Experiment:
The experiment is set up as shown below
To create a standing wave, we can adjust the frequency generator.
.jpeg) |
| One end of the string is attached to a hanging mass and the other end is attached to an oscillator connected to a frequency generator. |
Data and Analysis:
Length of string
|
1.954 ± 0.02 m
|
Mass of string
|
0.00206 ± 0.00001 kg
|
Linear density
|
0.001054 ± 1.55E-5 kg/m
|
1, 2, and 3.
Case 1
Harmonics
(n-value)
|
Frequency (Hz)
|
# of Nodes
|
Distance between nodes
(m)
|
Wavelength (m)
|
1
|
15 ±2.5
|
2
|
1.522 ± 0.01
|
3.044 ± 0.01
|
2
|
30 ± 2.5
|
3
|
0.761 ± 0.01
|
1.522 ± 0.01
|
3
|
43 ± 2.5
|
4
|
0.507 ± 0.01
|
1.015 ± 0.01
|
4
|
61 ± 2.5
|
5
|
0.381 ± 0.01
|
0.761 ± 0.01
|
5
|
73.4 ± 0.1
|
6
|
0.304 ± 0.01
|
0.609 ± 0.01
|
6
|
87.9 ± 0.1
|
7
|
0.254 ± 0.01
|
0.507 ± 0.01
|
7
|
102.9 ± 0.1
|
8
|
0.217 ± 0.01
|
0.435 ± 0.01
|
8
|
117.2 ± 0.1
|
9
|
0.190 ± 0.01
|
0.381 ± 0.01
|
9
|
131.6 ± 0.1
|
10
|
0.169 ± 0.01
|
0.338 ± 0.01
|
10
|
146.5 ± 0.1
|
11
|
0.152 ± 0.01
|
0.304 ± 0.01
|
Calculated speed: 43.14 ± 0.86 m/s
Speed from graph: 44.39 ± 0.2982 m/s
Case 2
Harmonics
(n)
|
Frequency
(Hz)
|
#of Nodes
|
Distance between nodes
(m)
|
Wavelength
(m)
|
1
|
7.4 ± 0.1
|
2
|
1.522 ± 0.01
|
3.044 ± 0.01
|
2
|
15.0 ± 0.1
|
3
|
0.761 ± 0.01
|
1.522 ± 0.01
|
3
|
23.0 ± 0.1
|
4
|
0.507 ± 0.01
|
1.015 ± 0.01
|
4
|
30.3 ± 0.1
|
5
|
0.381 ± 0.01
|
0.761 ± 0.01
|
5
|
36.9 ± 0.1
|
6
|
0.304 ± 0.01
|
0.609 ± 0.01
|
6
|
45.5 ± 0.1
|
7
|
0.254 ± 0.01
|
0.507 ± 0.01
|
Calculated speed: 21.55 ± 1.25 m/s
Speed from graph: 22.92 ± 0.3424 m/s
4. Ratio of wave speeds for case 1 compared to case 2 is 1.94. This ratio is really close to the predicted wave speed which is 2.
5. Case 1
|
Harmonics
|
Frequency (Hz)
|
n*f1 (Hz)
|
% Difference
|
|
1
|
15
|
15
|
0.00%
|
|
2
|
30
|
30
|
0.00%
|
|
3
|
43
|
45
|
4.44%
|
|
4
|
61
|
60
|
1.67%
|
|
5
|
73.4
|
75
|
2.13%
|
|
6
|
87.9
|
90
|
2.33%
|
|
7
|
102.9
|
105
|
2.00%
|
|
8
|
117.2
|
120
|
2.33%
|
|
9
|
131.6
|
135
|
2.52%
|
|
10
|
146.5
|
150
|
2.33%
|
The table above shows that the measure frequencies for case 1 is close to nf1
6.
|
Harmonics
|
Case 1 Frequency
|
Case 2 Frequency
|
F1/F2
|
|
1
|
15
|
7.4
|
2.0
|
|
2
|
30
|
15
|
2.0
|
|
3
|
43
|
23
|
1.9
|
|
4
|
61
|
30.3
|
2.0
|
|
5
|
73.4
|
36.9
|
2.0
|
|
6
|
87.9
|
45.5
|
1.9
|
Some sources of error that may affect the results of this experiment are:
- Error contributed to equipment and measuring tools such as ruler and balance
- Error contributed to the first frequency generator we used which is not digital and has a large increments.
No comments:
Post a Comment