Copy of MAE 170 Lab 5
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Arizona State University *
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MISC
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Aerospace Engineering
Date
Apr 3, 2024
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Pages
9
Uploaded by MajorPorcupinePerson1026
Henry Anderson, Jacob Eyre, Hunter Risdon, Elen Hovhannisyan
MAE 170
10/31/23
Lab 5
Q1:
λ =
?
?
=
340?/?
5000𝐻?
= 0. 068?
Q2:
Figure 1
While amplitude among all values differs based on the time in both the average signal and the
last acquired signal, it is apparent to note that certain parts of the average and the last acquired
signal are similar (if not equal in amplitude). Similar portions of the last acquired signal and the
average are likely due to the reference signal. If both plots are similar, this is likely due to a
consistent source of sound across all measurements, considering the fact that only one sound
source is constant throughout our measurement (The Speaker) this means that similarities
between our plots originate, in all likelihood, from the speaker. Note how there is a similarity
between our plots a little bit after 2 ms, just after the speaker is finished transmitting. Other
sources of sound in the signal are likely background noise, but the portion of the signal received
between slightly over 2 ms and slightly over 3 ms into the measurement is from the speaker.
Q3:
Measuring the time the first peak of the reference signal is emitted by the speaker (
) against the time of the first major similarity between our plots (
1. 1020 × 10
−3
?
) we find a delay of
. We measured the horizontal distance
2. 2204 × 10
−3
?
1. 1020 × 10
−3
?
of the microphone to the speaker as 15 cm, and the vertical distance as 31 cm. Using the
pythagorean theorem gives us the distance between the speaker and the microphone of
34.348 cm or 0.34348 m. Dividing the distance of the microphone to the
31
2
+ 15
2
=
speaker by the time delay of the reference signal and the last captured/average similarity gives us
our calculated speed of sound
. This is within a 8.09% margin of
0.34348 ?
1.1020 ×10
−3
?
=
312. 50 ?
?
error to the given speed of sound (
).
340 ?
?
Q4:
Figure 2
Graphed are the speed of sound in air (red), the acquired data of time delay plotted against position
in meters along with error bars (blue), and the line of best fit for the acquired data (green).
The x-error bars are found using the percent error between the theoretical and measured distance
between the speaker and microphone where
.
??𝑎????? ?𝑖??𝑎???
=
????? ?? ????? (343?/?)
×
??𝑎????? ?𝑖??
The y-error bars are found using the average of the time intervals from when the first peaks of
the acquired signal start rising as this measures the actual first millisecond that the sound reaches
the microphone.
The equation of the line of best fit is y = - 0.002227x + 0.001137. From this, the experimental
speed of sound is found to be
. Note that the slope is negative
1
?????
=
1
0.002227
≈
449. 0 ?/?
because of the decreasing time delay but is made positive when finding the speed of sound as it
doesn’t dictate direction. This same principle is applied when graphing the real speed of sound,
where 0.001137 comes from the y-intercept of the line of best fit to
? =−
1
340
? + 0. 001137
fit the data.
Q5:
The initial measured distance between the microphone and the speaker was a 34.4 cm distance,
spaced by 31 cm x 15 cm. Following the experiment, the final measured distance between the
microphone and the speaker was 11.3 cm, spaced by 11 cm x 2.5cm. The prescribed distance by
the Arduino RAMBo set the microphone to a distance of 33.54 cm described by a 30 cm x 15 cm
distance, with a final distance of 0 cm. The Percent Error of our stepper motor can be described
by:
|
𝑇ℎ?????𝑖?𝑎? − 𝐸????𝑖????𝑎? 𝑇ℎ?????𝑖?𝑎?
| * 100 = |
(33.54 ?? − 0 ??) − (34.4?? − 11.3 ??) (33.54 ?? − 0 ??) | * 100 =
|
(33.54 ??) − (23.1 ??) (33.54 ??) | * 100 = 0. 31127 * 100 = 31. 12%
This significant difference in motor measurement v.s expectation is most likely due to incorrect
calibration of the steps per revolution, the mechanical load or backlash in the system,
environmental factors, and/or faulty/worn equipment. Stepper motors move in discrete steps.
They determine their position by the number of steps taken and lack feedback loops about their
actual position. Servomotors, on the other hand, utilize feedback mechanisms to precisely control
their position, velocity, and torque to continually adjust their position to match the intended
position. Using a Servomotor in our experiment can increase confidence in our measurements
because it reduces the chances of positional inaccuracies and provides a higher level of control
and precision. In order to reduce positioning uncertainty in our labs, we can explore the use of a
Servomotor, calibrate our equipment beforehand, and ensure a stable and controlled environment
to minimize the impact of uncertainty.
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Q6:
Figure 3
Figure 3 (above) represents the normalized amplitude of the signal received from the microphone
positioned along a fixed Y axis (7 cm), as the microphone moved closer to the speaker along a
varied X axis (0cm - 30cm). The x-axis represents the position of the microphone, starting at
position (0,7), traversing 1cm for 30 intervals, until moving 30cm towards the speaker to
position (30,7). The y-axis represents time. The red linear line represents the time it takes for the
speed of sound to travel at the indicated distances. The varying colors represent the amplitude of
the sound wave and reveal the speed at which the wave is reached by the microphone. From this
we are able to see that as the distance between the microphone and the speaker decreased, the
time it took for the sound wave to reach the microphone also decreased. Not only this, but we are
able to recognize that the slope of the peaks of the captured sound wave are parallel to the speed
of sound and decrease proportionally.
Q7:
Figure 4
Figure 4 (above) represents the normalized amplitudes of the sound field seen at 0.002 sec on the
scanning system. The x-axis represents the position X of the microphone, starting at position 0
and traversing 30 cm to position 30. The y-axis represents the position Y of the microphone,
starting at position 0 and traversing 15 cm to position 15. The normalized amplitudes at time
0.002 sec of the sound wave can be represented by the various colors, where the peaks and
valleys of the sound wave are represented by the bright yellow and deep blue colors,
respectively.
Q8:
Figure 5
Figure 5 (above) is an animated gif of the normalized amplitudes of the sound field along the
different X and Y positions of the scanning system. Figure 5 shows the spatiotemporal sound
field generated by the speaker throughout time. The x-axis represents the position X of the
microphone, starting at position 0 and traversing 30 cm to position 30. The y-axis represents the
position Y of the microphone, starting at position 0 and traversing 15 cm to position 15. The
normalized amplitudes of the sound wave can be represented by the various colors, where the
peaks and valleys of the sound wave are represented by the bright yellow and deep blue colors,
respectively.
Q9:
The scan took approximately 0.1846 hours to run with a total of 588 time intervals to analyze
and graph. Based on this observation, if the data averaged 64 times for each position, then it
would take a total of 0.0201 hours to run the scan.
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Q10:
Our step size acoustic wavelength ratio can be found by saying
𝛌
= 0.01m/0.068m = (as
determined in Q1) where
𝛌
= 0.146 Now we have established our ratio, we can use this as a new
wavelength to determine our signal frequency assuming that the speed of sound is 343m/s
This satisfies the Nyquist frequency as it would be expected
? = ?
λ
=
343?/?
0.146?
=
2349. 3 𝐻? to be
s
/
2 = 2500 Hz, where 5kHz is our sample frequency (ƒ
s
). So because 2349 < 2500, our
?
Nyquist frequency is not satisfied.
Q11:
See above captions.
Q12:
Understanding the characteristics of sound propagation in time and space is significant in diverse
fields of study ranging from communication systems to medical imaging. We exist within a
constant chaos of noise signals, and understanding how to reference and interpret specific signals
is crucial to performing a spatiotemporal analysis as is the case in this experiment. Controlled by
a speaker Arduino and a RAMBO Arduino, we are sending an input voltage through our speaker
into the microphone, from which a signal is generated using an oscilloscope from which average
signal, reference signal, and signal position are plotted with MATLAB. These generated signals
allow us to interpret the noise to signal ratio and perform experiments determining how these
signal characteristics are affected in different environments.
In Part 1, we are investigating the effects of averaging a signal by creating a voltage
divider and identifying the improvement of the noise to signal ratio we are measuring.
“Repetitive waveforms buried in noise can often be pulled out by a signal averager, an
instrument that takes advantage of the redundant information provided by repetition.“ - Charles
Trimble
2
We are generating this signal at a fixed distance between the speaker and the
microphone and comparing our generated reference signal to our average signal obtained using
the oscilloscope.
In Part II, we remove the voltage divider, and consider the signal generated by the
speaker as the microphone is attached to a roving sensor which moves in controlled steps, taking
a new measurement at each step. This generates a signal which measures amplitude over time at
each step, and allows us to evaluate the time delay within our 30cm x 15cm field, and perform a
more detailed analysis of that measured spatiotemporal sound field.
Q13:
Figure 6:
Figure 6 shows the setup used in Part I of the experiment. It includes a voltage divider between
the speaker and the Arduino output.
1
Figure 7
Figure 7 shows the setup of Part II of the experiment and does not include a voltage divider.
1
In Part I of the experiment, using the setup shown in Figure 6, we calculated the distance
between the speaker emitting the sound, and our microphone using Pythagoras theorem and
determined that distance to be
34.348 cm or 0.34348 m. Following that we
31
2
+ 15
2
=
determined the time delay between the reference signal, and the average signal determining the
time delay to be
. We can then use these two numbers of frequency and
1. 1020 × 10
−3
?
wavelength we can calculated our velocity or speed of sound, which is supposed to be ~340m/s
to be
which leaves us a percent error of 8.09%. This demonstrates
0.34348 ?
1.1020 ×10
−3
?
=
312. 50 ?
?
that there was some sort of outside noise interference, or external environmental factors that
influenced our output signal.
In Part II of the experiment which involved the setup shown in Figure 7, the time delay was
found by picking the first peaks of both the reference and acquired signals for all 30 positions
along y=7 and finding the difference between their time values. This time delay was then plotted
against the position of the microphone along the x-axis. As shown by 2, the time delay decreases
as the microphone gets closer to the speaker. This is because the closer the microphone, the more
accurate the exchange between them. The slope of the line of best fit of this graph gives the
speed of sound found by this experiment, 449m/s, demonstrating a percent difference of
compared to the real speed of sound. This significant difference,
449−343
|
|
449+343
2
× 100 = 26. 77%
also observed by the obvious difference in the green and red lines of Figure 2, can be due to the
experiment being conducted in unknown air conditions. The temperature and density of the
surrounding air impact the speed of sound with sound waves traveling faster in warmer air which
is also less dense than cold air
2
.
References
1
Hewlett-Packard Journal 1968, Volume Issued 1968.
2
“Sound.”
Wikipedia
, Wikimedia Foundation, 24 Oct. 2023, en.wikipedia.org/wiki/Sound.
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