(((Astounding Sound)))
Steven Berger
Orefield Middle School
8th Grade
Problem Statement
At what column height does sound resonate in a
cylinder of air and water? Will changing the
density of a liquid change the speed of sound
through that liquid?
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Hypothesis
If the speed of sound in an air and water
column can be established by finding its
natural resonance, changing the density of
the water (ex. saturating it with salt) will
decrease the speed of sound. According
to research, sound travels slower through
denser materials because there are more
molecules for the sound waves to vibrate.
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Research
• Sound Wave: A pressure disturbance that travels
by particle-to-particle interaction.
• Frequency: Number of times an object vibrates per
second.
• Tuning Fork: A fork shaped acoustic resonator.
• Natural Frequency: When the air column vibrates at
the same frequency as the tuning fork.
• Resonance: When an object vibrating at or near the
natural frequency of a second object causes it to
vibrate.
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Research (cont.)
Vibration: The complete
back and forth motion of
an object.
Fundamental: The lowest
frequency that an air
column will resonate at.
Forced Vibration: When
an object forces another
into vibration.
For the fundamental, only
¼ of the wavelength goes
into the column.
The tuning fork forces
sound waves into the top
of the tube. If the air
column’s natural
resonance matches that
of a tuning fork, the
sound will get louder and
produce a fundamental.
Add or decrease water in the
tube to find the natural
resonance of the air column.
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Materials
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set of Tuning Forks/with Striker
plastic tube 5.08cm x 91.44cm
tap water 2L
table salt 340 grams
sugar 340 grams
distilled water 1 ½ L.
magnesium sulfate 453 grams
plexiglass 16 x16 cm thick
gorilla glue
funnel
4 x 9 x 61 cm wood
1 x 122 cm flexible tube
masking tape
wood screws
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Procedure for Assembling Cylinder
1.
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Cut tube down to 61 cm.
Drill holes in plexiglass
Glue 61 cm tube to the
plexiglass base.
Glue flexible tube to other
side of plexiglass base.
Put strip of masking tape on
tube and mark off
centimeters.
Attach completed cylinder to
wood base.
Insert funnel into flexible tube.
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Procedure for Testing Liquids
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Pour the liquid you are going to test into the funnel.
Add or remove water until the desired air column
height is reached.*
Strike & hold a tuning fork over the top of the plastic
column.
Raise or lower the funnel (to change the water
column height) until the sound of the tuning fork
becomes the loudest.
Record the air column height in cm.
Repeat the whole procedure again testing different
liquids with different densities.
Calculate the speed of sound.
*most fundamentals occur between 18-33 cm
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Calculating the Speed of Sound
The formula for speed of sound is V=4F(L +0.4d)
V is the speed of sound in air column
F is the frequency of tuning fork
L is the length of the air column in meters
D is the diameter of the tube in meters
Sample Calculation: (D/288 Tuning Fork)
V= 4•288(.28+0.4•.0508)
V=1024(.28+.02032)
V= 1152•.30032
V=345.97 m/s
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Data/Graphs
Fundamentals
Column Heights in CM
70
60
15
50
16
18.75
21
23.5
25
28
32
A/426.6
G/384
F/341.3
E/320
D/288
C/256
40
30
20
10
0
C/512
B/480
Note/Tuning Fork
water
air column
This graph shows the fundamentals of my control group, tap water. As the
tuning fork frequency decreases, the fundamental column height gets
longer. (Note column heights shown are proportionate to actual testing.)
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Data/Graphs
Formula for speed of sound: V=4f(L+.4d)
This graph shows the speed of sound for my control group tap water. Most
speeds are within 1.5% of the theoretical speed of sound. The researcher
multiplied .6 by the temperature and added 331 to find theoretical speed or
sound. (V=331+.6T)
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Data/Graphs
This graph shows the speed of sound for all the liquids categorized by
tuning fork and density.
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Conclusion
• The original hypothesis was incorrect in
thinking that changing the density of water
would affect the speed of sound.
• The sound waves that caused a
resonance did not go to the bottom of the
tube and back. They went to the bottom of
the air column and back when the tuning
fork goes through one vibration.
• When the frequency of the tuning fork
matches the height of the air column the
fundamental occurs.
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Conclusion (cont.)
• Benefits: People who design instruments might want to
know the fundamental of a note so they know how to
design the instrument. Architects might benefit because
they need to know how sound travels in open spaces.
Sound waves are also being used to treat people with
tremors.
• Areas to Improve:
Develop a way to strike the tuning fork the same way for
each trial.
Be more careful holding the tuning fork in the same
place for each trial.
• For further study: To extend this experiment the
researcher could try tuning forks with higher and lower
frequencies and try other diameter columns.
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Resources/Bibliography
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Rahn, Joan Elma. "Chapters 1-2." Ears, Hearing & Balance.
New York: Atheneum, 1984. Print.
"Sound." The New Book of Popular Science. Vol. 3. Danbury,
CT: Scholastic Library Pub., 2008. 198-208. Print.
Silver, Jerry. 125 Physics Projects for the Evil Genius, The
Speed of Sound Resonance in a Cylinder, New York: McGrawHill, 2009. 188-90. Print.
"Sound Is a Mechanical Wave." Sound Waves and Music –
Lesson 1 The Nature of a Sound Wave. The Physics
Classroom. Web. 27 Oct. 2011.
<http://www.physicsclassroom.com/Class/sound/u11l1a.cfm>.
"Resonance." Sound Waves and Music Lesson 5, Musical
Instruments The Physics Classroom. Web. 27 Oct. 2011.
<http://www.physicsclassroom.com/Class/sound/u11l5a.cfm>.
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