Data and Observations

We applied hanging masses in the following sequence: 200 g, 300 g, 400 g, 500 g, 100 g, 450 g.

Our attempt using 500 g yielded no data. The string would not vibrate, at least not enough for us to detect. This weight evidently produced string tension sufficient to inhibit the mechanical actuator - possibly by offsetting the actuator node from its bearing.

The 100 g mass, on the other hand, provided barely enough weight to stabilize the string's vibration along one axis. The string flopped around and growled a lot, making life difficult for the person trying to "find" any of the string's vibrational modes. We found it necessary to make our length measurements quickly, before the string could lapse into non-modal behavior.

The 450 g mass gave just enough "slack" for the string to vibrate. The wave amplitude, though, was small enough to again make life difficult for the person on the frequency knob - as well as making it difficult to distinguish the center of any node for the purpose of measuring length of a half-wave:

Where's the node ???

Each length measurement - including that of the string sample (for finding linear density) - required at least two scale readings by two different persons. (Each half-wave, as well as the string sample, was too wide for one person to take both scale readings while keeping a scale reference aligned.) Therefore, all lengths were measured "by committee." Then, the length taken as the difference of two measurements was doubled to give the recorded wavelength (which also doubles the magnitude of estimated error). Moreover, we noticed substantial variation, among the various combinations of tension and frequency, in our ability to distinguish center-node.

A rigorous treatment of error estimation and propagation would have required us to record a literal error estimation for each individual measurement - two for each recorded length, each specified by one person for the specific condition being viewed. Those error estimations would then be combined, using standard rules, to find a good estimate of probable error for each recorded and derived quantity.

Under certain conditions (work performed as original research or under paid contract, for example), such detail might be desired, out of caution not to overstate nor understate the precision of our measurements. In this circumstance we agreed to lump these sources of probable error into a single conservative estimate for each recorded wavelength.