Mechanical Waves: Design An Experiment

          The goal of this exercise is to design an experiment that derives the relationship between wavelength and period. The only things provided for the use in this experiment was a stopwatch, a meter stick, and a long spring. By making standing waves in the spring, it would be possible to measure wavelength and frequency/period of a standing wave. One thing that is noteworthy, to maintain roughly the same rate of wave propagation, the period would go up with an increase in wavelength. This suggest a proportionality between period and wavelength. The period (T) is a measurement of how long it takes for the wave to complete one cycle. The amount of cycles was counted in ten seconds and then that number of cycles was divided by ten.

 

          The above picture is the observations and data from the experiment. Below is a picture of our setup. It's difficult to discern the spring and the standing wave on it. The picture on the whiteboard (above picture) is a sketch of what the lower picture is depicting.

           After performing the experiment, the data was plotted in logger pro with period being the x-axis and wavelength being the y-axis. Below is the table of data with the corresponding graph and curve fit.

Period (s)	Wavelength (m)
0.8215	4
0.8875	6
1.075	8

         The linear fit is rough at best. When the elements of this experiment are considered, the fit is not so bad. The nodes used to measure wavelength might have not been exactly nodes. This is due to trying to keep the standing wave at a fundamental frequency as wavelength changed. Another aspect in this experiment is trying to count cycles in ten seconds. The standing wave moves relatively fast and its expected that there is a high degree of inaccuracy with time due to using a stopwatch.

          The fit shows the slope of the plot has units of meters over seconds. Looking at the proportionality Wavelength = C*Period, it can be assumed that C has units of velocity (meters over seond). This is a rough derivation for the relationship of wavelength and period. The relationship is as follows:

where v is the transverse wave velocity.