Lab Report 2: Digital Signal
Processing
Sean Michelino Lim (2022360012)
Department of Mechanical Engineering, Sampoerna University
MECH3316 - A: Instrumentation Laboratory
Nikolas Krisma Hadi Fernandez
March 19th, 2025
1
Table of Contents
Table of Contents ....................................................................................................................... 2
List of Figures ............................................................................................................................ 3
List of Tables ............................................................................................................................. 3
List of Equations ........................................................................................................................ 3
Chapter I Introduction ................................................................................................................ 4
Chapter II Methodology............................................................................................................. 5
2.1 Materials and Apparatus used .......................................................................................... 5
2.2 Experimental Procedure ................................................................................................... 5
2.3 Key Equations .................................................................................................................. 5
Chapter III Result and Discussion ............................................................................................. 6
3.1 Result................................................................................................................................ 7
3.2 Discussion and analysis.................................................................................................... 7
Chapter IV Conclusion ............................................................................................................ 12
References ................................................................................................................................ 13
2
List of Figures
Figure 1: Schematic of the experiment [2] ................................................................................ 6
Figure 2 Sine wave at 3Hz-10cm ............................................................................................... 8
Figure 3: Figure of wave at 3kHz 10cm Sine(All0062) .......................................................... 10
Figure 4:Figure of wave at 3kHz 50cm Sine(All0057) ........................................................... 10
Figure 5: Figure of wave at 3kHz 94cm Sine (All0056) ......................................................... 11
List of Tables
Table 1: Materials and Apparatus list ......................................................................................... 5
Table 2: Experiment results ....................................................................................................... 7
Table 3: table of distance, frequency, wavelength, and wave velocity of the experiment ......... 9
List of Equations
Equation 1 used to calculate the velocity of the sound waves ................................................... 6
Equation 2 Sinusoidal wave equation ........................................................................................ 6
Equation 3 shows the equation to find sensitivity of an instrument .......................................... 6
3
Chapter I Introduction
Digital Signal Processing (DSP) plays a crucial role in analysing and manipulating
signals, particularly in the research fields. The importance of DSP is due to the way computers
work as analogue data cannot be processed using computer directly as it requires data sets
instead of 1 continuous data, it has to be converted for it to be processed automatically. This
experiment focuses on understanding DSP principles by observing sound wave phenomena.
By generating and analysing different waveforms, we explore the fundamental properties of
sound, such as frequency, amplitude, and resonance.[1]
Through the use of function generators, digital storage oscilloscopes, and sound level
meters, this lab report investigates how sound propagates and interacts with its environment.
By measuring key parameters such as resonance and signal waveforms, we gain deeper insights
into the physics of sound and its digital representation. The results from this experiment will
help reinforce key DSP concepts and their applications in real-world scenarios.
Through this experiment, we aim to reinforce theoretical concepts of DSP while
developing hands-on experience with signal measurement and analysis tools. The results will
help in understanding real-world signal processing applications, particularly in acoustics and
instrumentation.
4
Chapter II Methodology
2.1 Materials and Apparatus used
Table 1: Materials and Apparatus list
Materials
Name
Amount
Note
Apparatus
Function
Generator (4011A
5 MHz)
1x
Generates different types of waveforms,
including sine, square, triangular, and
sawtooth signals
Digital Storage
Oscilloscope
(DSO)
1x
Captures and analyzes signals digitally for
waveform visualization and frequency
analysis.
Sound Level
Meter
1x
Measures the intensity of sound waves in
decibels (dB SPL).
Resonance Pipe
1x
Used to study acoustic resonance by
amplifying sound waves at specific
frequencies.
Connecting Wires
-x
Used to establish electrical connections
between
the
function
generator,
oscilloscope, and other components.
Table 1 displays the apparatus that are necessary and crucial to conduct this experiment.
2.2 Experimental Procedure
This experiment follows the following procedure:
Connect all instruments as shown in the schematic figure 1.
Set the function generator output level to maximum for all trials.
Select the desired waveform (sine, staircase, or triangle) on the function generator.
Adjust the function generator to different frequency values (3 Hz, 300 Hz, 3000 Hz, 30
kHz).
5. Measure the distance of the resonance pipe for each frequency setting.
6. Use the sound level meter to record the intensity of the sound wave.
7. Capture and analyse waveforms using the digital storage oscilloscope.
8. Fill in the experimental data table with recorded measurements.
9. Analyse the effect of frequency and resonance pipe length on sound intensity.
10. Determine the sinusoidal equation for a waveform at 3 Hz and a 10 cm resonance pipe
distance.
1.
2.
3.
4.
5
11. Calculate the velocity of sound propagation under different conditions.
12. Evaluate the sensitivity of the sound level meter.
Figure 1: Schematic of the experiment [2]
2.3 Key Equations
𝒗=𝒇∗𝝀
(Eq.1)
Equation 1 used to calculate the velocity of the sound waves
𝒚(𝒕) = 𝐀𝐬𝐢𝐧(𝟐𝛑𝒇𝒕 + 𝛟)
(Eq.2)
Equation 2 Sinusoidal wave equation
𝑺𝒆𝒏𝒔𝒊𝒕𝒊𝒗𝒊𝒕𝒚 = 𝜟𝑶𝒖𝒕𝒑𝒖𝒕 / 𝜟𝑰𝒏𝒑𝒖𝒕
(Eq.3)
Equation 3 shows the equation to find sensitivity of an instrument
Key terms:
𝑓 = Frequency (Hz).
𝜐 = Wave velocity (m/s).
𝜆 = Wavelength (m).
y(t) = Displacement.
𝐴 = Amplitude.
𝑡 = Time (s).
𝜙 = Phase shift.
𝜟 = Change
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Chapter III Result and Discussion
3.1 Result
Table 2: Experiment results
Frequency
(Hz)
Distance of
the
Resonance
Pipe (cm)
Sound Level Meter (scale 0-10) Waveform
(Folder name)
Sine
Staircase
Triangle
Sine
Staircase
Triangle
3
10
0
0.1
0
ALL0042 ALL0043 ALL0044
300
10
0.5
2
0.5
ALL0047 ALL0046 ALL0045
50
0.5
1.1
0.5
ALL0048 ALL0049 ALL0050
94
0.2
1.5
0.2
ALL0051 ALL0052 ALL0053
10
3
3.3
2.5
ALL0062 ALL0061 ALL0060
50
3.1
3.3
3.3
ALL0057 ALL0058 ALL0059
94
3
3.4
2.5
ALL0056 ALL0055 ALL0054
10
0
0
0
ALL0063 ALL0064 ALL0065
50
0
0
0
ALL0068 ALL0067 ALL0066
94
0
0
0
ALL0069 ALL0070 ALL0071
3 000
30 000
Table 2 shows the data collected from the sound level meter as well as the saved
file name of each test.
3.2 Discussion and analysis
To allow for analysis we need to be able to process the data beforehand. Using (Eq.2)
we can transcribe the obtained data into a function on its own. Take 3Hz at 10cm for instance,
applying the equation gives us the function of the sound wave which is:
𝒚 (𝒕 ) = 𝑨 𝒔 𝒊 𝒏 (𝟐 𝝅 𝒇 𝒕 + 𝝓 )
𝒚(𝒕) = 𝑨𝒔𝒊𝒏(6𝜋𝑡 + 𝝓)
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Figure 2 Sine wave at 3Hz-10cm
using the data from the experiment in table 2, since the sound level equates to
zero, the amplitude would also be 0 as seen in figure 2 as well. Which makes the value
of y(t):
𝒚(𝒕) = 𝑨𝒔𝒊𝒏(6𝜋𝑡 + 𝝓)
𝒚(𝒕) = 0 ∗ 𝒔𝒊𝒏(6𝜋𝑡 + 𝝓)
𝒚(𝒕) = 0
We can determine the sensitivity of the sound meter using (Eq.3):
Where 0 unit is detected at 0 amplitude as seen in the previous calculation, and a reading
of 3 at 0.4092m amplitude as seen on 3000Hz at 10 cm
𝑺𝒆𝒏𝒔𝒊𝒕𝒊𝒗𝒊𝒕𝒚 =
0𝑢𝑛𝑖𝑡 − 3𝑢𝑛𝑖𝑡
𝟎𝒎 − 𝟎. 𝟒𝟎𝟗𝟐𝒎
= 𝟕. 𝟑𝟑𝟏
𝒖𝒏𝒊𝒕
𝒂𝒎𝒑𝒍𝒊𝒕𝒖𝒅𝒆(𝒊𝒏 𝒎)
Using equation 1 we can calculate the velocity and sound propagation of every single
wavelength in the table.
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Table 3: table of distance, frequency, wavelength, and wave velocity of the experiment
Distance
(cm)
Frequency
(Hz)
Wavelength
(m)
Wave velocity
(m/s)
3
114.333333333
343
300
1.14333333333
343
3000
0.11433333333
343
300000
0.00114333333
343
300
1.14333333333
343
3000
0.11433333333
343
300000
0.00114333333
343
300
1.14333333333
343
3000
0.11433333333
343
300000
0.00114333333
343
(cycle/s)
10
50
94
Knowing that the velocity of sound is fixed at 343 m/s we can calculate the
wavelength of each sine experiments to be
Moving forward, this experiment shows us the phenomenon of resonance, which
is a phenomenon where the system’s vibration is amplified due to having the same phase
of vibration.
Analyzing the experimental data, the result seems to show a trend where in low
frequency it emits a low reading on the sound meter, which goes up as the frequency of
the vibration is turned up, then goes back down after 3000Hz. This shows that there is a
certain frequency where the sound level is highest between 3 and 30000 Hz, that can be
determined to be the natural frequency of the oscilloscope tube.
Between the few configurations we tested, the highest sound level is displayed
on the 3000 Hz range, amongst which they have a pattern which can be seen where it
starts at a certain value for 10cm, goes up on the 50cm mark, and goes back down on
94cm. This shows that the resonance peak of the 100cm tube is around the middle at
50cm. This finding suggests that the standing wavelength of the tube might be twice the
tube length.
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Figure 3: Figure of wave at 3kHz 10cm Sine(All0062)
Figure 4:Figure of wave at 3kHz 50cm Sine(All0057)
10
Figure 5: Figure of wave at 3kHz 94cm Sine (All0056)
Figure 3, 4, and 5 shows the sine wave at 3kHz at varying distance. The figures show
that at 10cm and 94cm the yellow function which indicates the sound waves are out of sync,
while the one on 50cm seems to be in sync with the light blue wave. The synchronization allows
for the increase in sound volume as the amplitude of the wave increases.
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Chapter IV Conclusion
This lab module displays an interesting view on DSP, where the continuous sine
function sound is digitized and displayed on the oscilloscope display. It highlights the
difference between analogue data taken from the sound meter and the digital data as seen in
the oscilloscope, where one gives us continuous data which can only be read in real time, while
the other digitize the data by saving the points and allow us to store and analyse the data
afterwards through the use of computers. It is certainly interesting to see the effects of sound
wave amplification through natural frequency to highlight the difference between analogue and
digital signal processing.
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References
[1]
“What is digital signal processing (DSP)_ _ Definition from TechTarget”.
[2]
“ENGR 3311-Instrumentation Laboratory Experiment module #02 Digital Signal
Processing Objectives.”
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