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Final - Physics 1240 – Spring, 2010 – version 2
SIL difference
(in decibels)
1 dB
2 dB
3 dB
4 dB
5 dB
6 dB
7 dB
8 dB
9 dB
Intensity
ratio
1.3
1.6
2.0
2.5
3.2
4.0
5.0
6.3
7.9
Bubble in questions 1-40 ON YOUR BUBBLE SHEET!
1. Consider a string on a bass guitar with a fundamental (n=1) frequency of the note we call E2. When
you are hearing this 4th harmonic (n=4) of this string, what note are you perceiving?
A) E12
B) E7
C) E5
D) E4
E) None of the above corresponds to the 4th harmonic of this string.
2. Consider a giant organ pipe which plays a tone whose fundamental frequency is at the very low end
of normal human hearing (which typically ranges from about 20 Hz to 20,000 Hz). Which harmonic
number of this pipe is about the highest one most people could perceive?
A) Somewhere around n=20,000.
B) Somewhere around n=1,000.
C) Somewhere around n=200.
D) Somewhere around n=10.
E) Somewhere around n=3.
3. A native American bass flute is roughly 1 meter long, and is open at both ends. What is the lowest
note can be played on this instrument?
A) About 340 Hz.
B) About 170 Hz.
C) About 34 Hz.
D) About 1 Hz.
E) There is no “lowest note” on an open flute, a highly skilled player can go as low as they want.
4. If you cap off one end of the flute in the previous problem, what happens to the fundamental
frequency?
A) It goes down by an octave .
B) It goes down, but by much less than an octave
C) It goes up by an octave
D) It goes up, but by much less than an octave
E) It stays the same.
5. If the intensity of sound (measured in W/m2) increases by a factor of 5, what happens to the decibel
level?
A) It goes up by a factor of 20 from whatever value it starts at (decibels are multiplied by 20).
B) It goes up by a factor of 5 from whatever value it starts at (decibels are multiplied by 5).
C) It increases by +3 dB.
D) It increases by +5 dB.
E) It increases by +7 dB.
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The next few questions are based on the
Fletcher-Munson diagram, at right. This
diagram helps us understand the connection
between pitch, decibels, and perceived
loudness (or phons). (The vertical axis in the
graph is what we call in our class SIL, or
decibel level.)
6. According to the Fletcher-Munson diagram,
how many decibels are required for a normal
person to just barely detect a 10 kHz tone?
A) More than 20 dB
B) Between 10 and 20 dB
C) Less than 10 dB
D) 0 dB
E) The diagram doesn't give us the
information to figure this out.
7. Suppose I want a recording of a 90 Hz note on a bassoon to have a perceived loudness of 50 Phon.
Approximately what SIL do I need coming from my stereo?
A) 40 dB
B) 50 dB
C) 60 dB
D) 70 dB
E) 80 dB
8. Assume that you go to a very quiet classical concert: at your seat the loudness of all the frequencies
in the music is about 60 phons. You record the music, take it home, and crank it on your stereo. Your
stereo is set so all frequencies are increased from their original SIL by about +40 dB.
Which answer below best describes the change in your perception of the music?
A) It seems louder to you, but the balance between bass and treble is also shifted – it feels more “bass
dominated.”
B) It seems louder to you, but the balance between bass and treble is also shifted – it feels more “treble
dominated.”
C) No change in balance, all pitches just seem equally louder.
D) It seems the same loudness as at the concert, but the bass and treble are perceived as shifted up
(equally) in pitch.
E) It seems the same loudness as at the concert, but it seems like the bass and treble shift differently in
pitch, making the music more dissonant.
9. A violinist tunes her instrument before a concert by tightening one of the strings. As you listen to this,
you hear the pitch of the note she plays increasing slightly. How does the speed of the produced sound
wave (traveling through the air towards you) change as the frequency goes up?
A) The higher the frequency, the faster the sound wave travels to you.
B) The higher the frequency, the slower the sound wave travels to you.
C) Frequency makes no difference, sound waves of all frequencies travel to you at the same speed.
10. What is the period of the note A4 (concert A)?
A) About 440 seconds
B) About 2.3 seconds
C) About 0.78 seconds
D) About 78 milliseconds
E) About 2.3 milliseconds
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11. A mass hanging on a spring wiggles up and down in simple harmonic motion. If you double the
mass, how do you predict for the frequency of motion to change?
A) It will go DOWN by a factor of 2 (new frequency is half the original).
B) It will go DOWN, but not by a factor of exactly 2.
C) It will go UP by a factor of 2 (new frequency is double the original) .
D) It will go UP, but not by a factor of exactly 2.
E) It will stay the same, frequency does not depend on mass.
12. Which of these statements best describes the way a microphone works?
A) The sound particles in the air travel into the microphone, where they strike a membrane and
transform into electrons; the electrons create an electrical signal.
B) Inside the microphone is a very small antenna which detects the electromagnetic wave in the room
and amplifies it to create an electrical signal.
C) The sound wave in the room causes pressure variation on a small membrane inside the
microphone; the motion of the membrane is converted into an electrical signal.
D) The microphone takes an electrical signal and converts it into physical motion of a small
membrane, creating a sound wave.
The next two questions both refer to a giant
clothesline wiggling at the front of class, oscillating
in a simple standing wave pattern, driven by a piston
at some fixed frequency. (The picture is a snapshot
in time.)
13. If the length of the rope is L=5 m, what is the
wavelength of this wave?
A) 1 m
B) 2 m
C) 5 m
D) 10 m
E) 25 m
L
14. Consider a spot on the string located two fifths
of the way along (i.e. at 2/5 L ). (I have drawn a heavy dot in the picture there to guide your eye).
What can you say about the motion of this spot as time goes by?
A) The spot wiggles left and right.
B) The spot travels to the right.
C) The spot wiggles up and down.
D) The spot remains motionless.
E) The spot goes around in a circular pattern.
15. I have a speaker with a diameter of 50 cm. Which sounds will head out primarily in the forward
direction from the speaker, and which will spread out in all directions?
A) Frequencies above about 700 Hz will go forward, frequencies below about 700 Hz will spread.
B) Frequencies below about 700 Hz will go forward, frequencies above about 700 Hz will spread.
C) Frequencies above about 7 Hz will go forward, frequencies below about 7 Hz will spread.
D) Frequencies below about 7 Hz will go forward, frequencies above about 7 Hz will spread.
E) None of the above is a good description of which sounds will head forward and which will spread.
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16. A plane flies toward a stationary siren at ¼ the speed of sound. Then the plane stands still on the
ground and the siren is driven away from it at ¼ the speed of sound. In both cases, a person sitting in the
plane will hear the same frequency of sound from the siren.
A) True
B) False
17. The just noticeable difference (JND) of hearing is larger for softer sounds. For example, a 1 kHz
sound that starts at 80 dB has a JND of about 0.5 dB, while the same 1 kHZ sound that starts at 30 dB
has a JND of about 1 dB. Which statement below best describes the interpretation of this experimental
result?
A) It’s easier to hear small differences in frequency if the sound starts out louder.
B) It’s easier to hear small differences in loudness if the sound starts out softer.
C) It’s easier to hear small differences in loudness if the sound starts out louder.
D) It’s easier to hear small differences in loudness if the sound starts out higher in pitch.
E) It’s easier to hear small differences in loudness if the sound starts out lower in pitch.
The next two questions address the
picture at right. The picture shows
the air pressure in the room as a
function of position, at some
instant in time. It is a snapshot of
air pressure. The horizontal axis is
distance, in meters, away from the
source of the sound.
Note the distance scale at the
bottom of the graph. The entire
graph is 16 m, each of the tick
marks on the x axis is separated by
1 m, each of the faint vertical lines
is 0.5 m apart.
0
8m
16 m
18. What sound will you perceive when you hear this–in other words, what is the frequency of the
fundamental vibration of this waveform?
A) 344 Hz
B) 86 Hz
C) 43 Hz
D) 16 Hz
E) 4 Hz
19. In addition to the fundamental vibration, a higher harmonic is present in this graph. Which
harmonic is it?
A) the 7th harmonic
B) the 6th harmonic
C) the 5th harmonic
th
rd
D) the 4 harmonic
E) the 3 harmonic
20. A given note has a period of 0.4 milliseconds. What is its frequency? (Choose the closest answer.)
A) About 150 Hz
B) About 250 Hz
C) About 1.5 kHz
D) About 2.5 kHz
E) About 15 kHz
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21. Which pair of tones would have a slow very distinct beat? (Assume both are equally loud initially.)
A) 50 Hz and 52 Hz
B) 50 Hz and 60 Hz
C) 50 Hz and 100 Hz
D) 50 Hz and 500 Hz
E) 50 Hz and 5 kHz
22. In the middle ear, the eardrum is connected to the oval window by the ossicles, which transmit force
between the eardrum and the oval window. The eardrum is about 20 times larger in area than the oval
window. What effect does this difference in area have?
A)
B)
C)
D)
E)
The difference in area makes the force on the oval window larger.
The difference in area makes the force on the oval window smaller.
The difference in area makes the pressure on the oval window larger.
The difference in area makes the pressure on the oval window smaller.
The difference in area doesn’t much affect the force or the pressure.
23. When you strum a guitar, you produce a fundamental tone. If you now place your finger to play the
3rd harmonic (n=3), what does the new tone sound like?
A) The 3rd harmonic sounds 1 octave above the fundamental.
B) The 3rd harmonic sounds 2 octaves above the fundamental.
C) The 3rd harmonic sounds 3 octaves above the fundamental.
D) The 3rd harmonic sounds 4 octaves above the fundamental.
E) None of the above is a correct description of the sound of the 3rd harmonic.
24. Suppose I have a string vibrating in its third mode (n=3), and the string is 1.5 m long (like a long
string on a grand piano). If I start at one end of the string, how far do I have to go to reach the first
node on the string?
A) 0.25 m
B) 0.33 m
C) 0.50 m
D) 0.75 m
E) 1.0 m
25. Suppose the string in the previous problem is vibrating at a frequency of 100 Hz. This produces a
sound in the room (also at 100 Hz). If, at some instant in time, there happens to be an air pressure peak
right at my ears, how far away from me in the room is the next air pressure peak?
A) About 0.01 meters away
C) About 3.4 meter away
E) About 100 meters away.
B) About 1 meters away
D) About 0.3 meters away
26. You loosen a very tight guitar string, decreasing the tension by a factor of nine. What happens to
the speed of the wave on the string?
A) It goes down by a factor of 3.
B) It goes down by a factor of 9.
C) It goes up by a factor of 3.
D) It goes up by a factor of 9.
D) It stays the same, wave speed does not depend on tension.
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The next two questions refer to the picture at right,
which shows a waveform of a pure tone (think of an
oscilloscope trace, calibrated to measure pressure
versus time of a pure tone). Notice the features of the
graph labeled i and ii.
27. Which feature of the graph do you have to change
(and how?) in order to make the pitch go down by an
octave?
A) Make feature i larger by a factor of 2.
C) Make feature ii larger by a factor of 2.
E) None of the above changes will do the trick.
pressure
ii:
(above normal)
i:
time, t
(below normal)
B) Make feature i smaller by a factor of 2.
D) Make feature ii smaller by a factor of 2.
28. If you want to increase the sound intensity level (SIL) you hear by +6 dB, what change do you
have to make?
A) Increase feature i by a factor of 4.
B) Increase feature i by a factor of 6.
C) Increase feature ii by a factor of 4.
D) Increase feature ii by a factor of 6.
E) None of the above changes will do the trick.
29. I was singing while walking outside. When I walked into a tunnel, I noticed that my singing
sounds much better inside the tunnel than it does outside. Why? (Pick the best explanation.)
A) Because singing excites a resonance of the tunnel, and resonant sounds are more aesthetically
pleasing.
B) Because the sound waves inside the tunnel destructively interfere with each other, producing a
pattern of loud and soft spots in the tunnel that sounds nice.
C) Because the sound reflects (echoes) many times off the wall of the tunnel, and the time delay
between when the different echoes reach my ear creates a richer sound.
D) Because the sound waves diffract (spread out) when traveling through the opening of the tunnel, so
the sound is easier to hear.
E) Because the air temperature inside the tunnel is than from the temperature outside, which causes
the frequency of the sound to shift to more pleasing notes.
30. The speed of a wave on a 1 meter long bass string is.
A) 2 m/s
B) 1 m/s
C) 344 m/s
E) There is not enough information given to determine.
D) 172 m/s
31. What can you say about the allowed harmonics of an ideal wind instrument which is a simple
narrow pipe that is closed on one end, but open on the other end?
A) It has only odd numbered harmonics (i.e. you only hear frequencies which are an ODD number
times the fundamental).
B) It has only even numbered harmonics (i.e. you only hear frequencies which are an EVEN number
times the fundamental).
C) It has all harmonics, exactly the same pattern as a plucked string.
D) It produces NO harmonics, only the fundamental will be heard.
E) It produces a purely anharmonic pattern, where the higher frequencies are not related in any way to
the fundamental.
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32. You are listening to two speakers. The distance from you to one of the speakers is precisely half a
wavelength longer than the distance to the other one. Assume the speakers are wired to produce
sound in synch (in phase) with one another. What do you hear when the speakers play the same pure
tone?
A)
B)
C)
D)
E)
A sound the same loudness as either speaker alone.
A very soft or no sound (that is, it’s much softer than the loudness of either speaker alone).
A sound that beats (that is, it gets louder and softer, louder and softer, with time).
A sound louder than either speaker alone would produce.
A sound of distinctly different frequency than either speaker alone would produce.
33. In a concert, a solo violinist begins the piece, playing at a steady 40 dB. Then more violins join in.
They all play at the same intensity, and the sound intensity level (SIL) in the room is now 50 dB.
How many violins (total) are now playing?
A) 5
B) 10
C) 13
D) 15
E) 20
34. Our perception of sound comes from the inner ear. There is a basilar membrane which runs down the
cochlea, with hair cells located along this membrane. What mechanism associated with the inner ear best
helps us perceive how high or low the pitch of a given sound is?
A) The vibration rate of the individual hair cells carries much of the frequency information.
B) The amplitude of the vibration of individual hair cells carries much of the frequency information.
C) The spectrum of the electric signal produced by the individual hair cells carries much of the
frequency information.
D) The location of vibrating hair cells along the membrane carries much of the frequency information.
E) Brain signal processing (nothing physical, it's pure software) determines much of the frequency
information.
35. I play a pure tone of frequency 10 kHz, which reflects off the cliff I am facing. The bumps and
irregularities on the cliff are about 1 m wide. What will happen and why?
A)
B)
C)
D)
E)
The sound will largely reflect specularly because the surface is rough.
The sound will largely reflect specularly because the surface is smooth.
The sound will largely reflect specularly, it doesn’t matter whether the surface is smooth or rough.
The sound will largely reflect diffusely because the surface is rough.
The sound will largely reflect diffusely because the surface is smooth.
36. An car is driving very fast toward a group of stationary people, while blaring music from its
speakers. The sound hear by the stationary listeners sounds lower in pitch than the sound heard by
listeners in the car.
A) True
B) False
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37. I measure the just noticeable difference (JND) of a particular sound and find that it is 2 dB. What
intensity ratio is detectable for this sound?
A)
B)
C)
D)
E)
An intensity ratio of 2.0 or larger is a noticeable difference.
An intensity ratio of 1.6 or smaller is a noticeable difference.
An intensity ratio of 1.6 or larger is a noticeable difference.
An intensity ratio of 1.3 or larger is a noticeable difference.
An intensity ratio of 1.3 or smaller is a noticeable difference.
The next 2 questions refer to a half-closed 3 m long
pipe (one end is sealed, the other end is open to the
atmosphere).
This pipe has a standing pressure wave in it (that's
just one of the ordinary modes we've talked about in
class, the wave shown happens to have n=3).
OverPressure
1m
The overpressure in the tube at one instant in time is
shown as a solid line. The overpressure at a later time
is shown dashed.
2m
3m
L=3 m
38. A dust particle is located 2/3 of the way along the
tube, i.e. at the 2 m spot (shown as a black dot in the figure above). How will the dust speck move as
time goes by due to the standing pressure wave?
A) The speck wiggles up and down (i.e. towards the top and bottom of the tube, not towards the ends).
B) The speck wiggles left and right.
C) The speck travels steadily in one direction until it leaves the tube.
D) The speck remains essentially motionless.
E) The speck moves around in a circular pattern.
39. Which end of this pipe is the open end? Choose the correct answer and the correct reason.
A) The right end is open, because you should have a pressure antinode at the open end
B) The right end is open, because you should have a pressure node at the open end
C) The left end is open, because you should have a pressure antinode at the open end
D) The left end is open, because you should have a pressure node at the open end
E) The graph shown cannot possibly correspond to any real standing wave in a tube.
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40. Consider a sound wave which decomposes into the following three pure tones (the relative
amplitudes in these three pictures are drawn to scale).
overpressure
overpressure
overpressure
3f1
f1
time
5f1
time
time
The frequency spectrum for this wave looks like (choose the closest one):
Spectrum
Spectrum
A
Spectrum f
1
frequency
B
5f1
Spectrum f1
frequency
5f1
D
C
f1
frequency
5f1
f1
frequency
5f1