Temperature Dependence of the Speed of Sound in Different Gases
IB Extended Essay – Physics
Name: Rohit Rana
Candidate No: 002762-020
Supervisor: Curtis Hendricks
School: American International School/Dhaka
Date: 01/03/2009
Word Count: 3903
Rohit Rana, 002762-020
1
Abstract
This essay investigates the dependence of temperature and medium (air and carbon
dioxide) on the speed of sound. Instead of dismissing the air sound speed to be 343 m/s
and sound speed in CO2 to be 268 m/s, I measured the speed of sound at various
temperatures by using simple apparatus: an ultrasonic motion detector and a temperature
probe. For the carbon dioxide gas part of this experiment, I used a portable CO2 fire
extinguisher. A wooden box was also constructed which allowed for the data to be
collected with minimal impact from forces like movements or air currents that may exist
in an open room. From the data collected, the relationship between temperature and speed
of sound could be determined and later verified using
or the adiabatic constant of air
(1.4) and CO2 (1.3). I found that there is a positive correlation between speed of sound (in
air and in CO2) and temperatures (see results for graphs and data tables). For instance,
using the speed of sound in air vs. temperature graph, I measured the accuracy of the two
variables’ relationship and calculated values by comparing the best-fit line’s equation to
known textbook equation:
. In order to further know the
accuracy of the experimental values, I plotted (Speed of Sound)2 as a function of RT/M to
obtain an expected linear trend, whose best-fit line’s slope refers to known adiabatic
constant (ratio of the specific heats of the gas) for air and CO2. Finally, sources of error
regarding some leak of CO2 gas from the wooden box and temperature sensitive motion
detector were evaluated and ways to enhance and further investigate this experiment were
stated.
Word Count: 276
Rohit Rana, 002762-020
2
Table of Contents
1. Introduction
4
2. Theoretical Background
5
2.1 Sound
5
2.2 Analytical determination of the speed of sound
6
3. The measurements
8
3.1 The experiment planning
8
3.2 The method
9
3.3 Results
12
3.3.1 Speed of Sound in Air as a Function of Temperature
13
3.3.2 Speed of Sound in CO2 as a Function of Temperature
17
4. Conclusion & Evaluation
20
5. Bibliography
23
6. Appendix
24
Rohit Rana, 002762-020
3
1. Introduction
The speed of sound in air has been determined by various scientists from time to time. In
this experiment, I want to measure the speed of sound in different gases (air and carbon
dioxide) at various temperatures by using simple apparatus such as an ultrasonic motion
detector and a temperature probe. For the carbon dioxide gas part of this experiment, I
plan to use a portable CO2 fire extinguisher – a method not many physicists might have
investigated to conduct this common yet meaningful experiment.
One may just prefer to use the known value of 343 m/s instead of understanding the
importance of exact speed of sound. However, there can be drastic consequences of
having limited knowledge about sound speed.
The use of varying speeds of sound is important in Sound Navigation and Ranging
(SONAR) system in a submarine. SONAR uses sound pulse to locate objects underwater.
The system emits a pulse of sound and then the operator listens for the reflected sound
wave to determine the precise location of a foreign object (Sonar: Technology Gallery
for). One must consider that the sound speed will change according to the temperature of
water at different depths.
In addition, it is important to realize the relationship between our atmosphere’s gases and
temperature when using speed of sound to calculate the distance of a thunderstorm by
counting the number of seconds between a flash of lighting and the thunder sound.
Miscalculations can result in catastrophic events capable of killing many people in a
particular area.
Instead of dismissing the air sound speed to be 343 m/s, I have challenged myself to do
‘an investigation that is more “open” than the traditional ones.’ I want to examine the
dependence of temperature and medium (air and carbon dioxide in this case) on the speed
of sound. The research question of this extended essay is ‘How is the speed of sound in
mediums air and carbon dioxide affected by the temperature it travels through?” I suspect
Rohit Rana, 002762-020
4
that the relationships between sound speed, temperature, distance in mediums air and
CO2 will be similar; the actual values will probably differ as CO2 is much denser than air.
In this essay, I shall discuss the experimental methods used to make the measurements
and compare the results with theory and facts.
2. Theoretical background
2.1 Sound
A sound wave (a longitudinal wave) is a pressure disturbance which travels only through
a medium (such as solid, liquid, or gas) by means of particle-to-particle interaction at a
constant speed. As one particle in a particular medium becomes disturbed, it exerts a
force on the adjacent particle, thus disturbing that particle from rest and transporting the
energy through the medium. The particles of the medium must be present for the
disturbance of the wave to move from place to place. For this reason, sound cannot exist
in a vacuum (Henderson).
Like any wave, the speed of sound (wave) refers to how fast the disturbance is passed
from particle to particle. Sound travels through solids, liquids, and gases at considerably
different speeds, as Table 1 shows below. In general, sound travels slowest in gases,
faster in liquids, and fastest in solids (Cutnell and Kenneth, 459).
Table 1: Speed of Sound in Gases, Liquids, and Solids
Substance
Speed (m/s)
Gases
Substance
Speed (m/s)
Liquids
Substance
Speed (m/s)
Solids
Air (0°C)
331
Chloroform (20°C)
1004
Copper
5010
Air (20°C)
343
Ethyl alcohol
1162
Glass
5640
(Pyrex)
(20°C)
Carbon dioxide (0°C)
259
Mercury (20°C)
1450
Lead
1960
Carbon dioxide (20°C)
268
Fresh water (20°C)
1482
Steel
5960
Oxygen (0°C)
316
Sea water (20°C)
1522
Rohit Rana, 002762-020
5
Helium (0°C)
965
2.2 Analytical determination of the speed of sound in context of this essay
Newton knew that the speed of any wave depends upon the properties of the medium
through which the wave is traveling. Typically there are two essential types of properties
which affect wave speed - inertial properties and elastic properties. “Elastic properties are
those properties related to the tendency of a material to maintain its shape and not deform
whenever a force or stress is applied to it. The velocity of a sound wave, cs, is thus partly
governed by the modulus of elasticity (E = stress/strain) of the medium (Henderson).
“Inertial properties are those properties related to the material's tendency to be [resistive]
to changes in its state of motion.” The greater the inertia (i.e., mass density) of individual
particles of the medium, the less responsive they will be to the interactions between
neighboring particles and the slower that the wave will be. As stated above, a sound wave
will travel faster in a less dense material (solids) than a more dense material (gases). Thus,
it was also known that the velocity, cs, depends on the density, , of the medium. Hence,
Newton determined a general expression for the velocity of sound waves in air
(Henderson):
(1)
Newton was first to consider the speed of sound before most of the development of
thermodynamics, however, his deductions used isothermal calculations instead of
adiabatic.
Newton believed that these stresses and strains in the gas took place isothermically (i.e.
under the conditions of Boyle’s Law: pV = constant, where the relationship between
pressure, p, and volume, V, is constant at constant temperatures). Differentiating pV with
respect to V, we see that (MathPages):
(2)
Rohit Rana, 002762-020
6
Incidentally, the "bulk modulus" of an elastic substance is defined as
isothermal bulk modulus of a gas is equal to the pressure (
=
and the
= p). So, Newton rewrote
the equation of the speed of sound in a medium with bulk modulus K as
. This
led Newton to conclude that the velocity of sound in a gas (using 1.29 kg m-3 for the
density of air under standard conditions) would equal (MathPages):
(3)
Newton’s above calculated value was below the known experimental speed of sound
value (330 m/s). This discrepancy in Newton’s analysis was rectified by Laplace who
suggested that the adiabatic bulk modulus of a gas should be used (p and V change under
the conditions such that
= constant, where
= Cp / CV, the ratio of the specific heats
of the gas at constant pressure and constant volume) (MathPages).
Differentiating as above we now find:
(4)
Thus, the adiabatic bulk modulus of a gas equals
, using
= 1.4 and substituting into
Eq. (1) above gives an expression that conforms well to the modern experimental value
for the velocity of sound in air at s.t.p. (MathPages):
(5)
From the above adiabatic expression Eq. (5), many interesting expressions can be derived
to relate a gas to temperature dependence of the speed of sound.
Rohit Rana, 002762-020
7
For a mole of gas the air density,
= M/V (the molar mass divided by the volume),
giving the first relation below. Using the ideal gas law to replace p with nRT/V, and
replacing ρ with nM/V, the equation becomes:
(6)
where
is the adiabatic constant, R is the molar gas constant, T is the absolute
temperature in Kelvin, and M is molecular mass of a gas (MathPages).
Since , R, and M are all constants for a given gas, it follows that cs is independent of
pressure at constant temperature and that cs is proportional to the square root of its
absolute temperature. By squaring both sides of Eq. (6), we see that cs2 is proportional to
RT/M. This can be verified graphically (see figure 5 and 10 in results) and the slope of
the line should be a good estimate of
(the ratio of specific heats).
Using Eq. (6) with =1.4, R=8.314 J mol-1K-1, M = .02893 kg/mol, at To = 273.15K, cs =
331.39 m/s and at To=274.15K, cs = 332.00 m/s. This leads to a commonly used
approximate formula for the sound speed in air:
(7)
where Tc is the temperature in Celsius (Henderson).
Although it is possible to deduce Eq. (7) from thermodynamic principles, it is a “regular
physics textbook” equation used near room temperature and is more easily derived
empirically from data of a cs vs. Tc graph (see figure 4 in results).
3. The measurements
3.1 The experiment planning
In order to investigate the relationship of temperature and speed of sound in air and
carbon dioxide, an experiment had to be carried out. It was thought that the experiment
should take place in a controlled box/container rather than open room air in order to
Rohit Rana, 002762-020
8
achieve results with minimum errors. The next step was to make such a box that has
holes on top for air movement, is completely sealed from all other sides to prevent other
forces (like movements or air currents that may exist in an open room), allows the
ultrasonic motion detector and temperature probe to function properly. The first idea was
to construct the box out of ‘Glass-reinforced plastic.’ The obvious main problem was that
it would be very expensive to construct a box of the needed size. Therefore, a different
method was created using a fine wood box as shown in picture 1 below. The wooden box
was later wrapped in a plastic sheet to ensure its leakiness from all the sides. It was
decided to split the experiment into two separate parts. The first experiment, Speed of
Sound in Air as a Function of Temperature, is to measure temperature dependence of
speed of sound in air and to compare the experimental data with theory and facts. The
second experiment, Speed of Sound in Carbon Dioxide as a Function of Temperature, is
to measure temperature dependence of speed of sound in CO2 and to compare the
experimental data with theory and facts. This method didn’t seem to have any flaws and
thus did not require a different technique.
Picture 1:
3.2 The method
The measurements were carried out in a wooden box (2m x 0.5m x 0.5m) in the smallest
room available (2m x 3m x 3m) in order to ease the process of controlling the room
temperature using heaters and air conditioner. As stated earlier, this experiment requires
no specialized equipments and uses a common physics lab apparatus: an ultrasonic
Rohit Rana, 002762-020
9
motion detector, a temperature probe, a Logger Pro unit, and a laptop. An ultrasonic
motion detector ‘determines the distance to a body by measuring the time interval from
the time a sound pulse is sent out until the instant of time the reflected pulse from the
body is received.’ In order to determine the distance, the motion detector always uses a
calibration factor of 343 m/s, corresponding to dry air at 20˚C. ‘With this assumption,
one may, as in the following experiments, determine both the actual speed of sound in
gas mixtures and temperature variations of the speed of sound in air (Pettersen).’
To collect data to be used to measure the sound speed in air and other thermodynamic
properties, the motion detector was placed on the far left side of the box with the
temperature probe hanging through one of the holes made on top of the wooden box (as
shown below in Picture 2).
Picture 2:
Both the units were set-up in the usual way by connecting them to a single laptop with
Logger Pro 3 software. To receive accurate temperature data, the temperature probe was
calibrated by clicking the “Calibrate Now” button under the “Calibrate” tab of
“Experiment” option. The motion detector did not need to be calibrated as it was placed
in front of a stationary object (the wooden wall of the wooden box on the far opposite
right). Next, the ‘Data Collection’ under the ‘Experiment’ tab in Logger Pro was set to
collect 0.2 samples/second or 5seconds/sample. Before starting the 30 minute collection
of data process (Position vs. Time graph and a Temperature vs. Time graph), the room
was heated to about 40˚C using two 2000 watt heaters. After having somewhat stable
temperature of about 40˚C, click “Collect” to obtain the Distance vs. Time graph and
Rohit Rana, 002762-020
10
Temperature vs. Time graph – while slowly changing the room temperature (to about
20˚C) by turning on the cooling system (air conditioner). Original Graph 1 in the
appendix show a Position vs. Time graph and Temperature vs. Time graph respectively
as a sample from this setup.
By manipulating and selecting the smoothest part of the raw data in a spread sheet, we
can calculate the actual speed of sound (cs) in air for all the different temperatures by
following the steps below:
1. Determine the actual time (treal) it takes the sound wave to reach the end of the box by
using basic concept of
. In the spread sheet, make a new column for
the actual times (treal) by dividing all the entries in the distance column (apparent
distances recorded by the detector, sap) by the assumed speed of sound in air (i.e. 343
m/s (cas) for 20˚C).
.
2. To calculate the actual speed of sound (cs) in air column, divide the actual known
(measured by a ruler) distance (sreal) from the detector to the end of the box by the
actual times (treal) column determined in step 1 above.
.
3. Using Graphical Analysis, plot the actual speed of sound in air (cs column) vs.
temperatures column (original temperature data from detector, see Figure 4). Use the
curve fit option to linear fit this graph and verify if it conforms to the textbook
equation:
.
4. To determine further correlation between variables, graph other relationships
including but not limited to speed of sound in air (cs) vs. actual times (treal), speed of
sound in air (cs) vs. distance, and distance vs. temperature.
5. As explained previously in the theoretical background section, cs2 is proportional to
RT/M and the slope of the line should be a good verification of
or the adiabatic
constant (1.4) of air. To determine the cs2 column, simply square the speed of sound
in air column determined in step 3.
Rohit Rana, 002762-020
11
6. To determine RT/M column, all the temperatures must be in Kelvin units. Therefore,
add 273.15˚ to all the temperatures recorded by the detector. Knowing the constant R
value to be 8.314 J mol-1K-1 and the molar mass of air to be 0.02893 kg/mol, a new
RT/M column can be calculated.
7. Using Graphical Analysis, plot the (speed of sound in air)2 or cs2 vs. RT/M column
(determined above in step 6). Use the curve fit option to linear fit this graph (see
Figure 5) and verify if the slope of the line conforms to the actual adiabatic value (1.4)
of air.
For the carbon dioxide gas part of this experiment, I sprayed the inside of the box with
CO2 portable fire extinguisher. As CO2 is denser than air, it would stay in the bottom of
the “leak proof” box. In order to determine the distance, the motion detector always uses
a calibration factor of 268 m/s, corresponding to CO2 at 20˚C. Because CO2 fire
extinguisher exhausted dry ice into the box, the temperature of the system reached below
freezing temperature and it was later increased using two heaters.
Using the Logger Pro unit with motion detector and thermometer probe, I collected 30
minutes of raw data (Position vs. Time graph and a Temperature vs. Time graph) in CO2
gas – while slowly changing the temperature in the box (from less than 0˚C to about 30˚C)
by turning on the heaters. Original Graph 2 in the appendix show a Position vs. Time
graph and Temperature vs. Time graph respectively as a sample from this setup.
As also described above for medium air, I manipulated and selected the smoothest part of
raw data in a spread sheet to calculate the actual speed of sound (cs) in CO2 for all the
different temperatures.
3.3 Results
The data collected from the experiment was divided into two separate parts for Air and
CO2. Raw data (recorded by the detector) was manipulated in a spread sheet (see
Rohit Rana, 002762-020
12
appendix) and graphed in Graphical Analysis to draw conclusions and relationships tone
to theoretical values.
3.3.1
Speed of Sound in Air as a Function of Temperature Spread Sheet (see Appendix)
Sample Calculations:
Time
(s)
0
5
Temperature
±0.0001 ˚C
36.9451
36.8717
2
(Speed of Sound)
2 2
(m /s )
2
=(353.1483)
= 124713.756181
124675.759553
Distance
±0.0001 m
Actual Time Traveled
-7
±2.92x10 s
1.8376
1.8379
=(1.8376/343)
= 0.005357522
0.005358338
Speed of Sound (m/s)
=(1.892/0.005357522)
= 353.1483
353.0945
Uncertainty Speed
of Sound (± m/s)
0.0011
0.0011
Uncertainty (Speed
2
2 2
of Sound) (± m /s )
Temperature in Kelvin
±0.0001 K
RT/M
2
2
±0.0001 m /m
RT/M (x10000)
-8
2
2
±1.0x10 m /m
0.000006
0.000006
=36.9451 + 273.15
= 310.0951
310.0217
=(8.314*310.0951)/0.02893
= 89116.1653
89095.0713
=89116.1653/10000
= 8.91161653
8.90950713
Uncertainty for Actual Time Traveled:
= Uncertainty for Distance/343 (assumed velocity by detector for speed of sound in air)
= ±0.0001/343
= ±2.92x10-7 s
Uncertainty for Speed of Sound (Distance measured by ruler/Actual Time Traveled):
= Relative uncertainty for Distance measured by ruler + relative uncertainty for Actual
Time Traveled
= (±0.002/1.892) + (±2.92x10-7/0.005357522)
= ±0.0011 m/s
Uncertainty for (Speed of Sound)2:
= 2(Relative Uncertainty of speed of sound)
= 2(±0.0011/353.1483)
= ±0.000006
Uncertainty for RT/M (x10000):
Rohit Rana, 002762-020
13
= (Uncertainty for RT/M)/10000 (assumed velocity by detector for speed of sound)
= ±0.0001/10000
= ±1.0x10-8 s
Figure 1: Temperature vs. Time Graph
The above graph shows the slow drop in room temperature over about 20 minutes. Note
that the temperature drop is about 18.0˚C, a comfortable margin recommended for this
experiment.
Figure 2: Distance vs. Time Graph
Rohit Rana, 002762-020
14
The above graph shows the related drift in the apparent position of box’s back wall as
measured by the motion detector during the temperature drop of 18.0˚C.
Figure 3: Distance vs. Temperature Graph
Using the best straight-line fit in the above graph to the assumed temperature (20˚C)
gives the actual distance of the detector from the box’s back wall (measured at
1.892±.001m). Data shows a consistent ±1.239x10-5 m/˚C drift in the distance measured
by the detector.
Figure 4: Speed of Sound in Air vs. Temperature Graph
Rohit Rana, 002762-020
15
After determining the speed of sound, Cs, from the position data, Cs is plotted as a
function of temperature. The data collected shows a good linear trend and the slope
(.6021±.002306 (m/s/˚C) and y-intercept (330.9±.06256 m/s) of the best-fit line conform
well to textbook equation:
.
Figure 5: (Speed of Sound in Air)2 vs. RT/M Graph
A plot of Cs2 as a function of RT/M gives the expected linear trend and the slope of the
best-fit line (1.458) is an acceptable estimate of
(1.4), the ratio of the specific heats of
the gas.
Rohit Rana, 002762-020
16
3.3.2
Speed of Sound in CO2 as a Function of Temperature Spread Sheet (see Appendix)
Sample Calculations:
Time
(s)
1075
1080
Temperature
±0.0001 ˚C
20.2747
20.2982
(Speed of Sound)
2 2
(m /s )
2
=(271.0524)
= 73469.376786
74130.172072
2
Distance
±0.0001 m
Actual Time Traveled
-7
±3.73x10 s
1.7797
1.7718
=(1.7797/268)
= 0.006640784
0.006611119
Speed of Sound (m/s)
=(1.800/0.006640784)
= 271.0524
272.2686
Uncertainty Speed
of Sound (± m/s)
0.0011
0.0011
Uncertainty (Speed
2
2 2
of Sound) (± m /s )
Temperature in Kelvin
±0.0001 K
RT/M
2
2
±0.0001 m /m
RT/M (x10000)
-8
2
2
±1.0x10 m /m
0.000008
0.000008
=20.2747 + 273.15
= 293.4247
293.4482
=(8.314*293.4247)/0.044
= 55443.9316
55448.3730
=55443.9316/10000
= 5.54439316
5.54483730
Uncertainty for Actual Time Traveled:
= Uncertainty for Distance/268 (assumed velocity by detector for speed of sound in CO2)
= ±0.0001/268
= ±3.73x10-7 s
Uncertainty for Speed of Sound (Distance measured by ruler/Actual Time Traveled):
Rohit Rana, 002762-020
17
= Relative uncertainty for Distance measured by ruler + relative uncertainty for Actual
Time Traveled
= (±0.002/1.800) + (±3.73x10-7/0.006640784)
= ±0.0011 m/s
Uncertainty for (Speed of Sound)2:
= 2(Relative Uncertainty of speed of sound)
= 2(±0.0011/271.0524)
= ±0.000008
Uncertainty for RT/M (x10000):
= (Uncertainty for RT/M)/10000 (assumed velocity by detector for speed of sound)
= ±0.0001/10000
= ±1.0x10-8 s
Figure 6: Temperature vs. Time Graph
The above graph shows the slow increase in room temperature over about 15 minutes.
Note that the temperature drop is only about 3.5˚C, about the smallest temperature
change recommended for this experiment.
Rohit Rana, 002762-020
18
Figure 7: Distance vs. Time Graph
The above graph shows the related drift in the apparent position of box’s back wall as
measured by the motion detector during the temperature drop of 3.5˚C.
Figure 8: Distance vs. Temperature Graph
Using the best straight-line fit in the above graph to the assumed temperature (20˚C)
gives the actual distance of the detector from the box’s back wall (measured at
1.800±.001m). Data shows a consistent ±0.0009131 m/˚C drift in the distance measured
by the detector.
Rohit Rana, 002762-020
19
Figure 9: Speed of Sound in CO2 vs. Temperature Graph
After determining the speed of sound, Cs, from the position data, Cs is plotted as a
function of temperature. The data collected shows a linear trend and the Cs at 20˚C is
about 271 m/s, which conforms strongly to theoretical value (268 m/s) of speed of sound
in CO2 at 20˚C.
Figure 10: (Speed of Sound in CO2)2 vs. RT/M Graph
Rohit Rana, 002762-020
20
A plot of Cs2 as a function of RT/M gives the expected linear trend and the slope of the
best-fit line (1.272) is an acceptable estimate of
(1.3), the ratio of the specific heats
of the gas.
4. Conclusion & Evaluation
Analysis from the graphs indicates that speed of sound (in air and in CO2) and
temperatures are positive correlated. It can be supported by the idea that a sound wave (a
longitudinal wave) is a pressure disturbance which travels through a medium by means of
particle-to-particle interaction. If particles are moving faster, then the sound wave will
also move faster. In addition, temperature is a measurement of the average kinetic energy
of the molecules in an object or system. KE = 0.5mv2, which indicates that temperature is
directly related to velocity. If temperature in a medium is increased, then the sound speed
in that medium will also increase or vice versa.
Speed of sound in air vs. temperature graph is clearly more precise as compared to speed
of sound in CO2 vs. temperature because all the data points are very closely packed on
the best-fit line. The accuracy of its relationship and values were confirmed by comparing
the best-fit line’s equation:
to known textbook equation:
. In addition to very low uncertainty of its slope (±.002306
m/s/˚C) and y-intercept (±.06256 m/s) due to digital motion detector and temperature
probe, the percentage error of its slope (0.33%) and y-intercept (0.15%) was also very
low. One can notice excess data points collected towards the end of sound speed in air
experiment. This is simply because the air conditioner could not cause any further
significant change in system’s temperature.
The speed of sound in CO2 and temperature graph indicates that Cs at 20˚C is about 271
m/s, which conforms strongly to theoretical value (268 m/s) of speed of sound in CO2 at
20˚C with a percent error of about 1.11%. According to one source, the speed of sound in
CO2 is 259 m/s at 0˚C and increases 0.4 m/s for each degree Celsius. However, the bestfit line of the data indicates the y-intercept or sound speed at 0˚C to be 186.7 m/s and
Rohit Rana, 002762-020
21
slope to be about 4.217 m/s/˚C. This nonconformity present only in the CO2 experiment
indicates several sources of error. First, the wooden box might not have been sealed
properly as such discrepancy in data can occur due to a leak in CO2 gas outside the box.
Second, raw data manipulated for CO2 experiment did not consist of a large temperature
change (3.5˚C) as some of the data collected by the motion detector was missing because
the detector did not work for a while when cold (below 0˚C) CO2 fire extinguisher was
sprayed in the box.
As stated earlier, a plot of Cs2 as a function of RT/M gives a linear trend and the slope of
the best-fit line refers to , the ratio of the specific heats of the gas. For the experiment in
medium air,
/adiabatic constant/slope of Cs2 vs. RT/M graph turned to be 1.458, which
is an acceptable estimate of
(1.4) with a percent error of about 4.14%. On the other
hand, the slope of Cs2 in CO2 vs. RT/M graph turned to be 1.272, which is also an
acceptable estimate of
(1.3) with a percent error of about 2.15%. Overall, the
investigation regarding measuring sound speed in air conformed to theoretical values and
relationships more accurately as compared to the data collected in CO2 gas.
Instead of using an inexpensive wooden box, another expensive device (plastic glass box)
should be constructed to collect data for carbon dioxide part of the experiment. This will
ensure a leak-proof system for CO2 to settle and provide data closer to theoretical value
and thus reduce percent error. Second, a more accurate and precise motion detector that
will function in below zero degrees Celsius conditions should be used to ensure complete
gathering of all data points. In fact, this experiment’s results and relationships could be
immensely improved by doing this experiment for a longer period of time (collecting
more data points) with larger temperature change. This temperature change can be
achieved by varying the temperature in the box by carrying this experiment in a tiny wellinsulated room with more air conditioners and heaters. It might be a better option to
invest money on buying an actual CO2 cylinder rather than using a CO2 fire extinguisher
that gives of dry ice. It’s a good idea to run through the experiment twice, the first time
Rohit Rana, 002762-020
22
quickly to get familiarized with the measurement procedure, and the second time slowly
and carefully.
Further investigations into this experiment could include measuring speed of sound in
helium gas (much lighter than air and CO2) as a function of temperature. One may also
choose to investigate the effect of humidity on the speed of sound or use another simple,
practical, and accurate method of determining the speed of sound.
5. Bibliography
Cutnell, John D., and Kenneth W. Johnson. Physics. New York: Wiley, 2003.
Henderson, Tom. "The Speed of Sound." The Physics Classroom Tutorial. 24 Feb. 2009
<http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l2c.html>.
Pettersen, Inge H. "Speed of Sound in Gases Using an Ultrasonic Motion Detector." The
Physics Teacher 40 (2002): 284-86.
"Sonar: Technology Gallery for." Discovery of Sound in the Sea. 24 Feb. 2009
<http://www.dosits.org/gallery/tech/at/s1.htm>.
"The Speed of Sound." MathPages. 24 Feb. 2009
<http://www.mathpages.com/home/kmath109/kmath109.htm>.
Rohit Rana, 002762-020
23
Rohit Rana, 002762-020
24