Standing wave

Objective

Determine the right relationship between spring length, velocity to create a standing wave with different frequency.

Data:

Data of Case 1 (collected from experiment)

1/ λ, 1/m	frequency, Hz
0.25	12.1
0.5	23.7
0.75	34.3
1	46.3
1.25	57.5
1.5	68.9
1.75	80.2
2	90.6
2.25	103.8
2.5	115.4

The Slope of the line (f vs.1/ λ) is 45.70m/s.

 

Data of Case 2 (collected from experiment)

1/ λ, 1/m	frequency, Hz
0.25	4.7
0.5	10.3
0.75	15.6
1	20.9
1.25	26.3
1.5	31.3
1.75	36.7
2	41.6
2.25	46.7
2.5	51.5

The Slope of the line (f vs.1/ λ) is 20.81m/s.

The ratio of the wave speeds for the two cases (from the graph) is r = 45.70/20.81 = 2.196

The ratio of the wave speeds (apply equation v=(T/u)^0.5) is r = (0.25/0.05)^0.5 = 2.236

There is a 1.8% difference between two ratios.

 

The ratios of frequencies for case 1 and case 2

1/ λ, 1/m	f1/f2
0.25	2.57
0.5	2.30
0.75	2.20
1	2.22
1.25	2.19
1.5	2.20
1.75	2.19
2	2.18
2.25	2.22
2.5	2.24

We can see that the ratios are close to the theoretical value 5^0.5=2.236 and have a difference lower than 10%.

 

 

 

When we measured the length and the weight in this lab, the uncertainties were lower than 1%. However, when we try to determine some high frequencies, we cannot determine the exact frequencies which generate the given wavelength (2L/n) because the standing wave becomes hazy as the frequency increases, and the uncertainty increases as the frequency gets higher. When the nodes created by the high frequencies are more than 8, the uncertainties of the frequencies are as high as 15%, which are significantly high. To reduce the uncertainty, we should make the length of the string that participate in oscillation longer and reduce the weight of the hanging mass.