Copy of MAE 170 Lab 5
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Arizona State University *
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MISC
Subject
Aerospace Engineering
Date
Apr 3, 2024
Type
Pages
9
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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.
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.
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