Week 5 Lab
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School
University of California, Irvine *
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Course
52A
Subject
Aerospace Engineering
Date
Jan 9, 2024
Type
Pages
4
Uploaded by SuperHumanArtSwan38
Week 5
6.5 Spring Standing Wave
The lowest fundamental standing wave: Period =
1.38s
The Tension =
10N
Frequency given T is 1.38 =
0.72 Hz
Expected Frequency =
0.72 Hz
Percent Error: 0%
The frequency does not change very much when walking toward the center aisle and this makes sense
because when the length of a spring decreases, its stiffness (spring constant) increases, which causes the
natural frequency of a spring-mass system to increase. This inr eturen creates a balance keeping it the
same. The period that we got was
1.39s.
Stretched length in the aisle:
401 cm
Tension:
6.25 N
Frequency given T:
0.72 Hz
Expected frequency:
0.69 Hz
Percent Error: 8.69%
Tension =
10N
Unstretched length:
209cm
Stretched length:
591cm
Tension =
10N
First harmonic period:
0.66s
First harmonic frequency:
1.51 Hz
Expected frequency:
1.44 Hz
Percent Error: 4.8%
Tension =
10N
2nd harmonic period:
0.40s
2nd harmonic frequency:
2.50 Hz
Expected frequency:
2.16 Hz
Percent Error: 15.3%
Box: 93 grams
Spring + Box mass: 910 grams
Spring mass:
817 gram
*Graph is given at the end
n=1
n=2
n=3
Ratio to fundamental
0.72/0.72=1
1.51/0.72=2.097
2.50/0.72=3.472
Expected Ratio to
fundamental
0.72/0.72=1
1.51/0.72=2.097
2.16/0.72=3
# of Nodes
2
3
4
5.6 Speed of Sound
Instead of
5kHz
we started the sound at
20.05kHz
We set the waves amplitude higher and zoomed into the peaks so that we could see both of the waves
easier. To put in phase we aligned the peaks and to put it 180 degrees out of pase we put node to peak.
Distance between speakers for in phase: 15.8 cm
Distance between speakers for out of phase: 17 cm
Initial position in phase: 15.8 cm
Position out of phase: 17 cm
Postition back in phase 18.2
Wave length given distance: 2.4 cm
Observed Speed of Sound: 251 m/s
Theoretical speed of sound: 346 m/s
Discepency/ Percent Error: 37%
Increase frequency to 22 kHz
Wavelength: 1.8 cm
Speed of sound: 396.18 m/s
Discepency/ Percent Error: 14.58%
Decrease frequency to 19 kHz
Wavelength: 1.8 cm
Speed of sound: 396.18 m/s
Discepency/ Percent Error: 14.58%
Mathematically it does not vary that much or it shouldn’t. From 22-19 kHz there was no wave length
change which leads us to believe that there should not be a change for 20kHz but even with experimental
error there is still is minimal change. The difference in frequency was not sufficient but we believe that if
it changed inversely proportional. Increase in frequency is decrease in wavelength.
The wave velocity in a medium typically remains constant for a given type of wave. In such cases, there is
no direct relationship between wave velocity and frequency. However, when discussing waves on strings
or in other elastic materials, wave velocity can vary with frequency due to the material's properties. In
these cases, higher-frequency waves might have slightly higher velocities because the tension in the
material can affect the wave speed. Still, in most common situations, like sound waves in air or light
waves in a vacuum, wave velocity remains constant regardless of frequency, following the universal
constants of the medium involved. They are directly proportional.
6.6 Sound standing waves
Phase Angle (degrees)
Amplitude (V)
0
4
90
4.5
180
3.5
270
4.5
360
3.5
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There are 2 maxima per wavelength of motion. This is because when we go 0 - 360 degrees in phase and
back to phase we get a full wavelength and ahlaf which gives us 2 peaks and a trough essentially
equallting 2 maxes.
Bonus Question:
The minimum signal is not a perfect null (zero) due to the presence of noise, limitations
in measurement equipment, imperfections in system components, and environmental factors. Noise is
ever-present, measurement instruments have sensitivity limits, real-world components aren't perfect, and
environmental conditions can introduce small variations, all of which contribute to a minimum signal
level even when a null signal is desired.