Name:___________________________
Practice Problems
A. Wave Motion
Questions 1-3 Consider the following graph of a periodic wave.
Period:____________
b.
wavelength of the first harmonic
c.
frequency of the first harmonic
wave direction


1.
2.
3.
4.
5.
If this is a transverse wave in a steel beam, which way are
the iron atoms moving?
(A) 
(B) 
If this is a longitudinal wave in a steel beam, which way are the
iron atoms moving?
(A) 
(B) 
If this is a water wave, which way is the black dot moving?
(A) 
(B) 
(C) 
(D) 
If you wanted to make a sound by hitting a steel beam with a
hammer, which way would you strike the left side of the beam?

(A) 
(B) 
(C) 
(D) , , or 
The figure shows two wave pulses that are approaching each
other.
12. A 262-Hz tuning fork is set into vibration above a vertical
open tube filled with water. The water level is allowed to drop
slowly. As it does so, the air in the tube above the water level
resonates when the air column is 0.327 m and again at 0.982
m. What is the velocity of sound?
13. Determine the observed frequency of sound (f’) for 600 Hz
sound (f) for each of the following situations. (vw = 340 m/s)
a. The source approaches the observer at 34 m/s.
b.
The observer approaches the source at 34 m/s.
c.
The source recedes from the observer at 34 m/s.
d.
The observer recedes from the source at 34 m/s.
Which of the following best shows the shape of the resultant
pulse when points P and Q, coincide?
(A)
(B)
14. Two whistles are blown simultaneously. The wavelengths of
the sound emitted are 9.0 m and 9.5 m, respectively. How
many beats per second are heard? The speed of sound in
air is 340 m/s.
(C)
15. When the E-string of an old piano is sounded simultaneously
with a tuning fork of frequency 660 Hz, a 2-Hz beat is heard.
What are the two possible frequencies of the E-string?
(D)
Questions 6-8 A child swings from A to C back to A
16. A guitar string 0.5-m long has a mass of 0.010 kg and is
under tension of 4500 N.
a. What is the wave velocity?
6.
7.
8.
9.
A
B
C
Where would the child hear the highest frequency?
Where would the child hear the lowest frequency?
Where would the child hear the same frequency as the man?
Complete the following chart.
Velocity
Frequency
Wavelength
340 m/s
What is the frequency of the first harmonic?
c.
What tension would produce a first harmonic frequency
of 600 Hz?
17. The frequency of the second harmonic is 400 Hz. What is
the frequency of the fourth harmonic?
510 s-1
337 m/s
b.
3.5 m
0.067 s-1
75 m
10. 100-Hz and 85-Hz whistles are blown simultaneously. How
many beats per second are heard?
11. A guitar string 0.5-m long has a mass of 0.0125 kg and is
under tension of 4 x 103 N. Determine the
a. wave velocity
18. An ambulance, generating a 600 Hz sound, approaches a
listener at 17 m/s. What frequency does the listener hear?
(vw = 340 m/s)
B. Light
20. You look at your self in a full length mirror, where the bottom
half of the mirror is covered. What would you see?
(A) The top half of your body
(B) The bottom half of your body
(C) Your whole body full size
(D) Your whole body half size
21. Where would the image form?
observer
B
35. Light strikes a flat piece of glass (n = 1.50) at an incident
angle of 70o. Some of the light is reflected and some light
passes out of the glass on the opposite side.
a. What is the angle of reflection?
A
C
(object) X
mirror
D
Questions 22-24 Light travels from air to glass and bends as shown
in the diagram below.

b.
What is the angle of refraction inside the glass?

c.
With what angle does light exit the glass?
36. What is the critical angle for glass (n = 1.50) in water (1.33)?
22. Which side of the vertical line is the glass?
(A) left
(B) right
23. Would the diagram differ if the light went from glass to air?
(A) yes
(B) no
24. Would the diagram be different if the glass was under water?
(A) yes
(B) no
Questions 25-27 A light ray R in medium I strikes a sphere of
medium II with angle of incidence . The index of refraction
for medium I is n1 and medium II is n2.
A
B
C
D
E
25. Which path is possible if nI < nII?
26. Which path is possible if nI > nII?
27. Which path is possible if nI = nII?
Questions 28-29 You are on shore looking at a fish in a pond.
28. You want to spear the fish, where would you aim?
(A) directly at
(B) behind
(C) ahead
29. Where would you aim a laser light on a fish under water?
(A) directly at
(B) behind
(C) ahead
30. 600-nm light (in air) enters glass (n = 1.50). Determine the
a. frequency in glass.
b.
wavelength in glass.
c.
speed of light in glass.

C. Lenses and Mirrors
37. A mirror with 10-cm radius of curvature, has a focal length of
38. State whether the lens or mirror is converge or diverge.
Lens
Mirror
Concave
Convex
39. Convex-converging lens: Draw the two ray tracings.
F
Calculated di
F
F
F
Calculated hi
F
F
31. The rays of the sun strike the surface of a lake at an angle of
65o with the vertical. At what angle, measured from the
vertical, is the refracted ray in the water (n = 1.33)?
Calculated di
32. Determine the critical angle for light passing from diamond (n
= 2.42) into air (n = 1.00).
Calculated hi
40. Concave-diverging lens: Draw the ray tracings.
33. What is the index of refraction of glass for which the critical
angle at the glass-air interface is 37o?
F
34. Light of wavelength 450 nm passes from a vacuum into water
(n = 1.33). Determine the following in water
velocity
wavelength
Calculated di
F
Calculated hi
41. What is the + and – case for each of the following?
f
di
h
positive
negative
42. What does it mean to have a magnification that is
greater than 1
negative
43. Concave-converging mirror: Draw the two ray tracings.
F
Calculated di
F
47. Indicate the nature of the image when the object position (do)
is in the following ranges.
do
real/virtual
inverted/upright
|M|
do > 2f
do = 2f
2f > do > f
do = f
0 < do < f
48. An object 2.0 cm high is placed 20 cm from a convex lens of
focal length 10 cm.
a. Draw a ray diagram and locate the position of the image
formed. Draw in the image.
F
Calculated hi
F
b. Mathematically determine the following.
image distance, di
magnification, M
image height, hi
F
F
c. Circle the correct descriptions of the image.
real virtual inverted upright larger same size smaller
49. An object 2.0 cm high is placed 10 cm from a concave lens of
focal length 10 cm.
a. Draw a ray diagram and locate the position of the image
formed. Draw in the image.
F
F
F
Calculated di
Calculated hi
44. Convex-diverging mirror: Draw the ray tracings.
F
Calculated di
F
Calculated hi
45. A 1.5-cm-high diamond ring is placed 20 cm from a concave
mirror (r = 30 cm). Determine
a. the position of the image di.
b.
F
b. Mathematically determine the following.
image distance, di
magnification, M
image height, hi
c. Circle the correct descriptions of the image.
real virtual inverted upright larger same size smaller
50. An object 1.0 cm high is placed 30 cm from a concave mirror
of focal length 20 cm.
a. Draw a ray diagram and locate the position of the image
formed. Draw in the image.
F
F
the height of the image hi.
b. Mathematically determine the following.
image distance, di
magnification, M
image height, hi
46. Which type of mirror is the following
make-up mirror
passenger side mirror
c. Circle the correct descriptions of the image.
real virtual inverted upright larger same size
smaller
51. A mirror is convex on one side (left) and concave on the
other side (right). The center of curvature, C, is at 5.
1
2
3
4
C
5
54. Triangles S1RS2 and QPoP1 are nearly similar. Therefore, the
angles, , are equal.
6
a. Answer the following questions.
Which side is converging in function?
Which side could be used as a make-up mirror?
Which side could be used as a side mirror in a car?
Which point is closest to focus?
b. Where would an object be placed to produce
an upright magnified image?
an inverted unmagnified image?
an inverted image that is smaller than the object?
no image at all
an upright image that is smaller than the object?
an inverted image that is larger than the object?
52. A converging lens (f = 10 cm) is used to examine object A
that is held 6 cm from the lens.
a. Draw rays that show the position and size of the image.
a.
Complete the trig function: _______ = x/L.
b.
Complete the trig function: _______ = /d.
c.
Determine the sin and tan of the following angles.
1
2
3
4
5
6
7
8
9
o
10
sin
tan
d. What is the largest angle where the 3 place values for
o
sin and tanare equal?
e. Assuming that  is less than 7o and tan = sin, combine
the formulas into one and solve for x.
x=
tan = x/L and sin = m/d
b.
Is the image real or virtual. Explain your reasoning.
c.
Calculate the distance of the image from the lens.
d.
Calculate the ratio of the image size to the object size.
e.
The object A is moved to 20 cm. Describe the image
position, size, and orientation.
D. Interference
53. Consider the diagram of a light wave.

B
Order

____
____
____
____
____
____
____
____
____
____
____
____
____ ____
56. The diagram shows the relative intensity for each band.
D
A
tan = x/L and sin = (m + ½)/d x =
55. Consider the Young's double slit experiment below, which
demonstrated the wave nature of light.
a. Fill in the order for each bright and dark band.
b. Fill in the path difference between the rays.
E
C
a.
Which position(s) are in phase with the dot?
b.
Which position(s) are ½ out of phase with the dot?
c.
Which position(s) are ¼ out of phase with the dot?
What generalization can you say about the intensity as m
increases?
57. A 600 nm (600 x 10-9 m) laser beam is incident on a pair of
slits 0.500 mm (0.50 x 10-3 m) apart. Determine the angular
deflection, , for the following.
a. Second-order bright band?

b.
Zero-order dark band?
c.
Determine the distance from the center bright band to
the zero order dark band (x) on a screen 2.0 m away.
(1) Use the angular deflection from part b.
b.
What is the minimum thickness for a soap bubble?

61. A laser beam is incident on two slits separated by 0.5 mm.
The interference pattern is formed on a screen 1 m from the
slits and the first bright fringe is found to be 0.12 cm to the
right of the central maximum. Determine the
a. angular deflection of the first bright fringe.
b.
wavelength of light in nanometers.
c.
distance from the center to the zero order dark fringe.
d.
width of the zero order bright fringe.
e.
Would the width of the zero order bright fringe increase
or decrease if 700 nm light is used?
(2) Use the formula derived in 54e(2).
d.
e.
What is the width of the center bright band?
(Distance between the zero order dark bands.)
One slit is covered, so that the light only passes through
one slit which is 0.500 mm wide and 1.00 mm tall.
(1) What is the width of the light spot?
(2) What is the length of the light spot?
62. The hydrogen spectrum is analyzed using a 600 lines/mm
diffraction grating, which is 1.00 m away from the light
source. An aqua line appears at 30.5 cm and a red line
appears at 42.8 cm to the right of the light source. Determine
the
a. wavelength of aqua light.
(3) The slit is longer than it is wide. How would you
describe the shape of the spot light?
b.
58. A 500 lines/mm diffraction grating is used to observe mercury
light. The first-order green band is 28.4 cm away from the
light when the grating is 1.00-meter from the light.
a. What is the angle of deflection for the green band?
b.
What is the spacing between each groove on the
diffraction grating (d)?
c.
Determine the wavelength of the green band.
wavelength of red light.
63. What is the minimum thickness for a soap bubble that
appears red ( = 750 nm, n = 1.35)?
64. What is the thickness of a coating (n = 1.22) on glass
(n = 1.50) that will eliminate 550 nm light?
Practice Multiple Choice
d.
Use the formula derived in 54e(1) to determine .
e.
Which answer, part c or d, is correct? Explain.
Briefly explain why the answer is correct in the space provided.
Questions 1-3 The diagram represents a transverse wave
traveling in a string.
59. 500 nm light does not reflect off of a film (n = 1.25) that is on
a piece of glass (n = 1.5) viewed in air (n = 1).
a. What is the wavelength of light in the film?
1.
b.
What is the minimum thickness of the film?
6m
Which pair points is half a wavelength apart?
(A) A and D (B) D and F (C) B and F (D) D and H

c.
Would this coating work under water? Explain.
2.
What is the wavelength?
(A) 1 m
(B) 6 m
(C) 2 m
(D) 3 m

60. A soap bubble appears blue ( = 450 nm) in sunlight.
a. What is the wavelength in the soap film (n = 1.35)?
3.
What is the speed of the wave if its frequency is 9 Hz?
(A) 0.3 m/s (B) 1 m/s
(C) 3 m/s
(D) 27 m/s
4.
If the amplitude of a transverse wave traveling in a rope is
doubled, the speed of the wave in the rope will
(A) decrease
(B) increase
(C) remain the same
Question 5-6 Use the graph wavelength versus frequency of
waves to answer the questions.
14. A ringing bell is located in an airless chamber. The bell be
seen vibrating but not be heard because
(A) Light can travel through a vacuum, but sound cannot.
(B) Sound waves have greater amplitude than light waves.
(C) Light waves travel slower than sound waves.
(D) Sound waves have higher frequencies than light waves.
15. A partially filled tube of water resonates with a tuning fork
when the column of air above the water is 0.25 m long and
again when its length is 0.75 m. What is the wavelength of
the sound wave?
(A) 0.25 m (B) 0.50 m (C) 0.75 m (D) 1.0 m
16. Resonance occurs when a vibrating object transfers energy to
another object causing it to vibrate. The energy transfer is
most efficient when the two objects have the same
(A) frequency
(B) amplitude
(C) loudness
(D) speed
5.
What is the wavelength when the frequency is 2.0 Hz?
(A) 5.0 m (B) 2.5 m (C) 2.0 m (D) 1.0 m
6.
What is the speed of the waves generated in the spring?
(A) 2 m/s
(B) 5 m/s
(C) 7 m/s
(D) 10 m/s
7.
Sound in air can best be described as which of the following
types of waves?
(A) Longitudinal
(B) Transverse
(C) Gravitational
(D) Electromagnetic
8.
9.
Maximum destructive interference will occur when two waves
having the same amplitude and frequency
(A) meet crest to crest
(B) meet crest to trough
The motion of the individual particles in the medium
compared to the direction of the transverse wave, is
(A) perpendicular
(B) parallel
17. In the Doppler effect for sound waves, factors that affect the
frequency that the observer hears include which of the
following?
I. The speed of the source
II. The speed of the observer
III. The loudness of the sound
(A) I only
(B) II only (C) III only (D) I and II
18. A 100-Hz train whistle is sounded as the train approaches the
station at a velocity of 30 m/s, the whistle frequency that a
stationary listener hears is most nearly (vw = 330 m/s)
(A) 90 Hz (B) 110 Hz (C) 120 Hz (D) 240 Hz
19. The product of a wave's frequency and its period is
(A) one
(B) its velocity
(C) its wavelength
(D) Plank's constant
20. The figure shows two waves that are approaching each other.
Questions 10-12 A standing wave of frequency 5 Hz is set up on a
string 2 m long with nodes at both ends and in the center.
Which of the following best shows the shape of the resultant
pulse when points P and Q, coincide?
(A)
(B)
10. What is the harmonic of this standing wave?
(A) first
(B) second (C) third
(D) fourth
(C)
11. The speed at which waves propagate on the string is
(A) 0.4 m/s (B) 2.5 m/s (C) 5 m/s
(D) 10 m/s
12. The first harmonic of vibration of the string is
(A) 1 Hz
(B) 2.5 Hz (C) 5 Hz
(D) 7.5 Hz
13. The frequencies of the third harmonics of a vibrating string is
f. What is the fundamental frequency of this string?
(A) f/3
(B) f/2
(C) f
(D) 2f
(D)
21. A sound wave has a wavelength of 5.5 m when its velocity is
330 m/s. What is the wavelength of this sound in a medium
where its speed is 1320 m/s?
(A) 1.4 m (B) 2.2 m (C) 14 m
(D) 22 m
22. A cord of fixed length and uniform density, when held
between two fixed points under tension T, vibrates with a
fundamental frequency f. If the tension is doubled, the
fundamental frequency is
(A) 2f
(B) √2f
(C) f
(D) f/√2
Questions 23-24 An object, slanted at an angle of 45°, is placed
in front of a vertical plane mirror.
mirror
•A
•B
•C

•D
23. Which of the labeled points is the position of the image?
24. Which of shows the orientation of the object's image?
(A) 
(B) 
(C) 
(D) 
Questions 25-27 A ray of light ( = 6 x 10-7 m) in air (n = 1) is
incident on quartz glass (n = 2).
Air
Quartz glass
25. What is the angle of reflection measured from normal?
(A) 35o
(B) 55o
(C) 22o
(D) 33o
34. Light leaves a source at X and travels to Y along the path.
Which of the following statements is correct?
(A) n1 = n2 (B) n1 > n2 (C) v1 > v2 (D) f1 > f2
35. Which statement is correct about lenses and mirrors?
(A) Converging lenses are thinnest in the middle.
(B) Convex mirrors are curved inward.
(C) A real image formed by a convex lens is dimmed when
half of the lens is covered.
(D) A diverging lens or mirror can make a real or virtual
image depending on where the object is placed.
36. Two plane mirrors are positioned perpendicular to each other
as shown. A ray of light is incident on mirror 1 at an angle of
55°. This ray is reflected from mirror 1 and then strikes
mirror 2.
26. The angle of refraction measured from normal is closest to
(A) 25o
(B) 35o
(C) 55o
(D) 75o
27. Which is correct about the light in quartz glass is correct?
(A) v = 3 x 108 m/s
(B)  = 6 x 10-7 m
8
(C) v = 1.5 x 10 m/s
(D)  = 1.2 x 10-6 m
Question 28-32 A curved surface, with a 10-cm focal length is
mirrored on both sides.
A
B
C
D
|
|
|
10 cm
10 cm
20 cm
28. Which location would you place an object to form a virtual
image that is smaller than the object?
29. Which location would you place light source in order to
produce parallel rays of reflected light?
Which is correct?
I. The incident ray for mirror 2 is 55o measured from
normal.
II. The reflected ray for mirror 2 is 35o measured from
normal.
III. The reflected ray for mirror 2 is parallel to incident ray for
mirror 1.
(A) I only
(B) II only (C) I and III (D) II and III
37. A thin film with index of refraction nf separates two materials,
each of which has an index of refraction less than nf. A
monochromatic beam of light is incident normally on the film.
30. Which location would you place an object to form a real
image?
31. Which location would you place an object to form a virtual
image that is larger than the object?
32. Which location is the radius of curvature for this mirror?
33. The critical angle for a transparent material in air is 30°. The
index of refraction is most nearly
(A) 0.33
(B) 0.50
(C) 1.0
(D) 2.0
If the light has wavelength  in air, maximum constructive
interference between the incident beam and the reflected
beam occurs for which of the following film thicknesses?
(A) 2/nf
(B) /nf
(C) /2nf
(D) /4nf
38. 600-nm light passes through two slits. The first-order
interference maximum appears at 6°. What is the separation
of the slits? (sin6o = 0.10)
(A) 1500 nm (B) 4500 nm (C) 3000 nm (D) 6000 nm
39. How are electromagnetic waves that are produced by
oscillating charges and sound waves in air that are produced
by oscillating tuning fork similar?
(A) Both have the same frequency as their respective
sources.
(B) Both require a matter medium for propagation.
(C) Both are longitudinal waves.
(D) Both are transverse waves.
40. When observed from Earth, the wavelengths of light emitted
by a star are shifted toward the red end of the spectrum. This
red shift occurs because the star is
(A) at rest relative to Earth
(B) moving away from Earth
(C) moving toward Earth at decreasing speed
(D) moving toward Earth at increasing speed
Questions 47-49 A light ray R in medium I strikes a sphere of
medium II with angle of incidence . The index of refraction
for medium I is n1 and medium 2 is n2.
47. Which path is possible if n1 < n2?

48. Which path is possible if n1 > n2?
41. Parallel wave fronts incident on an opening in a barrier are
diffracted. For which combination of wavelength and size of
opening will diffraction effects be greatest?
(A) short wavelength and narrow opening
(B) short wavelength and wide opening
(C) long wavelength and narrow opening
(D) long wavelength and wide opening
49. Which path is possible if n1 = n2?
(A) A or B (B) C or D (C) All
(D) None
50. A beam of white light is incident on a triangular glass prism (n
= 1.5) for visible light, producing a spectrum. Initially, the
prism is in an aquarium filled with air.
Question 42-45 Consider a converging lens with focal length, f.
Which is true if the aquarium is filled with water (n = 1.3)?
(A) No spectrum is produced.
(B) The positions of red and violet are reversed.
(C) The spectrum produced has greater separation between
red and violet than that produced in air.
(D) The spectrum produced has less separation between
red and violet than that produced in air.
42. Where is the image formed for an object that is placed on the
left at 3/2f?
(A) On the right at 3f.
(B) On the left at 3f.
(C) On the right at ⅓f.
(D) On the left at f.
43. Where is the image formed for an object that is placed on the
left at ½f?
(A) On the right at 3f.
(B) On the left at 3f.
(C) On the right at ⅓f.
(D) On the left at f.
Practice Free Response
1.
44. Where would the object be placed in order to produce an
upright image that is larger than the object?
(A) at 2f
(B) between 2f and f
(C) at f
(D) between f and the lens
The figure shows a converging mirror, focal point F, center of
curvature C, and an object represented by the arrow.
a. Draw a ray diagram showing two rays and the image.
45. Where would the object be placed in order to produce an
inverted image that has a magnification of 2?
(A) 2f
(B) 3/2f
(C) 4/3f
(D) 5/4f
46. Which is true of a single-slit diffraction pattern?
(A) It has equally spaced fringes of equal intensity.
(B) It has a relatively strong central maximum.
(C) It can be produced only if the slit width is less than one
wavelength.
(D) It can be produced only if the slit width is exactly one
wavelength.
b.
Is the image real or virtual? Justify your answer.

c.

The focal length of this mirror is 6.0 cm, and the object is
located 8.0 cm away from the mirror. Calculate the
position of the image formed by the mirror.
Suppose that the converging mirror is replaced by a
diverging mirror with the same radius of curvature that is the
same distance from the object, as shown below.
d. Draw a ray diagram showing two rays and the image.
e.
Calculate the angle of refraction 2.
b.
What minimum angle 3 would result in total internal
reflection (4 = 90o)?
c.
Would the incident angle 1 be greater than or less than
40o in order to produce total internal reflection?
d.
The glass is coated with a thin film that has an index of
refraction nf = 1.38 to reduce the partial reflection.
(1) Determine the wavelength of the red light in the film.
For this mirror, determine
(1) the image distance from the mirror.
(2) the magnification.
2.
a.
A diffraction grating with 600 lines/mm is used to study the
line spectrum of the light produced by a hydrogen discharge
tube. The grating is 1.0 m from the source (a hole at the
center of the meter stick). An observer sees the first-order
red line at a distance yr = 428 mm (0.428 m) from the hole.
(2) Determine the minimum thickness of the film.
4.
To demonstrate standing waves, one end of a string is
attached to a tuning fork with frequency 120 Hz. The other
end of the string passes over a pulley and is connected to a
suspended mass M as shown in the figure. The value of M is
such that the standing wave pattern has four "loops." The
length of the string from the tuning fork to the point where the
string touches the top of the pulley is 1.20 m. The linear
density of the string is 1.0 x 10-4 kg/m, and remains constant
throughout the experiment.
Determine
a. the angular deflection.
b.
3.
Determine the wavelength of the standing wave.
b.
Determine the speed of transverse waves along the
string.
c.
The speed of waves along the string increases with
increasing tension in the string. Indicate whether the
value of M should be increased or decreased in order to
double the number of loops in the standing wave pattern.
Justify your answer.
d.
If a point on the string at an antinode moves a total
vertical distance of 4 cm during one complete cycle,
what is the amplitude of the standing wave?
the wavelength of the red light.
The 600 line/mm grating is replaced by a 800 lines/mm
grating. Determine
c. the angular deflection.
d.
a.
the distance, yr, where the observer sees the first-order
red line.
A beam of red light of wavelength 6.65 x 10-7 m in air is
incident on a glass prism at an angle 1. The glass has index
of refraction n = 1.65 for the red light. When 1 = 40o, the
beam emerges on the other side at 4 = 84o.