Experiment 4: Standing Waves

Experiment 4: Standing Waves

Introduction:
The purpose of this experiment is determine a relationship between wavelength and frequency in order to understanding the standing waves driven by an external force.
We are going to measure and compare different wavelength of waves on a single string by changing the frequency of the wave.The weight and length of the string to be 3.08 g and 140 cm; also the hanging mass is 199.8g. We had two cases for this lab, by changing the amount of tension we give to the string we should be able to change the wavelength and thus the frequency of the string.  We repeated this measurement multiple times to get an idea of the uncertainties involved.

Calculations & Graphs:

Case 1
Osciallation Frequency (Hz)	16.5	32.5	45.6	56.7	74.6	87.4
Nodes	2	3	4	5	6	7
Wave Length (m)	1.4	0.67	0.45	0.37	0.26	0.21
1/λ	0.71	1.49	2.22	2.70	3.85	4.76
Case 2
Osciallation Frequency	21.8	29.5
Nodes	4	5
Wave Length	0.46	28

Both cases' frequencies followed the patter of f = vn/2L where v is the wave velocity, n is the number of antinode, and L is the length of the string. As we expected, when the wave lengths are the same, the lower velocity requires lover frequency inorder to reach certain resonance frequency. On the other hand, the higher the velocity requires higher frequency to reach the resonance frequency.

By looking at the graph, it is clear that there is a linear relationship between frequency and wavelength. As the wavelength is increased, the frequency correspondingly decreases. The ratio of velocities between case 1 is about 1.48, which is close to radical 2 as we expected. However, we cannot get enough data for case 2 since the tension on the string is too small.

Conclusion:

The uncertainties relating to the wavelength is due to our ability to correctly measure the spring using a large 2-meter stick, and to correctly hold that measured length during that phase of the experiment.  Finally, the uncertainty related to the frequency is naturally derived from the uncertainties related to the time.