SPH 3U0: Exam Review: Sound Waves and Projectile Motion
True/False
Indicate whether the sentence or statement is true or false.
____
1. A trough is a negative pulse which occurs in a longitudinal wave.
____
2. When a student sends a positive pulse towards the fixed-end of a spring, the reflected pulse returns as a negative
pulse.
____
3. The nodal point of a standing wave forms due to the continuous destructive interference of two waves at that
point.
____
4. A suspended pendulum can be forced to move if an identical pendulum is suspended from the same support due
to the effect of sympathetic vibrations.
____
5. The nodal lines in a two-point source interference pattern are parabolic in shape.
____
6. Sound is a torsional wave.
____
7. Increasing the amplitude of a sound wave also increases the pitch.
____
8. The frequency of a string is determined by its length, tension, amplitude, and diameter.
____
9. Resonating air columns that are closed at one end create a node at the open end.
____ 10. Open air columns (i.e., open at both ends) create resonant lengths which are
, and so on, of the
original sound wave.
____ 11. Most high quality sound systems utilize three individual speakers to reproduce sound as authentically as
possible.
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____ 12. During complete destructive interference, which of the following could be produced?
a. supercrest
d. antinode
b. supernode
e. resonance
c. node
____ 13. An acoustic guitar contains a sound box that increases the loudness of the sounds the strings make. This is due
to the property called
a. amplification
d. resonance
b. refraction
e. interference
c. reflection
____ 14. A standing wave with three loops is generated in a string. If the wavelength is 10 cm, how far apart are the nodes
created?
a. 2.5 cm
d. 20 cm
b. 5.0 cm
e. 30 cm
c. 10 cm
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____ 15. A three-loop standing wave is generated in a string by attaching one end to a wall and letting the transmitted and
reflected waves interfere. If the wavelength of the wave is 15 cm, how far from the wall is the first antinode
created?
a. 3.75 cm
d. 30 cm
b. 7.5 cm
e. 45 cm
c. 15 cm
____ 16. Which of the following frequencies is ultrasonic?
a. 12 Hz
d. 5000 Hz
b. 25 Hz
e. 25 000 Hz
c. 332 Hz
____ 17. During destructive interference in sound, which of the following could be produced?
a. louder sound
d. resonance
b. antinode
e. supercrest
c. quieter sound
____ 18. When two trumpets are played together, 20 beats are heard in 4.0 s. If the frequency of the lower pitched
trumpet is 440 Hz, what is the frequency of the higher pitched trumpet?
a. 460 Hz
d. 520 Hz
b. 444 Hz
e. 456 Hz
c. 445 Hz
____ 19. The intensity level of sound does not depend on which of the following?
a. amplitude of the vibrating source
d. frequency of the source
b. vibrational energy of the source
e. none of the above
c. distance from the source
____ 20. The amount of diffraction in a sound wave depends upon
a. wavelength and opening size
d. amplitude and opening size
b. frequency and amplitude
e. wavelength and speed
c. wavelength and amplitude
____ 21. Sound cannot propagate in which of the following?
a. solidified air
d. ice
b. water vapour
e. perfect vacuum
c. water
____ 22. A 256-Hz tuning fork creates sound which travels through the air at 344 m/s. The distance between adjacent
rarefactions is
a. 67.2 cm
d. 1.34 m
b. 2.69 m
e. 88.0 m
c. 88.0 cm
____ 23. For every 10ºC increase in air temperature, the speed of sound in the air
a. decreases by 10 m/s
d. increases by 6.0 m/s
b. increases by 10 m/s
e. remains relatively unchanged
c. decreases by 6.0 m/s
____ 24. Which of the following frequency ratios would provide the most pleasant sound?
a. 3 : 2
d. 2 : 1.15
b. 1.15 : 2
e. all the above
c. 1 : 1
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____ 25. The frequency produced by a vibrating string is 800 Hz. What will its frequency be if its diameter is
quadrupled?
a. 200 Hz
d. 1600 Hz
b. 400 Hz
e. 3200 Hz
c. 800 Hz
____ 26. When standing waves are formed on a string fastened at both ends, how many nodes should be present in the
third overtone?
a. one
d. four
b. two
e. five
c. three
____ 27. Adjacent nodes that are formed in a resonating air column closed at one end form at a distance of
a. one-quarter wavelength from one another
b. one-quarter wavelength from each end
c. one-half wavelength from one another
d. one-half wavelength from each end
e. one wavelength from one another
____ 28. An air column closed at one end is vibrating in its third resonant length. If the wavelength of the sound is 80 cm,
the length of the air column is
a. 100 m
d. 1 m
b. 1 cm
e. 1.2 m
c. 120 cm
____ 29. The first and second resonant lengths of an air column that is closed at one end are 15.5 cm and 45.5 cm,
respectively. The best value for the wavelength of the wave is
a. 30 cm
d. 62 cm
b. 31 cm
e. 91 cm
c. 60 cm
____ 30. Which of the following is not a type of percussion instrument?
a. single, indefinite pitch instruments (triangle, castanets, bass drum)
b. multiple definite pitch instruments (marimba, xylophone, carillon)
c. variable pitch instruments (timpani, kettle drum)
d. variable indefinite pitch (electric drum, electric marimba)
e. none of the above
Short Answer
31. State the type of vibration that occurs in each of the following:
(a) the spring in a pogo stick as a child bounces up and down on it
(b) a tree swaying in the wind
(c) the rotating masses on an anniversary clock
32. For each of the following, calculate the frequency, in hertz, and the period, in seconds:
(a) a bee beating its wings 3000 times in 30 s
(b) a tuning fork completing 2048 oscillations in 8.0 s
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33. Sketch the resultant wave form when the following two pulses meet. (Assume the meeting point corresponds to
the centre of each pulse.)
34. You are standing in a room that has two speakers, one placed at each corner at the front of the room. The
speakers are connected to the same source and are emitting a pure 500-Hz signal. As you walk across the back
of the room, you notice the sound from the speakers varies in intensity from louder to quieter. Explain this
observation.
35. The engine of a Grand Prix race car sounds different as it approaches you than when it is moving away from
you. Explain why.
36. You know that the pitch of a train whistle is about 5.0 kHz. As you stand at a railway crossing, you hear a train
whistle whose frequency is only 4.0 kHz. Is the train approaching you or travelling away from you? Explain
your answer.
37. People with inner ear infections can often have problems with balance. Explain why.
38. For each pair of frequencies listed below, calculate the ratio of their frequencies as a simple fraction, then
determine which pair has the higher dissonance.
(a) 261.6 Hz (Middle C) and 392 Hz (G4)
(b) 349.2 Hz (F4) and 392 Hz (G4)
39. What happens to the wavelength of a wave on a string if
(a) its length is doubled?
(b) its diameter is doubled?
(c) both the length and the diameter are doubled?
40. A ball rolls off a table and falls to the ground below. Its entire flight is captured on a stroboscopic photograph.
Sketch what the photograph would look like if you viewed the motion with the ball initially moving to your
right.
Problem
41. Calculate the period and frequency of a pendulum that completes 150 vibrations in 1.5 min.
42. The distance between two successive crests in a wave is 1.5 m, and the source generates 25 crests and 25
troughs in 5.0 s. What is the speed of the waves?
43. The distance between the second and sixth crests in a wave is 75 cm, and one crest travels a distance of 25 cm in
3.0 s. Find the frequency of the wave.
44. A sound wave with a frequency of 1.25  104 Hz travels at 344 m/s. What is its wavelength?
45. A wave on a coiled spring travels at 6.2 m/s with successive crests separated by a distance of 1.25 m. What is the
period of the waves?
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46. The distance between the first and fourth nodes in a standing wave is 30.0 cm. If the waves travel at 2.50 m/s,
what is the frequency of the waves?
47. A standing wave with five loops is generated in a string. If the waves travel at 17.5 m/s with a frequency of 1.40
 102 Hz, how long is the string?
48. What is the speed of sound on a warm, summer day when the temperature is 30ºC?
49. The average young person can hear frequencies that are between 20 Hz and 20 kHz. If the speed of sound is 350
m/s, what range of wavelengths can this person hear? [Assume data is accurate to two significant digits.]
50. A train with a blowing whistle that has a frequency of 550 Hz is travelling at a speed of 80 km/h towards a
railway crossing where a car waits behind the barrier. If the speed of sound is 345 m/s, what is the frequency of
the sound that reaches the car as the train approaches the crossing?
51. The speed of sound at an altitude of 10 km (the height at which most jumbo jets fly) is approximately 295 m/s.
If a jumbo aircraft flies at speeds of 675 km/h when cruising, what is its Mach number?
52. A brass string with a density of 8.7 g/cm3 and a diameter of 0.25 mm produces a frequency of 256 Hz. What
frequency would a brass string with a diameter of 0.60 mm produce?
53. An 85 cm long guitar string produces a 392 Hz (middle G) note. What frequency will it produce if the guitarist
places his finger on a fret to shorten the string to 64 cm?
54. Certain pipe organs act like air columns closed at one end. If the speed of sound is 343 m/s, how long does a
pipe need to be to produce a fundamental frequency of 75.0 Hz? Include a diagram.
55. A tuba can be considered as an air column open at both ends. When straightened out, it is approximately 3.5 m
in length. The instrument is played in a room where the air temperature is 25ºC. Ignoring end corrections, what
is the lowest frequency the tuba can play at this length (i.e., find the fundamental frequency). Include a sketch.
56. Luggage racks mounted on the roof of a car can act as air columns open at both ends if the caps are removed. If
each rack is 1.20 m long and the speed of sound is 346 m/s, find the frequencies for the fundamental frequency,
first overtone, and second overtone that the racks can produce.
57. A football quarterback attempts a pass to one of the receivers. As the ball is snapped, the receiver leaves the line
of scrimmage and runs directly down field. The quarterback releases the ball 2.0 s later and from a position 3.0
m behind the line of scrimmage. He throws the ball with a speed of 26 m/s at an elevation of 60 above the
horizontal. The receiver makes a diving reception, catching the ball just as it reaches the ground. See the
diagram below.
(a) What is the time of flight of the football?
(b) What is the average speed of the receiver?
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58. A circus clown is fired from a cannon into a net that is situated 2.0 m above the cannon and some distance from
it. The cannon is elevated at 50.0 to the horizontal and the clown’s speed at launch is 15 m/s. See the diagram
below.
(a) Find the horizontal distance from the cannon where the net needs to placed in order for the clown to land in
it.
(b) Calculate the clown’s velocity as he lands in the net.
59. A boat is 50.0 m from the base of a cliff, fleeing at 5.0 m/s. A gun, mounted on the edge of the cliff fires a shell
at 40.0 m/s and hits the boat when it has fled another 50.0 m. See the diagram below.
(a) At what angle above the horizontal must the gun be aimed so that the shell will hit the target?
(b) How high is the cliff?
(c) With what velocity does the shell hit the boat?
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ExamReviewSoundWaves
Answer Section
TRUE/FALSE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
F
T
T
T
F
F
F
F
F
T
T
MULTIPLE CHOICE
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
D
B
A
E
C
C
D
A
E
D
D
A
A
E
C
D
C
D
SHORT ANSWER
31. ANS:
(a) longitudinal
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(b) transverse
(c) torsional
32. ANS:
For each solution, the following formulas were used:
(a) frequency = 100 Hz, period = 0.010 s
(b) frequency = 256 Hz, period = 0.0039 s
33. ANS:
Use the principle of superposition.
34. ANS:
You are experiencing a two-point source interference pattern between the two speakers. Since the speakers are
identical sources, there is a symmetrical pattern of alternating areas of constructive interference (louder areas)
and destructive interference (quieter areas) radiating outward from the speakers as the sound signals from each
speaker interfere with one another. As you walk across the back of the room, you are walking across this
pattern.
35. ANS:
Since the car is moving relative to you, the sound it makes is subject to the Doppler effect. As the car
approaches, its engine produces a sound with a higher apparent frequency than when the car is moving away, so
the pitch appears to change as the car races past you.
36. ANS:
Since the apparent frequency of the whistle is less than the true frequency, the train must be travelling away
from you. This is due to the Doppler effect.
37. ANS:
The inner ear contains the semicircular canals that are used for maintaining balance. If the inner ear has an
infection, these canals can also be affected, leading to problems with maintaining balance.
38. ANS:
(a)
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(b)
Pair (b) has the higher dissonance.
39. ANS:
(a) Since
, then the wavelength is also doubled.
(b) Since
, then the wavelength is also doubled.
(c) If both the length and the diameter are doubled, the changes are multiplied, thus the wavelength is
quadrupled.
40. ANS:
The horizontal component of the motion would be uniform and the vertical component would show the
acceleration due to gravity.
PROBLEM
41. ANS:
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The period is 0.60 s and the frequency is 1.7 Hz.
42. ANS:
The speed of the waves is 7.5 m/s.
43. ANS:
The distance across four waves is 75 cm, therefore,
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The frequency of the wave is 0.44 Hz.
44. ANS:
The wavelength is 2.75  10–2 m.
45. ANS:
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The period is 0.20 s.
46. ANS:
The frequency is 12.5 Hz.
47. ANS:
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The string is 0.313 m long.
48. ANS:
The speed of sound at 30ºC is 3.5  102 m/s.
49. ANS:
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The range of wavelengths is between 18 m and 0.018 m.
50. ANS:
The frequency of the sound that reaches the car is 5.9  102 Hz.
51. ANS:
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The Mach number of the aircraft is 0.636.
52. ANS:
The frequency produced would be 1.1  102 Hz.
53. ANS:
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The frequency the string produces would be 5.2  102 Hz.
54. ANS:
The length of the pipe must be 1.14 m.
55. ANS:
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The lowest frequency the tuba can produce is 5.0  101 Hz.
56. ANS:
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The frequencies are fundamental (144 Hz), first overtone (288 Hz), and second overtone (432 Hz)
respectively.
57. ANS:
(a)
Time of flight: let “up” be (–) and “down” be (+)
v1 = –26 m/s(sin 60º) = –22.5 m/s
a = 9.8 m/s2
d = 2.0 m
t = ?
2.0 = (–22.5)t + 4.9(t)2
Solving the quadratic: t = 4.68 s
The time of flight is 4.7 s.
(b)
Horizontal range: d = vt = 26 m/s(cos 60)(4.68 s) = 60.8 m
The receiver must run: 60.8 m – 3.0 m = 57.8 m.
The time the receiver has to reach the football: 4.68 s + 2.0 s = 6.68 s.
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The average speed of the receiver:
The receiver must run with an average speed of 8.7 m/s.
58. ANS:
(a)
Time of flight: let “up” be (–) and “down” be (+)
v1 = –15 m/s(sin 50) = –11.5 m/s
a = 9.8 m/s2
d = –2.0 m
t = ?
–2.0 = (–11.5)t + 4.9(t)2
Solving the quadratic: t = 0.19 s (way up) and 2.16 s (way down)
Horizontal range: d = vt = 15 m/s(cos 50º)(2.16 s) = 21 m
The net must be placed 21 m away from the cannon.
(b) Horizontal component of final velocity: 15 m/s(cos 50) = 9.64 m/s
Vertical component of final velocity: v2 = v1 + at = –11.5 m/s + 9.8 m/s2(2.16 s)
v2 = 9.67 m/s
Using Pythagoras:
=
The shell lands with a velocity of 14 m/s at an angle of 45 below the horizontal.
59. ANS:
(a)
Time of flight of shell:
Horizontal range of shell: 100 m
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Horizontal component of shell’s velocity:
Angle of projection:
10 m/s = 40.0 m/s(cos )
 = 76º
The gun must be aimed at an angle of 76 to the horizontal.
(b)
Vertical component of shell’s velocity: 40.0 m/s(sin 75.5) = 38.8 m/s [up]
let “up” be (–) and “down” be (+)
v1 = –38.8 m/s
a = 9.8 m/s2
t = 10 s
d = ?
The cliff is 1.0 102 m high.
(c) Horizontal component of final velocity: 10 m/s
Vertical component of final velocity: v2 = v1 + at = –38.8 m/s + 9.8 m/s2(10 s)
v2 = 59.2 m/s
Using Pythagoras:
=
The shell lands with a velocity of 59.2 m/s at an angle of 9.6 to the vertical.
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