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Unformatted text preview: PHYSICS 203NYC—05 FHVAL EXAMINATION
December 14I 2001 Salve only 10 out of the following 12 problems (10 marks each):
1. The two speakers, 31 and 82, shown in the ﬁgure, are in phase and emit 1.0kHz signals. The distance d is equal to 0.70 In. Determine all the possible values of x for which the signals
ﬁ‘om the speakers will be (a) in phase,
(b) 180° out of phase. 2. Two waves are propagating on the same very long string. A generator at the left end of the
string creates a wave given by yl and one at the right end of the string creates the wave given by J12:
y] = (6.0 cm) cos(2r: x — 41: I) and y; = (6.0 cm) cos(27r x + 4n t),
where x is in meters and t is in seconds. (a)Use the superposition principle to determine an expression for the resultant standing
wave. Explain every step and indicate the trigonometric identity used. (b) Use the above result to determine the position of the third antinode.
(c) (i) At t= 1.2 5, what is the displacement of the string at the position x = 0.60 In?
(ii) What is the maximum displacement of the string at x = 0.60 In? Do not forget to include units in ALL your answers. 3. An object is 5.00 In to the left of a ﬂat screen. A converging lens for which the focal length
is f = 0.800 m is placed between object and screen. (a) Show that two lens positions exist that form images on the screen, and determine how
far these positions are ﬂow the object. (b) How do these two images differ in size and in attitude (upright or inverted) ﬁorn each
other? 80 4. Light of wavelength 440 nm passes through a double slit yielding an intensity pattern as a
ﬁmction of the angle of deviation as shown in the graph below. The slits cannot be considered
as point sources. Find (a) the width of each slit (in mm), and
(b) the distance between the two slits (in mm). DoubleSlit Intensity as a Function of Angle of Deviation £7
to
c
E
E o.4 0.3 o.2 o.1 0 0.1 0.2 0.3
Angle theta (degrees) 5. Two narrow parallel slits separated by 0.85 mm and are illuminated by 600nm light, and the
viewing screen is 2.80 m away from the slits. (a) What is the phase difference between the two interfering waves on a screen at a point
2.5 mm ﬂora the central bright fringe? (b) What is the ratio of the intensity at this point to the intensity at the center of a bright
fringe? 6. The wave ﬁmction for a traveling wave on a taut copper wire of diameter 2.0 mm is
y = y(x, t) = (0.15 m) sin(8n:x —— 120111.‘ + 75/4)
where x is in meters and t is in seconds. (a) Find the wavelength, frequency, and speed of the wave. (b) Find the tension in the wire if the density of copper is 8.92 g/cm3. (Watch your units.)
(0) Find the transverse velocity of a point on the wire at x = 0 and t = 0. (d) Explain the difference between transverse velocity and wave velocity. (e) At what rate is the energy transmitted by this wave along the wire? 81 7. A speaker is placed between two observers, A and B, who are 121 m apart along a line
connecting them. If observer A records a sound level of 70 dB, and observer B records a sound level of 90 dB, ﬁnd
(a) how far the speaker is from each observer,
(b) the power output supplied by the speaker, and
(c) the energy produced by the speaker in 15 seconds. A.  <ae;—:a>>>~B
t w t 8. A light ray, traveling from air, enters a rectangular block of plastic at an angle of 45° and
emerges at an angle of 75", as shown in the ﬁgure. (a) Determine the index of refraction for the plastic. (b) If the light ray enters the plastic at a point L = 50 cm from the bottom edge, how
long does it take the light ray to travel through the plastic? Recall that sin(—9) = — sine, cos(—9) = cosB, sin(90° — 9) = c059, cos(90° — B) = sine. 9. (a) What assumptions did Einstein made to explain the experimental features of the
photoelectric effect? (b) Explain the meaning of the work function of a metal.
(c) Molybdenum has a work function of 4.2 eV.
(i) Find the cutoff wavelength (in am) for the photoelectric effect to occur. (ii) Suppose that light of 350nm wavelength is incident on the metal. Would the
photoelectric effect take place? Explain why or why not. (iii) Calculate the maximum kinetic energy and the maximum speed of the emitted
photoelectrons if the incident light has a wavelength of 180 nm. 82 10. A 0.50kg block on a horizontal frictionless surface is attached to a spring of force constant 50 N/m. The spring is initially stretched 0.060 m from its equilibrium position and the block
is given a velocity of 0.80 Ill/S to the right. (a) Find the angular ﬁequency, the period of oscillation, the amplitude of oscillation, and
the phase constant. (b) Find the shortest time (t > 0) needed for the block to pass through the equilibrium
position. (c) Use energy conservation to ﬁnd the magnitude and direction of the velocity
(velocities) when the block is at the position —0.030 In. Frictionless surface 11. A photon is emitted as a hydrogen atom undergoes a transition ﬁom the n = 6 state to the
n = 2 state. (a) Ifthe transition is direct from the n = 6 state to the n = 2 state, calculate the energy
(in eV), the wavelength (in 11111) and the frequency of the emitted photon. (b) Find the possible number of allowed quantum transitions between the two given
states, and show all these transitions in an energy level diagram. 12. A ﬁeshly prepared sample of a certain radioactive isotope has an activity of 10.0 mCi. After
4.00 h, its activity is 8.00 mCi. (5.) Find the decay constant and halflife. (b) How many atoms of the isotope were contained in the freshly prepared sample?
(c) What is the sample's activity 30.0 h after it is prepared? Exam NYC / Fall 2001
83 Answers to Problems on Final Exam
December, 2001
Waves and Modern Physics 1. (a) When inphase: x1: 0.543 m and x2= 0.0141 m
(b) When 180° out ofphase: x1 = 1.43 m and x2: 0.219 m 2. (a) y (x, t) = (12.0 cm) cos(21rx) cos(4rtr) Where x is in meters and t is in seconds. (b) x = 1.00 m
(c) i) y (0.60 m, 1.2 s) = 7.85 cm
ii) ymax = 9.71 cm 3. (a) To form real images on the screen, the lens must be at either 4.00 m or 1.00 m from the
object. (13) The two images are inverted, but one image is 16 times smaller than the other. 4. (a) The width of the slit is a = 0.0504 mm.
(b) The slit separation is d = 0.252 mm. 5. (a) (l): 7.95 rad I
—— = 0.452
(b) I max 6. (a) i=0.250 m; f= 60.0 Hz; 0:150 m/s
(b)T=6.31N (c)At t=0 and x=0,vy = ayéj") =—40.0m/s. (d) The transverse velocity refers to the velocity with which the particles of a medium
oscillate in a direction perpendicular to the direction in which the wave propagates. The
wave velocity refers to the velocity with which the wave propagates in the medium. In
the present problem, the medium is the Wire, the transverse velocity is along the y—
djrection, and the wave velocity is in the positive xdirection. (e) P = 672 W 84 7. (a) The speaker is 110 m from observer A, and 11 m ﬁom observer B.
(b) P = 1.52 W (c) E=22.8 J
3. (a) n = 1.20
(b) t=3.39 ns 9. (a) Read Section 40.2, on p1295 of Serway. (b) The work function of a metal is the minimum energy required by an electron in the metal to be ejected from its surface. (Such a minimum energy must exist or electrons would
leave metals all the time.) (c) (i) 70.1 = 296 nm (ii) The cutoff wavelength is the maximum wavelength of light incident on a metal that
will cause emission of photoelectrons from the metal. Since 350 nm is greater than the cutoff wavelength, the photoelecnic effect will not take place if the incident light
is 350 nm. (iii) Km... = 2.70 eV = 4.32 x 10'19 J
umx = 9.74 x 105 We 10. (a) 0) = 10.0 rad/s; T= 0.628 s; A = 0.100 m; d): —0.927 rad
(b) t= 0.250 s (c) When the block is at x = — 0.030 m and moving away ﬁom the equilibrium position, its
velocity is 0.954 rule in the negative x—direction. When the block is at x = — 0.030 m and moving toward the equilibrium position, its velocity is 0.954 this in the positive x
direction. 11. (a) a: 3.02 eV; 7L =411nm; f= 7.30 ><1014 Hz
(b) There are 10 possible transitions between the n = 6 state and the n = 2 state. 12. (a) it = 5.58 x 10—2/11 = 1.55 x 10%; Tm =12.4 h = 4.47 x 104 s (b) N0 = 2.39 x 1013 atoms
(c) R = 1.87 mCi 85 ...
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This note was uploaded on 10/03/2010 for the course PHYS. 203NYA05 taught by Professor Ms.simpson during the Fall '09 term at Dawson College.
 Fall '09
 MS.SIMPSON

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