Practical Report Physics 113
Fill in the first page of this document with your name and student number, up to four students per group.
Name
Student number
Dylan Kok
2
9
3
2
0
5
3
4
Charl Hofmeister
2
9
0
7
6
7
5
7
Inacio Marques
2
9
0
6
7
2
2
7
Indicate the prac code with a X in the box:
V1: Prism spectrometer: Dispersion and the index of refraction.
V2: Simple Harmonic Motion
V3: Determination of the speed of sound in air
Prac code
V1 V2 V3
X
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Instructions on how to produce a typical practical report
This document is a template to a physics practical report with important information regarding the structure
of the report itself and the type of information required so that the reader can comprehend how you have
tested a physics principle. Obviously, we also need to assess your work so it is in your interest to produce a
report which is clear, concise and presented in a scientific manner with all necessary information.
A possible way to achieve this is using the following framework:
Objective: State what you want to achieve in this experiment. A formal way to do this is to state a question or
hypothesis that you want to address.
Method: You should include a summary of the lab procedure in your words; do not merely copy what is in
the manual. This section should demonstrate your understanding of what exactly you measured and how.
Data: You should include the raw data you measured.Be sure to present your data in an organized manner
(e.g. a data table) and to include units.
Data Analysis: In this section you will manipulate the data in order to help you address your question or
hypothesis. Usually this entails performing calculations and/or creating graphs of the data.
Uncertainty & Error: You cannot draw any final conclusions from your data until you think carefully about
how well you can trust your data and what factors may have affected or biased it. To begin with, you must
simply list factors that might have affected the accuracy of your measurement, and stipulate whether you
think these factors had a large, medium or small effect. In this section you must also explain why you have
decided to round off your results to a particular number of significant figures.
Conclusion: Finally go back and answer the question you stated in the beginning. Does your data allow you
to support or reject your hypothesis, or is the data inconclusive? Also do you have anything you can compare
your results with (e.g. a value in the literature, a second measurement, a measurement with a different
method, other lab groups)? How well does it compare to such a value?
-------------------------------------------------------------------------------------------------------------------------------For administrative use only
Marks
Total
DETERMNATION OF THE SPEED OF SOUND IN AIR
Introductory exercise:
-
F : Frequency of sound produced (Hz)
L : Displacement of black stopper (m)
A : Amplitude of graph (V)
F = 400 Hz
L
0.24
0.23
0.22
0.21
0.20
0.19
0.18
A
0.01325
0.03000
0.02750
0.06000
0.10700
0.05000
0.03710
Objective:
The aim of this experiment is to determine the speed of sound in air using a resonance tube setup (described
below). Resonant frequencies will be analysed conjunctly with their corresponding lengths with the aim of
verifying whether the equipment is accurate in measuring the speed of sound.
Hypothesis:
The speed of sound in air can be determined with precision using the experimental setup described below by
measuring the resonant frequencies relative to varying tube lengths and taking their average in a tube with
one closed end. I believe the equipment will be suitable for this task.
Method:
1. Setup
1. First, we had to connect the signal generator to the loudspeaker at one end of the glass tube and set it
up using the Skorost app.
2. Set the loudspeaker to produce sound waves at a chosen frequency between the range 1000 and 2000
Hz.
3. Ensure the microphone is positioned correctly to detect sound waves inside the tube. (Most of this
setup was done already)
2. Data Collection
4. Gradually pull the black stopper further away from the starting point until a standing wave with
maximum amplitude is observed on the Skorost app with our own eyes.
5. Record the stopper’s position (resonant length) with a ruler and the set frequency, corresponding to
the first harmonic.
6. Increase the frequency by 200 Hz and repeat steps 4–5.
7. Continue this process until data is collected for five different frequencies.
3. Data Analysis
8. Plot the collected data (resonant length vs. harmonic number) in Desmos.
9. Fit a straight-line graph and determine its gradient.
10. Use the gradient to calculate the speed of sound using the v = 4f x gradient
4. Uncertainty Calculation
11. Determine the residuals in Desmos and calculate the RMSE (root mean square error).
12. Use RMSE to calculate the uncertainty in the speed of sound.
5. Conclusion
14. Compare the calculated speed of sound with the theoretical value v≈331.3+0.6T (where T is the
temperature in °C which was 25°C on the day of our practical).
15. Then we are able to assess whether the experimental results are within an acceptable range of
accuracy.
16. Finally, then conduct a final evaluation to determine whether the equipment effectively measures the
speed of sound.
Data:
Resonant Lengths and Harmonic Numbers for Different Frequencies in a Sound Speed
Experiment:
-
F : Frequency of sound produced (Hz)
Ln : Displacement of black stopper (m)
n : harmonic number of the tube with one closed end
F = 1000 Hz
n1
1
3
5
L1
0.08
0.25
0.42
F = 1200 Hz
n2
1
3
5
L2
0.065
0.205
0.35
F = 1400 Hz
n3
1
3
5
7
L3
0.055
0.17
0.295
0.42
F = 1600 Hz
n4
1
3
5
7
9
L4
0.045
0.15
0.26
0.365
0.47
F = 1800 Hz
n2
1
3
5
7
9
L2
0.04
0.135
0.225
0.325
0.415
Data Analysis:
The raw data in the tables above was plotted on a set a axis, The graph shows the relationship between
Length and Harmonic number for the different frequencies we set.
We are given the equation for the resonant frequency:
𝑓𝑛 =
𝑛𝑣
4𝐿
If we rearrange the formula to make L(n) the subject the formula becomes:
𝐿(𝑛) =
𝑛𝑣
4𝑓𝑛
Since the applied frequency and speed of sound is constant the graph becomes a straight-line graph that
passes through the origin where the gradient can be calculated as:
𝑚=
𝑣
4𝑓𝑛
Length(m) vs Harmonic number graph:
Graph Interpretation:
Given Desmos gradients:
Frequency f (Hz)
1000
1200
1400
1600
1800
Gradient m
0.08371
0.0694
0.05928
0.052
0.04594
Calculating Speed of Sound:
Frequency f (Hz)
Gradient m
Calculation (v =4m.fn)
1000
1200
1400
1600
1800
0.08371
0.0694
0.05928
0.052
0.04594
(4)( 0.08371)(1000)
(4)( 0.0694)(1200)
(4)( 0.05928)(1400)
(4)( 0.052)(1600)
(4)( 0.04594)(1800)
𝒗𝒂𝒗𝒈 =
343 + 343.2 + 343 + 345.6 + 342
5
= 343.36m/s1
-
v- velocity
m- gradient of the graph
fn – frequency
Speed of Sound
v (m/s1)
343
343.2
343
345.6
342
Uncertainty:
Calculations:
This means the mean uncertainty for velocity is 3.09 m/s. From this value we can give the range of an
acceptable speed of sound and compare that to see if the actual real-world speed of sound falls in that range.
This range is v ∈ [340.27, 346.45].
Conclusion:
The experiment aimed to determine the speed of sound in air using a glass tube, signal generator and a
microphone. By measuring the resonant frequencies for various lengths of the tube and corresponding
harmonic numbers, we were able to calculate the speed of sound.
Results:
The calculated speeds of sound were consistent with the theoretical value of the speed of sound (v ≈ 331.3 +
0.6T m/s). T is the temperature of the environment in degrees Celsius which was 20 in this case.
T = 343.3m/s which falls in the range v ∈ [340.27, 346.45].
In this experiment the uncertainties in the measurements were analysed using the root mean square error
(RMSE). The uncertainties were minor, and the average speed of sounds was found to be within an
acceptable range of accuracy.
Consistency:
The measured values and their associated uncertainties overlapped with the theoretical value of the speed of
sound. This indicates that the equipment used in this experiment is indeed capable of accurately measuring
the speed of sound in air.
The calculated values of the speed of sound in air also overlapped with their uncertainties which further
strengthens the idea that the measurements are reliable.
The average calculated speed of sound and uncertainty is consistent with the theoretical value of the speed of
sound indicating that the measurements were accurate and correct.
Final Assessment:
The equipment used in this practical experiment is effective in measuring the speed of sound in air to an
acceptable degree of accuracy. The results that were gathered remained consistent with the theoretical
expectations and the uncertainties are within an acceptable range0.
Concluding Exercise:
Hypothesis:
-
Open-Closed Pipe: Resonance occurs at odd harmonics (n = 1, 3, 5, ...).
Closed-Closed Pipe: Resonance occurs at all harmonics (n = 1, 2, 3, 4, ...).
Test Procedure:
1. Setup:
The setup is the exact same as mentioned on the first page of this report where we use the glass tube
and the Skorost app.
2. Measure Resonant Frequencies:
-
Start with the lowest frequency possible (1000 Hz in this case) and increase the frequency gradually
using small increments.
Adjust the length of the tube using the black stopper and observe the amplitude of the sound wave
using the Skorost app.
Tabulate the lengths at which resonance occurs.
3. Identify the Harmonics:
-
4𝐿𝑓
Using the formula 𝑛 = ( 𝑣 ) calculate the harmonic number for each resonant length. L is the length
of the tube, f is the frequency of the simulation, v is the speed of sound in air at room temperature.
4. Analyse Harmonics:
-
Check of the harmonic numbers are odd or if they include even numbers.
Calculation:
-
F : Frequency of sound produced (Hz)
L : Displacement of black stopper of resonant length (m)
n : harmonic number of the tube with one closed end
F = 1000 Hz
n
1
3
5
L
0.08
0.25
0.42
For L = 0.08m:
𝑛=
4∗0.08∗1000
≈1
343
𝑛=
4∗0.25∗1000
𝑛=
4∗0.42∗1000
For L = 0.25m:
343
≈3
For L = 0.42m:
343
≈5
Conclusion
Each of the harmonic numbers are odd. This means that this is an Open-Closed Pipe and not a Closed-Closed
Pipe.