The purpose of this experiment was to understand the standing wave driven by external force.
Experiment
The experiment was set up as the picture showed:
T= 1.96±0.000049N
Correction: the number of node was the number shown plus 2.
T= 0.49±0.000049N
Questions
1. Found the wavelength and n for case 1, where T= 1.96±0.000049N.
n= # of node -1L= nλ/2
λ= 2L/n
Mode
|
ƒ(Hz)
|
Number of nodes
|
Distance
between nodes(m)
|
λ (m)
|
n
|
fundemental
|
24±1
|
2
|
1.800±0.005
|
3.600±0.005
|
1
|
1st
|
47±1
|
3
|
0.900±0.005
|
1.800±0.005
|
2
|
2nd
|
71±1
|
4
|
0.600±0.005
|
1.200±0.005
|
3
|
3rd
|
94±1
|
5
|
0.450±0.005
|
0.900±0.005
|
4
|
4th
|
110±1
|
6
|
0.360±0.005
|
0.720±0.005
|
5
|
5th
|
150±1
|
7
|
0.300±0.005
|
0.600±0.005
|
6
|
6th
|
173±1
|
8
|
0.257±0.005
|
0.514±0.005
|
7
|
7th
|
195±1
|
9
|
0.225±0.005
|
0.450±0.005
|
8
|
Found the wavelength and n for case 2, where T= 0.49±0.000049N
Mode
|
ƒ(Hz)
|
Number of nodes
|
Distance
between nodes (m)
|
λ (m)
|
n
|
fundemental
|
10±1
|
2
|
1.800±0.005
|
3.600±0.005
|
1
|
1st
|
20±1
|
3
|
0.900±0.005
|
1.800±0.005
|
2
|
2nd
|
25±1
|
4
|
0.600±0.005
|
1.200±0.005
|
3
|
3rd
|
---
|
5
|
---
|
---
|
4
|
4th
|
45±1
|
6
|
0.360±0.005
|
0.720±0.005
|
5
|
5th
|
55±1
|
7
|
0.300±0.005
|
0.600±0.005
|
6
|
6th
|
65±1
|
8
|
0.257±0.005
|
0.514±0.005
|
7
|
Note: the wave for third harmonic was hard to see.
2. Plot of ƒ vs. 1/λ, where T= 1.96±0.000049N
% difference = (89.143-79.096/89.143) *100% = 11.3%
3. Plot of ƒ vs. 1/λ, where T= 0.49±0.000049N
% difference = (39.599-32.786/39.599) *100% = 17.2%
4.
5.
6.
Source of errors
The percent difference of the propagated speed from the plot and calculated from foumula v= sqrt T/u was 11.3%, where the tension was 1.96±0.000049N, and 17.2%, where T= 0.49±0.000049N. Possible errors could be the string we used streched when generating a wave; the mass hung did not provide enough tension, thus the string vibrated and affecting the generation of the wave.
No comments:
Post a Comment