2.), 5.) See attached sheets please.
B.1.) There is a clear relationship between the number of harmonics and the force pulling on the string. As the harmonics increase the mass hanging decreases exponentially.
2.) See graph for working out. Our graph starts from the second harmonic, since we only got results starting from the second one. It is quite clear, just by looking at the graph that it is exponential and if you continue the line beyond what the graph shows us, you can estimate what force would be needed for the 1st harmonic. It is around 4.9 N.
3.) The graph “The Relationship Between the Inverse of the Square Root of Force (to 3 s.f.) to the Number of Harmonics” shows, more or less, a straight line. The means that the graph has a constant slope and therefore there is a direct proportionality between the x-axis and y-axis values.
4.) Nothing happened when we placed our finger at a node. The node is a place where the wave has no amplitude, so there is nothing to affect at that point in the string.
5.) As the tension is increased the number of nodes decreases. The tension affects the speed of a wave. “The speed of a wave on a string depends on the tension on the string, T, and the mass density, mu, of the string”. We also know that v=fλ; and since the frequency stays constant throughout the experiment (40 Hz) the wavelength has to change. So, as we increased the tension, we decreased the velocity, decreased the wavelength and decreased the harmonic number.
6.) The definition of a node on a string is a point that does not move. Therefore you can argue that because the buzzer is moving the place where it is attached is moving so it is not a node. An antinode is a point on the string where the amplitude is highest, and it is obvious that near the buzzer the amplitude is minute. Therefore, if you’re given the choice node or antinode, node would describe the point the best. The point on the string does not really have amplitude because it is fixed. It is also known that a standing wave always has two nodes and 1 antinode.
Conclusion
This lab shows important relationships in standing waves. F= (n/2L) (F/μ) 1/2 is a key to understanding why the one graph is exponential and the other linear. This lab shows how tension affects the wavelength. From the results, it is suggested that the wavelength decreases as the tension increases, because more mass was needed to get the lower harmonic. And the lower harmonic obviously had a smaller wavelength.
However, there are sources which make you think otherwise. The formula v = (T/ μ)1/2 suggests that, if the mass density (μ) stays constant, the speed of the wave will proportionately to the square root of the tension on the string T. So if you increase the tension, the velocity increases.
v=fλ is another well known formula about the speed of waves. And since in this experiment the frequency was constant, the velocity is proportional to the wavelength.
From these to proportional formulas you can conclude that the tension is proportional to the wavelength, BUT this definitely does not apply to the results that we got out of this experiment.
It also seems logical that, when you tune a guitar string and you increase the tension, the frequency increases giving you a higher pitched sound. Yet if you theoretically keep the frequency constant, you should be increasing the wavelength, which you’re NOT doing in this experiment. In this lab, as the tension increased, the wavelength decreased, and we lowered the harmonics.
Nevertheless, there is clearly some relationship between the tension in the string and the harmonic.
Evaluation
This lab showed a clear proportion between the tension and the harmonics in a standing wave. However, there were weaknesses in the procedure. It was very difficult to decide upon when the standing wave has a certain amount of nodes. This is because the mass did not have a great affect if it was ±0.015 kg. This made our data collection weak and made it useless to use uncertainties. This is because there is a great human error in this experiment. Perhaps the procedure should help us distinguish a “real” node, so that we can be certain of which force is needed to create it.
