224
Final Physics Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
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Use a PEN, use a PEN, use a PEN, use a PEN, use a PEN, use a PEN, use a PEN !!!!
THIS PAGE IS FOR SCRATCH WORK ONLY IT WILL NOT BE GRADED
Final Exam
Do NOT Turn Over until instructed Theres an equation sheet attached to the back which you may tear off
This is a Closed-Book Quiz, No Conferring is allowed, Calculators ARE allowed. (but no Ti83s - If in doubt ask!) You will have a maximum of 1hr and 50 minutes to complete this exam Attempt to answer all Questions on the sheets provided
(if you need more paper, raise your hand)
Points will be deducted for writing in pencil USE A PEN If you have a question, raise your hand.
(any color except red)
(If I think it is appropriate/necessary, I will inform the other students of both the question and my response.)
The reverse-side of this sheet is for scratch & will not be marked If you need them, there are additional pages at the end which can be used for any question. These will be graded. To Cross out anything put an X through the relevant section(s).
(Anything under the X will not count either for or against your mark.)
There are 11 questions on this Exam, (but they are not all worth the same number of points) The total number of points available is 118
Set-B Set-B v.2006-dec-10 v.2004-aug-20 1 Students: Do not mark in here Set-B Set-B v.2006-dec-10 v.2004-aug-20 2 Students: Do not mark in here
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Last Name
First Name
Date
Last Name
First Name
Date
Question 1 (7 points)
A boat at anchor bobs up and down with the waves, moving up 6.00 cm and down 6.00 cm from its equilibrium position. The boat makes one complete cycle every 5.00 s. For these oscillations, what is (a) the amplitude? (b) the period? (c) the frequency (in Hz)? (d) the angular frequency? If the oscillations were perfect simple harmonic motion, (e) What would be the maximum vertical speed of the boat?
Question 2 (8 points)
You blow across the open mouth of an empty test tube and produce a standing wave within the air column inside. The speed of sound in air is 344.0 m/s and you may assume the test tube acts as if it were closed at both ends. If the test tube is 14.0 cm long, (a) What is the frequency of the fundamental standing wave? (b) Make sketches to illustrate any displacement nodes and antinodes for the fundamental standing wave, and for the 1st and 2nd harmonics. (c) True or False? The air in the tube will vibrate with one or other of the above frequencies, but cannot vibrate at all three frequencies simultaneously.
Set-B Set-B v.2006-dec-10 v.2004-aug-20
3
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Set-B Set-B v.2006-dec-10 v.2004-aug-20
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Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Last Name
First Name
Date
Last Name
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Date
Question 3 (12 points)
True or False? (a) Blue EM-waves have a longer wavelength than red EM-waves (b) A (time) stable interference pattern requires coherent sources (c) The speed of light in a medium is independent of wavelength (d) On a perfect cloudless day, the blue sky directly above you is linearly polarized (e) Swimming pools are deeper than they appear to people standing on edge (f) You see yourself upside-down when you are further away from a (concave) Make-Up Mirror than the radius of curvature. (g) Your image appears left-right reversed in a plane mirror. If you rotate the mirror 90O youll see an up-down reversed image. (h) The angular width of the central maximum of a diffraction pattern is inversely proportional to the width of the aperture. (i) EM waves carry momentum (j) All sound waves are reflected by human flesh (k) The walls in this room can be seen due to specular refelection (l) The peak of a Black Body EM spectrum from a hot source is at higher frequencies than that for a cooler source
Question 4 (18 points)
A damped, harmonic oscillator of mass m is forced to vibrate, with a force given by F0cos(!t). Assume the damping force is given by bv. (a) Write down the equation of motion of the oscillator, if the restoring force of the oscillator is given by kx when the displacement is denoted by x (b) Using the complex exponential method assuming a solution of the form z=A ej(!t-!), show the full derivation of the expressions for A(!) and "(!) given on the equation sheet (once the steady-state has been achieved). (a) Make a sketch of both these functions for an oscillator with a very high Q-factor, and an oscillator with a moderate Q-factor.
Set-B Set-B v.2006-dec-10 v.2004-aug-20
5
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Set-B Set-B v.2006-dec-10 v.2004-aug-20
6
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Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Last Name
First Name
Date
Last Name
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Date
Extra Space for Question 4
Question 5 (9 points)
The passenger-side mirror on a car is typically not a simple plane mirror. (a) Is it usually Concave or Convex? (b) In 2 or 3 sentences describe the advantages and disadvantages of using such an optical element. The rear-view mirror on the windshield of most cars is usually a plane mirror behind a sheet of flat glass. In normal operation, the mirror is positioned at an angle such that objects behind the cars rear window are reflected so as to form an image in the drivers eyes. However for night-time use, there is usually a lever which moves the mirror (only) such that the image of following vehicles with their high-beams on is not reflected into the drivers eyes by the mirror. (c) In one or two sentences, describe why the driver can still see a faint image of the lights of a following car.
Set-B Set-B v.2006-dec-10 v.2004-aug-20
7
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Set-B Set-B v.2006-dec-10 v.2004-aug-20
8
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Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam Dec (2006 15)
(2006 Fall)
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Question 6 (10 points)
A converging lens has a focal length of 30.0 cm. (a) Draw the ray diagram for an Object placed 30.0 cm to the left of the lens. (b) Draw the ray diagram for an Object placed 50.0 cm to the left of the lens (c) Calculate the image distance s and image size y if the object in ( b) is 2.50 cm high (d) The Object in (b) is actually a upwards-pointing Neon Arrow. A sheet of paper is positioned so that the Image can be seen. In fact the Object is so bright that its image can be seen through the back a sheet of paper. To an observer viewing the image from behind the paper, what happens to the image when the Object is slowly rotated in a clockwise direction from the point of view of the observver around the optical axis? (ie. does it stay the same, or rotate in a clockwise or counter-clockwise direction?)
Question 7 (10 points)
Prof.G goes to a school nativity concert where the sweet sounds of the kids are relayed via 2 speakers, one 1.63m to the left of center stage, the other 1.63m to the right of center stage. Prof.G is happy to see the show, but does not want to hear the music! When the two speakers are in phase and emit sound with a wavelength of 0.80 m, (a) If he is sitting on the centerline of the stage (equidistant from each speaker), what is the minimum distances from the stage Prof.G can sit in order that the 0.80m sound from the speakers cancels out? (b) If instead, the speaker A is 1/6th of a period behind speaker B, where should Prof.G now sit (relative to the centerline)? (c) In a sentence or two explain why Prof.G is unlikely to actually hear silence throughout the entire concert.
Set-B Set-B v.2006-dec-10 v.2004-aug-20
9
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Set-B Set-B v.2006-dec-10 v.2004-aug-20
10
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Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
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Date
Last Name
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Date
Question 8 (10 points)
Monochromatic light of wavelength 620 nm from a distant source passes through a slit 0.450 mm wide. The diffraction pattern is observed on a screen 3.00 m from the slit. In terms of the intensity I0 at the peak of the central maximum, what is the intensity of the light at the screen 4.13 mm from the central maximum?
Question 9 (10 points)
A commonly used lens coating material is magnesium fluoride with a n(550nm) = 1.38. You may assume that air has n(550nm) = 1.00, and water has n(550nm) = 1.33. (a) How thick should the coating be if it is to be applied to glass with n(550nm) = 1.52 so as to provide the lens with a non-reflective coating for light with a wavelength 550 nm? (b) In one or two sentences, discuss whether or not such a coating will be equally effective under water. (c) In one or two sentences discuss what factors one would have to consider if one instead wanted the single coating on the lens to be non-reflective at a visible wavelength much shorter than 550 nm.
Set-B Set-B v.2006-dec-10 v.2004-aug-20
11
Students: Do not mark in here
Set-B Set-B v.2006-dec-10 v.2004-aug-20
12
Students: Do not mark in here
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Physics 224
Final Exam (2006 Dec 15)
(2006 Fall)
Last Name
First Name
Date
Last Name
First Name
Date
Question 10 (12 points)
A ray of light is incident on a plane surface separating two sheets of glass (A & B) with indices of refraction nA = 1.70 and nB = 1.58. (a) If the ray originates in sheet-A and has an angle of incidence of 62.00 to the boundary, what is the angle of refraction of the ray in sh...