2012 sample test 1

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Name: _______________________________________ Section ______ Student ID: ***-** ___________ Last First M.I.

Physics 20800 CC s Sample Test# 1 Spring 2012

General Instructions1. The test has 5 problems with parts. Solve all problems.

2. State all assumptions. Work neatly explaining what you are doing. No credit will be given if workis not shown.

3. Use proper units. Points will be deducted if proper units are not used.

4. Work in the designated space for each part of a problem.

5. Use the back of the page if you need additional space, making sure you write the ProblemNumber and the Part number of the problem clearly.

Useful Constants and formulae

y(x,t) = y m sin(kx t) y(x,t) =2y m sin(kx)cos( t) v = ( )1/2

f f [(v + vd ) / (v + v s)] = 10 dB log ( I / I 0)

n1 sin n2 sin cos p) + q) = f

c = 3 x 10 8 m/s

Score

Problem 1. __________

Problem 2. __________

Problem 3. __________

Problem 4. __________

Problem 5. __________

TOTAL:

This sample test is meant to give you an idea about the scope of test.

DO NOT EXPECT THIS TO BE A TEMPLATE OF THE REAL TEST!

You are responsible for all the materials covered in the class.

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Name: _________________________________________________ Student ID: ***-**-_ _____________Last First M.I.

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Problem 5. In a double-slit experiment, the distance between the slits is 0.5 mm and thescreen is 2.0 m away from the plane of the slits. Two interference patterns appear on thescreen, one due to light of wavelength 480 nm, and the other due to light of wavelength 600nm.

(a) What is the distance between the 5 th interference maximum of 600-nm light and the3rd interference minimum of the 480-nm light on the screen? How will the distancechange if the entire experimental arrangement is submerged under water (index ofrefraction of water 1.33)? (7 +3 pts.)

(b) What is the maximum number of bright fringes of 600-nm light and of 480-nm light

that can be observed in this arrangement? Justify your answer. Find the lowest ordermaxima of the two patterns that overlap. (4+4 +4 pts.)

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Problem 1 . A string of mass 5 grams is stretched between two poles 2.5 m apart. The 5 th harmonic has a frequency of 300 Hz. The amplitude at the antinodes is 4 mm.

(a) What is the tension in the string? (12 pts.)

(b) Write down an equation for the displacement of the string as a function of position ( x)and time ( t ). (6 pts.)

(c) What is the maximum transverse speed of an element of the string at an antinode?What is the transverse displacement of the string element when the transverse speedis the maximum? Justify your answer. (4 + 4 pts.)

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Problem 2. Jane is standing on the platform waiting for the train. The train approaching the platform from north at 20 m/s blows its whistle when it is 100 m away from Jane. John, runningtowards the platform from south, is 50 m away from Jane when the whistle is blown. Thefrequency of the whistle when the train is at rest is 440 Hz, and the speed of sound in air is 340

m/s.(a) What frequency of sound does Jane hear? (6 pts.)

(b) John hears a frequency of 475 Hz. How fast is he running? (6 pts.)

(c) What is the difference in sound level between Jane and John assuming the whistle to be a

point source of sound? (8 pts.)

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Problem 3. Argon-ion laser light of free-space wavelength 488 nm is incident on the compositemedium of glass, water and air as shown in the figure. The speed of light in free space is 3x10 8 m/s. Distance d along the water-air interface is measured from the vertical line in the middle.

(a) What is the wavelength of this light in glass? What is its speed in water? (2+2 pts.)

(b) There is a target at the water-air interface atd = 6 m. Find the value of for which thelaser light will hit the target. Find thedirection(s) of propagation of the laser lightafter it hits the water-air interface?(5+5 pts.)

(c) Assume that the incident beam is unpolarized. For what value of will the reflectedlight from the glass-water interface be completely plane polarized? What will be thedirection of polarization? An ideal polarizer is placed in the path of the reflected

beam with its polarizing axis at an angle of 60 0 with the plane of incidence. If thereflected polarized beam has an intensity of 0.02 W/m 2, what will be the intensity ofthe beam after it passes through the polarizer? (4+1+3 pts.)

5 m

Glass, n =1.52

Water, n =1.33

Air, n =1.0

d

5 m

Glass, n =1.52

Water, n =1.33

Air, n =1.0

d

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Problem 4. (a) An 8 mm tall arrow is placed 15 cm to the left of a concave mirror of radius focallength 5 cm as shown in the figure. Find the position, size, and nature (real or virtual, erect orinverted) of the image. Complete the figure by drawing a neat principal ray diagram showing theformation of image. (4+2+2+2+4 pts.)

(b) A thin symmetrical glass lens (radii of curvature have the same magnitude) has thesame focal length as that of the above-mentioned mirror. Assuming the index ofrefraction of glass to be 1.5, what is the magnitude of the radii of curvature ? Whattype of a lens is it? Find the position, size, and nature (real or virtual, erect orinverted) of the image if the arrow is placed 3 cm to the left of the lens as shown inthe figure below. Complete the figure by drawing the outline of the lens and a neatray diagram showing the formation of image. (4+1+3+2+2+2+4 pts.)

L

2012 sample test 1

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