Standing Waves

Statement of Purpose
To analyze the properties of a standing wave.

Procedure

Tie one end of a string to an oscillator and for the first case tie a 200g mass to the other end, and in another case tie a 150g mass. Adjust the frequency of the oscillations until standing waves are identified.

Data

CASE 1:

Harmonic n	frequency +/- 1Hz	fn = nf1 +/- n1Hz	λ  +/- .01m	Δx nodes +/- .005m
1	24	24	3.32	1.66
2	48	48	1.66	0.83
3	72	72	1.11	0.555
4	96	96	0.83	0.425
5	120	120	0.66	0.33
6	144	144	0.55	0.275
7	169	168	0.465	0.233
8	193	192	0.405	0.203
9	217	216	0.365	0.183
10	241	240	0.33	0.165

CASE 2:

Harmonic n	frequency +/- 1Hz	fn = nf1 +/- n1Hz	λ  +/- .01m	Δx nodes +/- .005m
1	12	12	3.32	1.66
2	24	24	1.66	0.83
3	36	36	1.11	0.555
4	48	38	0.83	0.415
5	60	60	0.663	0.332
6	72	72	0.543	0.272
7	84	84	0.475	0.238
8	96	96	0.412	0.206
9	109	108	0.369	0.185
10	121	120	0.334	0.167

Plotting frequency vs 1/λ :

Conclusion

There is a linear growth between the frequency and wavelength which affirms that they are inversely proportional. This relationship is given by v=fλ, where v is the slope of graph.