wavelength lab

The fundamental relationship between wavelength and period can be studied with a length of spring and a stopwatch.

This movie shows a standing wave set up in a spring. The benefits of using a standing wave to study wavelength are that the distance from person to person is a good approximation for the wavelength, and frequency measurements can be simplified.

For this experiment, our procedure is as follows:

• two students stand approximately 4 meters apart
• each student takes one end of a 4 meter spring and allows it to hang between them
• one student sets up an oscillation in the spring until a given number of anti-nodes are established
• a stopwatch is used to record the time for the standing wave to oscillate ten times
• the time is divided by ten in order to determine the period of one oscillation

The relationship between period on wavelength was determined for 4 data points.
all wavelengths are accurate to plus or minus .1 meter
all times are accurate to plus or minus .15 seconds
wavelength              period
8 meters                  1.04 seconds
4 meters                  .587 seconds
2.66 meters             .350 seconds
2 meters                  .262 seconds

these data points, when plotted, imply a linear relationship between wavelength and period.

This supports the formula for a standing wave, where the velocity of a wave in a given medium is a constant based on its linear density and the tension in that medium, and that velocity is equal to the wavelength divided by the period. This relationship is of the form;