulse of the form y(x,t) = f(x-vt) is propagating towards a fixed end. What is the from of the pulse when it has been fully reflected from the fixed end? (A) Inverted and mirrored. (B) Mirrored. (C) Inverted. (D) Same (E) none of the above 7. A pulse of the form y(x,t) = f(x+vt) is propagating towards a free end. What is the from of the pulse when it has been fully reflected from the free end? (A) Inverted and mirrored. (B) Mirrored. (C) Inverted. (D) Same (E) none of the above Part II: Reflection of an Electromagnetic Pulse (20 points) You do need to show work. An electromagnetic pulse (plane wave) is traveling with speed c in the negative x- direction towards an infinite conducting plate, which is placed in the yz-plane at x=0. The electric field vector E(x,t) = (O,Ey(x,t),0) is polarized in the y-direction. At t=0 the electric field of the pulse has the shape shown below. conductor in E0 Since the conductor represents a boundary, our pulse will be reflected at x=0. It helps to imagine a right moving pulse coming from the left. We use the following convention when sketching: ‘ left traveling pulse __________ ' right travelingpulse ...................... ’ superposition of the pulses (A) (4 points) The boundary condition associated with a perfect conductor is that Ey(0,t) = 0 for all times. Given this, sketch on the graph above the electric field associated with the imagined reflected pulse for time t = 0. (Remember to use the conventions above for left/right moving pulses. rid (B) (6 points) Using the convention from the previous page, sketch the incoming and reflected electric field pulses at time t= 4d/c on the upper graph, and sketch the net electric field in the physical region (x>0) at the same time t = 4d/c on the lower graph. % Ey (Wild/c) § single pulses RUM PM +2 ’ R: e .1 /\}\30 6h+ Ska/9 l" / \\ (cfif'n‘ch Mishke ‘l) (K / x / \ i/ g 4 \ Kid -5 —4 —3 -i2 —1 1 2 3 4 5 6 t , "-> ‘ Ey (tz4d/c) superposition _ E0 +3— qalaleol (ofrzcflj 1 2 ‘s ’4. 5 a (C) (4 points) ~ The sketch below shows the associated magnetic field pulse B(x,t) = (0,0,Bz(x,t)) traveling to the left at t = 0. 4} 132 (1:0) conductor » 1230‘ {a w W M... MLMWW m w w WW. MW: Wééwvwwmwcgm N.-- x ""“i m»... m m M mm... —5 --»‘-‘«l —3 I -—1 —l A l 2 \ x 3 4 I I ' \ I I ’ ‘ K i " » 2 s. -’ s ' , f \ I ,, I I r . > \ \ x ’ f . I L. r \ ’ v ‘ "Ev C +2 nedqith FK’SQ A A 3‘) X (3) r X “H "63‘” flitc $0 §: __1\ Tl ru‘fll’lt shq‘oc On the axes above, sketch the (imagined) magnetic reflected pulse that is moving from left to right, at t=0. Hint: Pay attention to the relation between the direction of the electric field vector, the magnetic field vector, and the direction of propagation. (D) (6 points) Using the same conventions as above for the electric field, sketch the incoming and reflected field pulses at time t = 4d/c on the upper graph, and sketch the net magnetic field in the physical region (x>0) at the same time t = 4d/c on the lower graph. ‘2 Bl (tz4d/C) single pulses Eo/C xid . . l 1‘ t . F —n —5 -4 —3 —-.\ -1 i /o 2 1 4 5 6 9 \ /‘ o x g z“ o o ‘l V —E(}/C +9 nb’fi- 63’7“; +9~ r901» shape 3.2: ([1:4(l/c) superposition C l (and Umj Hro’ ibnm £)) +01 «Mug Comet-l. ’J Kid Part III: Lab Experiment (20 points) You do need to show work. ‘31 I frictionless rod 1 / :flf/ / QTfTTfW"W"‘”—'MTQTZTTTV{ ”WWW ‘‘‘‘‘ 7"me shaker (freq l) (length L) ,/ adjustable _ massless ring In your first laboratory experiment you studied a Vibrating string with two fixed ends. Consider now the modification of the experiment in which the right hand end 'of the string is attached to a small massless ring which slides frictionless up and down a horizontal post. The post is attached through additional strings to a pulley on the other side of which a spring scale provides constant tension (see Figure above). L is the length of the string between the rod and the shaker. The frequency of the shaker is f, the tension is F and the u is the constant mass per unit length of the string. The shaker vibrates in and out of the page. Assume that the left end is fixed at the shaker, while the horizontal motion on the other end is free. (A) Fundamental (7 points) Sketch the shape of the standing wave corresponding to the lowest (fundamental) mode. Find an expression for the lowest (fundamental) frequency f] in terms of L, F, and u. 1;; -V (B) Higher Modes at Fixed Length (7 points) Sketch the shape of the standing wave corresponding to the second mode. What should the frequency f2 of the shaker be for this mode to be formed? (Express f2 in terms of L, F, and u.) (B) Higher Modes at Fixed Frequency (6 points) Now suppose you vary the length of the string. Find the new string length l at which the 2"d standing wave mode will be formed if the frequency of the shaker is fixed to f] and the tension F remains constant. Express 1 in terms of the original length L. ’5 _E___ \fE 'QZHLM— Lu.” Part VI: Wave Equation(25 points) You do need to Show work. A thin string of linear mass density {J and length L is fixed to the ceiling of a room. Due to its own weight it is under a tension F(x). Choose the origin of the coordinate system at the ceiling . (A) What will the wavespeed be along the string? (4 points) (a) Larger towards the bottom? (b) Smaller to towards the bottom? (c) Same? Fifi Af:\j AA FOX) frat/€57! ed” 7(0/6 10 (B) Calculate the tension F(x) (5 points). (El/x) : Al;(L”/X) ¢=O of (cl/I314? +¢ cllré'c‘llrou ‘lwqrcl {XMP (C) Show graphically the force balance for a segment of length Ax ( 4 points). ll (D) Derive the total transverse force of a curved segment of length Ax for a tension F(x). Hint: remember the derivation in lecture for a constant tension (4 points). : ’ M4212 2F? {’(4 .)\ 0‘44 l4+b¢ , «9‘? F“) 3: . 4. (E) calculate the acceleration of the string segment ( 4 points). 35:”: W14 f «2 g. a \f— :xMA’K 4.1:? at?- EF/‘y, 827-7 AAA/X 0152 12 (F) Use the results from above to calculate the wave equation ( 4 points). ’2 22,2 \ Z .AIAV gt THE END 13 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern