Standing Waves

In this experiment we try to understand the behavior of standing waves driven by a function generator.

We set up the experiment using a taut string connected to a weight. Varying the weight and the length of string gave us different values for our nodes and frequency as the velocity of the string depended on the tension in the string and the mass per unit length.

In performing the experiment, we collected many data values:

Case 1:

frequency(hz)	wavelength(m)	length (m)	mass(g)	mu_string(g/m)	velocity(m/s)	n
15.52	1.25	1.25	198.67	1.25	19.4	2
31.52	0.621	1.25	198.67	1.25	19.57392	4
47.41	0.41	1.25	198.67	1.25	19.4381	6
62.21	0.31	1.25	198.67	1.25	19.2851	8
78.76	0.255	1.25	198.67	1.25	20.0838	10
91.38	0.23	1.25	198.67	1.25	21.0174	11

Case 2:

frequency(hz)	wavelength(m)	length (m)	mass(g)	mu_string(g/m)	velocity(m/s)	n
8.2	1.25	1.25	50	1.25	10.25	2
16.6	0.621	1.25	50	1.25	10.3086	4
25.3	0.41	1.25	50	1.25	10.373	6
34	0.31	1.25	50	1.25	10.54	8
46	0.255	1.25	50	1.25	11.73	10
63.8	0.23	1.25	50	1.25	14.674	11

The ratio of wave speeds is roughly 2:1. It is the same as the ratio predicted by equation 5.

The measured frequencies are all multiples of f_1, the fundamental frequency.