Physics Lab Report
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Resonance and speed
of sound Laboratory report
Tuvshinzaya Erdenekhuu
S05 MI-19-0106
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Introduction:
Objective of this experiment was finding speed of sound
using a tuning fork and a tube with one closed end.
First ever value of speed of sound, 478.4 metres per
second, taken by the French scientist and philosopher Pierre
Gassendi in the 17th century. This value was then changed
and improved by number of scientists till 331.45 metres per
second achieved in 1942. (Berg, 2019)
In this experiment, length of pipe varied till tuning fork
resonance then that length noted with frequency of tuning fork
used. This procedure repeated with tuning forks with different
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frequency in order to get enough measurements to create
graph that can be used to find voice.
Theory:
Resonance happens in pipe with one closed end when the
wave, which produced by sound source at end of the pipe, hit
other end of pipe then reflect to opposite direction.
Additionally, reflected wave should be in phase with initial
wave to create wave with larger
amplitude than original wave
sounds (Aljlal, 2015). Thus, speed
of sound can be calculated by
measuring where resonance
happens for different frequency waves.
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During experiment, resonance happening in pipe assumed
to be first harmonic resonance which can be seen on figure 1.
Formula to find wavelength from the length of pipe shown on
Figure 2. (λ is wavelength, L is length of pipe)
However, end correction needs to
be added to length so “L” should be changed by “L+c”.
Furthermore, using formula in figure 3 we can substitute “λ”
with “v/f”. In the end, equation in figure 4 can be achieved.
Figure 1: First harmonic in pipe with one closed end (INTO Manchester, 2020)
Figure 2: Formula to find wavelength using length of pipe. (Puantha et al, 2018)
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Figure 3: formula of wavelength (Puantha et al, 2018)
During the experiment, length of pipe where resonance
happens should be noted with frequency of tuning forks used.
After repeating this for enough time, graph should be drawn
using value obtained. On the graph, 4L should be on y-axis
and 1/f should be on x-axis. This is graph expected to be linear
and gradient should be speed of sound. Furthermore, end
correction can be found be finding meeting point of graph and
y-axis.
Figure 4: equation for experiment (Author’s own creation, 2020)
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Health and safety:
This experiment involves water in high tube, so tube
containing water should be handled with care to prevent from
any slippery surface. This can be hazardous to people who is
not aware of it, especially if that person carrying fragile
apparatus.
Apparatus:
• Pipe
• Open pipe
• 1m ruler
• Clamp
• Tuning forks
• Water
• Beaker
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• Small wooden tile
Method:
Pipe should be secured with clamp that attached to leg of table.
Water was then poured inside a
pipe till certain amount where there
is no danger of water getting spilled
out of pipe. Then open pipe placed
inside the pipe. After this
preparation, tuning forks vibrated
by hitting it on wooden tile then held above the opening of
open pipe. By moving open pipe up and down, area with air
can be varied as wanted. During this period, open pipe should
be avoided from losing contact with water. When resonance
happens, open pipe need to be stationary by holding with
Figure 5: Experiment diagram (Author’s own creation, 2020)
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hand or any other method. Finally, distance between water
level and opening section of open pipe should be measured
and noted down. This same procedure should be repeated for
all tuning forks for 3 times to diminish the affect of mistakes.
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Results:
Table 1: Results (Author’s own creation, 2020)
Length uncertainty: 0.237 ± 0.005m
Frequency uncertainty: 376 ± 5 Hz
Frequency/ Hz
Length where resonance happened
/ cm
Average length /
cm
Average length in
m / m 1/Frequency
/s 4*L(length) /
m 256 34.0 33.5 32.3 33.3 0.333 0.00391 1.331 288 28.4 29.4 30.1 29.3 0.293 0.00347 1.172
320 25.1 27.6 26.5 26.4 0.264 0.00313 1.056 341.3 24.4 26.5 23.0 24.6 0.246 0.00293 0.985 384 21.4 25.5 20.0 22.3 0.223 0.00260 0.892
425.6 20.4 20.2 18.2 19.6 0.196 0.00235 0.784 480 17.5 18.5 17.8 17.9 0.179 0.00208 0.717 512 15.6 16.4 16.0 16.0 0.160 0.00195 0.640
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Analysis:
Figure 6: 4L against 1/f graph (Author’s own creation, 2020)
y = 343.98x - 0.017
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
0.00000 0.00050 0.00100 0.00150 0.00200 0.00250 0.00300 0.00350 0.00400 0.00450
4 *
Le n
g th
/ m
1/Frequency /s
4L against 1/f
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Calculations:
Figure 6 shows graph made from measurements taken
during experiment. Straight trendline formed using Excel
software and equation of trendline shown below.
y = 343.98x - 0.017
Gradient of trendline is equal to speed of sound according
to equation shown in figure 4.
Hence speed of sound= 343.98 m/s
Furthermore, -1*(y-intercept) should be equal to end
correction. Thus, end correction is = -1*(-0.017)
Hence end correction= 0.017m= 1.7cm
All the points on graph is on or near to trendline. This
shows that experimental error was low.
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Uncertainty calculation:
Equation to find speed of sound if end correction ignored
is: 𝑣 = 4𝐿𝑓
Uncertainty in length is ±0.005m
So average percentage uncertainty is 0.005
(0.333+0.160)/2 ∗ 100% =
2.0%
Uncertainty in frequency is ±5Hz
So average percentage uncertainty is 5
(256+512)/2 ∗ 100% =
1.3%
Therefore, percentage uncertainty for speed of sound is = 2.0
+ 1.3 = 3.3%
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Finally, average uncertainty in speed is = 3.3%*
343.98=11m/s
So, the experimental value of speed= 344 ±11 m/s
Error:
Globally agreed value of speed of sound is 331m/s in
atmosphere at 21°C.
So percentage error in experimental value of speed of
sound= (344−331)
331 ∗ 100% = 3.9%
End correction should be equal to 0.3*Diameter. Therefore,
end correction expected to be 0.3*2=0.6cm.
However, experimental value of end correction was 1.7cm
which is 3 times higher than expected value. In other word,
200% higher.
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Errors:
Errors occurred during experiment because of errors in
equipment. Ruler used to measure length of resonance space
and error in ruler is ±0.001m. Moreover, water surface in pipe
is curved which makes measuring more difficult. This can be
lead to error of around ±0.001m. Thus total error is ±0.002m.
Discussion:
Error in this experiment was unavoidable due to human
mistake and limitations. First, human ear is not great at
pinpoint when resonance happening. This created range on
value of lengths where sound is acceptable as a resonance to
human ear. Therefore, in order to eliminate this error, device
that can measure amplitude or magnitude of sound can be
used. Secondly, human hand can’t hold ruler in one exact
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position for long amount of time to take accurate
measurement. However, this can be solved by attaching open
pipe to table leg while allowing pipe to move freely vertically
when needed. By doing this, measurement can be taken
accurately, and open pipe wouldn’t be moved after finding
resonance position. Finally, accuracy can be improved by
these steps.
Addition to these limitations, there was an environment
sound issue. More specifically, half a dozen group done this
experiment in a same room. This results in experimenter
having trouble hearing his/her own experiment. Whereas if
experiment done in a quiet room, resonance can be identified
easier and more accurately.
End correction error was so high. It might have been
because of varying distance between tuning fork and end of
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open pipe during experiment. In order to abolish this error,
tuning forks can be attached to open pipe temporarily.
Conclusion:
Goal of experiment was measuring speed of sounds using
tuning fork, 2 pipes, water and ruler. Experiment was
successful because experimental value was only 3.9 percent
higher than globally agreed value of speed of sound. The
experiment used known fact to find correlation between length
where resonance happened and frequency of tuning fork used.
Exact correlation is not equal to speed of sound, so correlation
between 4 times length and 1/f found. Latter correlation is
equal to speed of sound according to known theory. Therefore,
that correlation calculated from graph. In the end, this theory
was near to results and can be said that the theory was correct.
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One important significance of this experiment is that it only
requires simple equipment. For example, one of other way of
measuring speed of sound requires microphone and data
logger. This experiment goes like having one sound source
and put 2 microphones at known and different distances and
measure difference in time taken. This experiment can
measure speed of sound to certain degree of accuracy.
However, it can’t be done in classroom by whole class.
Therefore, measuring speed of sound with resonance is more
practical and doable than this one.
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Reference link:
• Aljalal, A. M. (2015) “Sound resonance in pipes with
discrete Fourier transform”, European Journal of Physics
36(5) Available at: https://iopscience-iop-
org.manchester.idm.oclc.org/article/10.1088/0143-
0807/36/5/055030 (Accessed: 9 March 2020)
• Berg, R. E. (2019) Measuring speed of sound. Available
at:
https://www.britannica.com/science/acoustics/Measuring-
the-speed-of-sound (Accessed: 9 March 2020 )
• Figure 1: Swire, T. (2020) “Wave” [Diagram], INTO
Manchester. Unpublished
• Figure 2: Puantha, R., et al. (2018) formula to find
wavelength from length of pipe [Formula], Available at:
https://iopscience-iop-
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org.manchester.idm.oclc.org/article/10.1088/1361-
6552/aaea12#references (Accessed: 9 March 2020)
• Figure 3: Puantha, R., et al. (2018) formula to find
wavelength from speed and frequency [Formula],
Available at: https://iopscience-iop-
org.manchester.idm.oclc.org/article/10.1088/1361-
6552/aaea12#references (Accessed: 9 March 2020)
• Figure 4: Equation of correlation between speed and
frequency (2020). Author’s Own creation.
• Figure 5: Diagram of experiment (2020). Author’s own
diagram
• Figure 6: 4L against 1/f graph (2020). Author’s own graph