Physics 130
Wave Motion, Optics and Sound
Final Examination
18 December, 2008
2:00 PM – 5:00 PM Pavilion
All Sections (Consolidated)
Course Convenor: Dr M.Heimpel
NAME:_____________________________________ ID # ______________________
A single 8 1/2” x 11” formula sheet (front and back) is permitted.
Calculators without communications features are permitted. All other electronic devices
are prohibited.
The exam is 3 hours (180 minutes) in length.
Attempt ALL questions.
Answers must be clearly indicated on the answer sheet using an HB pencil.
Use the provided exam booklets for rough work. (You may write on this exam paper).
Five sheets of scratch paper are appended in the back of the booklet (you may separate
these extra pages). At the end of the exam, turn in this exam paper, your answer sheet,
your formula sheet and the exam booklet(s), including the scratch paper . Enclose all in
the exam booklet, and turn everything in to the box for your section.
ON THE ANSWER SHEET ENTER:
Your Name (Surname followed by space then given names)
Student Identification Number
Course Section in Special Codes:
Section
Instructor
Lecture Time
A01
MacDonald
09:00 – 09:50 AM
A02
Heimpel
10:00 – 10:50 AM
A03
Jung
02:00 – 02:50 PM
A04
Nouri
03:00 – 03:50 PM
Code
J=1
J=2
J=3
J=4
Grading: 3 points per question
There is only one correct answer to each question. If you believe the correct answer
is not listed, choose the closest matching value. There are 11 pages with 40 questions
for a maximum total of 120 points for this exam.
IF ANYTHING IS UNCLEAR, PLEASE ASK!
1.
Which of the following is a FALSE statement?
A) Not all waves are mechanical in nature.
B) A wave in which particles move back and forth in the same direction as the wave is moving is
called a longitudinal wave.
C) Waves transport energy and matter from one region to another
D) The speed of a wave and the speed of the vibrating particles that constitute the wave are different
entities.
E) In a transverse wave the particle motion is perpendicular to the velocity vector of the wave.
2.
What happens when a periodic driving force is applied to a vibrating system?
A) The system will stop vibrating and finally come to a stop.
B) It will vibrate at some multiple of the driving frequency (called a harmonic or “overtone”)
C) The system will vibrate at its natural frequency.
D) The system will vibrate at the frequency of the driving force.
E) The system will exhibit chaotic motion.
3.
In the figure below, a 2.4 kg ball is suspended from a string 3.68 m long and is pulled slightly to the left. As
the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring
pushes against the ball and eventually the ball is returned to its original starting position. Find the time for
one complete cycle of this motion if the spring constant is 12 N/m. (Assume that once the pendulum ball
hits the spring there is no effect due to the vertical movement of the ball.)
A) 6.7 s
B) 3.9 s
C) 1.9 s
D) 3.3 s
3.68 m
2.4 kg
4.
A 250 g mass is hanging from a spring with force constant k = 85 N/m. The mass is immersed in a fluid
which yields a damping of b = 70 g/s. How long does it take for the amplitude of the damped oscillation to
drop to one half its original value?
A) 2.5 s
B) 5.0 s
C) 10 s
D) 25 s
1
5.
A string with tension T is attached to a solid wall lying on the x-axis. A transverse wave pulse is
introduced in the string travelling toward the wall. Which of the following statements best describes what
happens after the pulse hits the wall?
A) The pulse will be reflected in phase.
B) The pulse will be reflected 180° out of phase.
C) The pulse will be annihilated.
D) The pulse will travel through the wall.
6.
Use the following information to answer question this question.
The amplitudes and phase differences of four pairs of waves of equal wavelengths are depicted in the table
below. Each pair travels along the same direction on the same string.
Pair
A
B
C
D
Amplitude of Wave 1
3 mm
5 mm
9 mm
2 mm
Amplitude of Wave 2
6 mm
1 mm
7 mm
2 mm
Phase difference
π rad
0 rad
π rad
0 rad
Rank the four pairs according to the amplitudes of their resultant waves, greatest to smallest.
A) B, D, A, C
B) C, A, B, D
C) B, A, C, D
D) C, B, A, D
7.
A sinusoidal transverse wave is traveling along a string in the negative x direction. The figure below shows
the displacement as a function of position at time t = 0 s. The y-intercept is 4.0 cm. If the string has a
tension of 3.6 N and a linear density of 25 g/m, the equation that best describes the wave is (where x is in
meters, t in seconds),
A) (5.0 cm) cos(16x +190t – .64)
B) (5.0 cm) cos(16x – 190t + .64)
C) (5.0 cm) cos(0.16x +19t – .64)
D) (5.0 cm) cos(0.16x -19t – .64)
E) (5.0 cm) cos(16x +190t + .64)
2
8.
A 3.0-g string, 0.14 m long, is under tension. The string produces a 200-Hz tone when it vibrates in the
third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in SI units, is closest to:
A) 10
B) 6.1
C) 8.8
D) 4.8
E) 7.5
9.
Which one of the following statements is true?
A) If the intensity of sound A is twice the intensity of sound B, then the intensity level (in decibels) of
A is twice the intensity level of B.
B) If two different sound waves have the same displacement amplitude, then they must have the same
intensity.
C) If two sound waves have the same intensity level (in decibels), they must have the same intensity.
D) If the intensity level (in decibels) of sound A is twice the intensity level of sound B, then the
intensity of A is twice the intensity of B.
E) If two different sound waves have the same displacement amplitude, then they must have the same
intensity level (in decibels).
10. An open pipe, 0.61 m long, vibrates in the third harmonic (second overtone) with a frequency of 888 Hz. In
this situation, the length of the shortest stopped pipe, which has the same resonant frequency as the open
pipe in the second overtone, in cm, is closest to:
A) 21
B) 10
C) 31
D) 5.2
E) 12
11. Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the
same oscillator at a frequency of 875 Hz. You are standing midway between the speakers, and the speed of
sound in the room is 344 m/s. The minimum distance you can walk toward either speaker in order to hear a
minimum of sound is closest to:
A) 0.393 m
B) 0.590 m
C) 0.197 m
D) 0.0983 m
E) 0.295 m
3
12. A carousel, 5.0 m in radius, has a pair of 600-Hz sirens, mounted on posts at opposite ends of a diameter.
The carousel rotates with an angular velocity of 0.80 rad/s. A stationary listener is located at a distance
from the carousel. The speed of sound is 350 m/s. (Hint: for circular motion v = rω.) In this situation, the
maximum beat frequency of the sirens at the position of the listener, in SI units, is closest to:
A) 8
B) 14
C) 12
D) 10
E) 6
13. A 6.53 × 1014 Hz electromagnetic wave propagates in carbon tetrachloride with a speed of 2.05 × 108 m/s.
The wavelength of the wave in vacuum is closest to:
A) 459 nm
B) 505 nm
C) 368 nm
D) 413 nm
E) 314 nm
14. In the figure below are some wavefronts emitted by a source of sound S. This picture can help us to
understand
A) why the siren on a police car changes its pitch as it races past us.
B) why it is that our hearing is best near 3000 Hz.
C) the phenomenon of beats.
D) why a sound grows quieter as we move away from the source.
E) how sonar works.
4
15. When light travels from air into water,
A) its velocity and wavelength change, but its frequency does not change.
B)
its velocity, wavelength, and frequency all change.
C) its wavelength changes, but its velocity and frequency do not change.
D) its velocity changes, but its frequency and wavelength do not change.
E) its frequency changes, but its velocity and wavelength do not change.
16. Rainbows are produced
A)
when light reflected outside and within raindrops interferes, causing different wavelengths to be
seen at different observation angles.
B)
by reflection and refraction of light in rain drops. Different colors are seen at different anlges
because the refraction index of water varies slightly for different frequencies of light.
C)
as a result of the Doppler shift. Raindrops blown by the wind away from the observer appear
red, while those blown toward the observer appear blue.
D)
by Bragg diffraction in raindrops, which occurs when light waves interfere constructively when
they are scattered off atoms. That is why particularly vivid rainbows appear at the Bragg angle.
17. Light enters a medium with a refractive index n2 = 2.0 from a medium with refractive index n1 = 1.5. The
ratio of the speed of light in medium 2 to the speed of light in medium 1 is:
A) 3/4
B) 1 (i.e. the speed of light is constant)
C) 4/3
18. A certain prism in air has a critical total internal reflection angle θ. If this prism is immersed in water
(refractive index of water is nw=1.33) does the critical angle for total internal reflection change? (index of
refraction for the prism is 1.39)
A) It remains the same
B) It decreases
C) It increases
19. A concave mirror has a radius of curvature of 21.0 cm. If the mirror is immersed in water (refractive index
of water is nw=1.33), what is the magnitude of its focal length?
A) 31.8 cm
B) 14.0 cm
C) 10.5 cm
D) 7.89 cm
E) 3.47 cm
5
20. Convex spherical mirrors produce images which
A) Are always larger than the actual object
B) Are always smaller than the actual object
C) Are sometimes the same size as the actual object
D) Are sometimes larger, sometimes smaller
21. An object is a distance 30.0 cm to the left of the centre of a silvered sphere which has a diameter of 30.0
cm, as shown below. What is the magnification of the resulting image (the sphere acts like a curved
mirror)?
A) M = + 1.00
B) M = + 1/3
C) M = - 1/3
D) M = -1.00
E) M = - 3
22. A concave makeup mirror is designed so the virtual image is twice the size of the object, when the distance
between the object and the mirror is 15 cm. The radius of curvature of the mirror is
A) 15 cm
B) 20 cm
C) 40 cm
D) 60 cm
23. An object is placed at the center of curvature of a concave spherical mirror. The image formed by the
mirror is
A) Located at the focal point of the mirror
B) Located between the focal point and the center of curvature of the mirror
C) Located at the center of curvature of the mirror
D) Located at distances much larger than the radius of curvature of the mirror
6
24. A beam of light of wavelength 600 nm (in air) undergoes a total internal reflection at the critical angle of
40 degrees at the glass-air interface. The wavelength of the light in glass is
A) 386 nm
B) 478 nm
C) 933 nm
D) 600 nm
25. A spherical mirror is polished on both sides. When the convex side is used as a mirror, the magnification is
+1/4. What is the magnification when the concave side is used as a mirror, the object remaining the same
distance from the mirror.
A) +1/4
B) -1/2
C) +1/2
D) -1/3
26.
27.
Which of the following statements is true when the diameter of a converging lens is increased?
A)
This would have no effect on the appearance of the image.
B)
The focal length decreases.
C)
The magnification increases.
D)
The intensity of the image increases.
If two convex lenses identical in size and shape are manufactured from glass with two different
indices of refraction, would the focal length of the lens with the greater index of refraction (lens 1) be
smaller or larger than that of the other lens (lens 2)?
A)
Smaller.
B)
Larger.
7
28.
A converging lens and an object, Q, are at positions as shown below. Which of the rays A, B, C, and
D could have come from the point Q on top of the object?
29.
Diana, Duck of Science, looks out through the spherical view port of her submarine to see her
assistant, Bob the Thrill-Seeking Cat, SCUBA-diving just outside the window. The window glass is thin
(but strong!) and of uniform thickness, so you can assume any refraction is due entirely to the water. The
window bulges outward (away from Diana), with a radius of curvature of 30 cm. The index of refraction of
air is nA = 1.00, and that of water is nW = 1.33. If Bob is 60 cm long and is swimming 1.00 m from the
window, how long does Diana see him to be?
A)
41.2 cm
B)
32.8 cm
C)
18.6 cm
D)
235 cm
E)
30.2 cm
30.
An object is placed 12 cm away from a lens with a focal length f = +6.67 cm. Which of the following
describes the image formed by the lens?
A)
real and inverted
B)
real and upright
C)
virtual and inverted
D)
virtual and upright
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31.
An object 1.00 cm tall is placed 5.00 cm behind a diverging lens. The magnitude of the lens’s focal
length is 10.0 cm. Where is the image located?
A)
10.0 cm behind the lens
B)
3.33 cm behind the lens
C)
0.909 cm in front of the lens
D)
3.33 cm in front of the lens
32.
When an object is placed 30 cm from a converging lens, the image formed is positioned 60 cm from
the lens. If the object is moved 5 cm closer to the lens, the position of the image changes by 40 cm. What is
the focal length of the lens?
A)
32 cm
B)
25 cm
C)
16 cm
D)
20 cm
E)
36 cm
33. If light traveling in material of index n1 is reflected from a material of index n2, then in the case where
n2 > n1 the light undergoes a 180° phase shift on reflection. This helps us to understand:
A) why the separation of fringes due to two slit interference increases with increasing angle of
deviation.
B) why non-reflective coatings on lenses are made using coating material with a greater index of
refraction than that of the glass they are coating.
C) why a dark fringe appears on the axis (θ = 0) in a double slit interference pattern.
D) why no factor of two appears in the equation d sin θ = mλ.
E) why the first fringe is dark for an air wedge of increasing thickness between glass slides.
34. Monochromatic laser light of frequency 5.20 × 1014 Hz is shone on a pair of thin parallel slits in air, and the
pattern is viewed on a screen 1.20 m away. The fifth bright fringes (not counting the central fringe) occur at
±2.12 cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent
liquid. When the experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central
bright fringe. The index of refraction of the liquid is closest to:
A) 1.23
B) 1.43
C) 1.48
D) 1.54
E) 1.65
9
35. Light of wavelength λ = 525 nm passes through two slits separated by 0.500 mm and produces an
interference pattern on a screen 2.9 m away. Let the intensity at the central maximum be I0. What is the
closest distance on the screen from the center of this central maximum to the point where the intensity has
fallen to I0/2? (Assume that the slits are sufficiently narrow that diffraction effects may be ignored.)
A) 0.65 mm
B) 0.76 mm
C) 0.95 mm
D) 1.1 mm
E) 1.3 mm
36. A soap bubble, when illuminated with light of 529 nm, appears to be especially reflective. If the index of
refraction of the film is 1.35, what is the thinnest thickness the soap film can be?
A) 529 nm
B) 265 nm
C) 132 nm
D) 98 nm
E) 82 nm
37. Two radio antennas are 100 m apart. The two antennas radiate in phase at a frequency of 10 MHz. All radio
measurements are made far from the antennas. At how many directions in the whole 360 degree angle
around the two antennas do we have maximum intensity?
A) 6 directions
B) 8 directions
C) 10 directions
D) 12 directions
E) 14 directions
38. A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the
screen is 1.00 cm wide, as measured between the dark fringes that border it on either side. Which of the
following actions would decrease the width of the central bright fringe?
A) decrease the width of the slit.
B) put the apparatus all under water.
C) increase the wavelength of the light.
D) increase the width of the slit.
E) both B and D.
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39. In a single slit experiment, we consider a point on the screen, close to the central bright fringe, where the
total phase difference between the wavelets from the two sides of the slit is 50 degrees. The ratio of
intensity at this point to that of the central maximum is closest to:
A) 0.94
B) 0.85
C) 0.50
D) 0.017
E) 2.9 × 10-4
40. A laser beam of wavelength 450 nm shines at normal incidence on the reflective side of a compact disc.
The tracks of tiny pits in which information is coded onto the CD are 1600 nm apart for what angles of
reflection measured from the normal will the intensity of light be maximum?
A) 0, 16.3°, 32.6°, 49.0°
B) 0, 16.3°, 34.2°, 57.5°
C) 0, 12.6°, 23.2°, 37.8°
D) None of the above
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