Description of the Experiment
This experiment investigated the phenomenon of standing wave propagation in a stretched string. A frequency generator triggered a dynamo, which drove a stretched string — one side of the string was attached to the dynamo, and the other side was pulled over a pulley and tied to a weight. The generator generated sinusoidal waves with a given frequency, resulting in a specific number of antinodes and nodes depending on the frequency (OpenStax, 2022). Data collection involved recording the distances between two nodes at a given frequency up to and including the tenth harmonic. Based on the collected data (Table 1), the average inter-node distances for each harmonic were calculated, and the corresponding wavelengths and propagation velocities were calculated.
Discussion
The data on the characteristics of the string used were used to calculate the theoretically possible speed of its oscillation using the proposed formula. The calculations show that such a string would have to vibrate at a speed of 40.3 m.s-1 with a tension force of 4.79 N and a linear string density of 0.00295 kg.m-1. However, calculated results of the averaged velocity for the conducted experiment have shown that the average velocity of such a string is 47.03 m.s-1, which is 16.7% higher than the theoretically expected value.
The reason for the difference between the theoretical and practical results may be the errors associated with the experiment. In particular, the measurement of the inter-nodal distance occurred during intense oscillations, which could lead to inaccurate readings. In addition, the scatter of the data when measuring such a distance for the harmonics was different, which strongly influenced the average values used and thus could lead to a bias in the results. This could be eliminated by using large samples of data, leading to a reduction in error. On the whole, however, the experiment can be considered successful since all of the objectives were achieved.
Reference
OpenStax. (2022). Wave interference — standing waves and beats. LibreTexts Physics. Web.
Appendix
Table 1 – Standing Waves on a String
Table 2 – Standing Waves on a String: Velocity Comparison
