Spring Term 2013

The second major experiment to be performed for the class will take place in BL114 on Thursday, March 28, 2013.  The experiment that will be performed is entitled "Resonances in Strings", a description of which begins on page 5-1.

For the "Resonance in Strings" experiment, you will be evaluating two models for waves on strings and determining the wave speed for a particular tension.  The first part of the experiment will involve finding at least five (5) resonance frequencies for a particular tension in a string.  Make sure that you mention in your procedure section how you determined the correct resonance frequency for a particular mode of vibration.  Next, you will need to choose a single mode of vibration that was easy for you to work with in the first experiment (say, the n = 3 mode), and then change the weight hanging off the end and find the new frequency for the new tension.  Since you have done one tension already in the first experiment, you need to do two more (at a minimum, but you can do more since it is rather easy) so that you have at least three different tensions.

In the Analysis section, make a graph of frequency vs. mode number (n) WITH ERROR BARS!.  Fit a line to this and evaluate the model by seeing if a majority of the error bars for the points cross the fit line or not.  If they do, the model is appropriate for your situation.  If not, the model is not appropriate for your situation.  The slope of this line is equal to the fundamental frequency for the string.  Use this value (with its uncertainty) to determine the speed of waves on the string for the particular tension.  Compare this experimental value to the theoretical value of SQRT(Tension/mass per unit length) (again, make sure you include uncertainties!).  The second graph you should make is a plot of f_n vs. SQRT(Tension), with error bars.  If a majority of the error bars for the points cross the fit line, the model is appropriate for your situation.  If not, the model is not appropriate for your situation.

One of your tasks for this lab is to determine the fundamental frequency in the string and calculate an experimental and theoretical value for the wave speed in the string - compare these two values.  The fundamental frequency can be found from a graph of frequency vs. order number (n) in Logger Pro.  Fit a line to your data and the fundamental frequency will be the slope of the line.  Logger Pro will give you the uncertainty in the slope that can be used in computing the uncertainty in the wave speed calculation.

The procedure section is the only section that must be completed in ink and handwritten.  The other sections can be word processed if you like.  If you do any calculations in Excel or Maple, you may printout the worksheets that you generate and attach them in your notebook.  Please remember to include a sample calculation, if you do any by hand, and propagate the uncertainties.

The lab reports are due Friday, April 12, 2013 by 5:30 PM in the green bin outside my office.

A complete lab report must have the following sections:

Do not forget to update your Table of Contents and to number the pages in your lab notebook!

The first page of your report must have a title, the name of the P.I. (explicitly indicate who was the P.I.), the name of the lab assistant, and the date that the report was turned in (not the date that you performed the experiment!).

*Abstract - a BRIEF description of what you were investigating, how you conducted the experiment and your conclusions based on your experience.  The abstract should not be a discussion of what you are going to do in the lab.  The abstract cannot be written before you have analyzed your data.  In the lab notebook, skip a page or two so that you can write this in at the beginning of the report after you have analyzed your data.

Introduction - a discussion about any details that you think would help someone perform the experiment.  This should include a discussion about the model or the method selected for performing the tests.  If you use models (equations) in your analysis, list the models in this section and describe what each of the variables represent.

**Procedure - a detailed description of what you did in the lab.  At the beginning of this section, place the date and the time that you began the experiment.  This section must include a schematic, detailing how things were connected, where appropriate.  The raw data must appear in this section immediately following the description about how the data was taken.   A person must be able to read your procedure section and be able to duplicate your results without having the lab manual present.  Do not do any calculations in this section, just record how you performed the experiments and record the raw data.  If the data is taken by computer, you must specify the path and filename where the data is stored.   This information must be listed in this section right after the description of how the data was taken.  Do not simply list all of the files generated at the end of the section.

Analysis - a sample of the calculations made in the lab.  This section should include a sample of the error calculations and propagation of errors used in your analysis.   The final data that you are analyzing to generate conclusions, the values with appropriate uncertainties, must be shown in this section.  The actual calculations for each one does not have to be included, as long as you show an example for one, but you may include them all if you wish.  The calculations may be done by the computer, but include printouts of the worksheet in your lab book.  Any graphs or printouts that are placed in your notebook must occupy one whole page and be trimmed to fit within the page and not hang outside of the notebook.

*Conclusion - this section must have a conclusion that is based on your experiments and analysis.  If your conclusions do not following logically from your analysis, your grade will be deducted significantly.  This section must also contain a brief description of significant factors that you think affected your data, in particular, the uncertainties in your data (factors that contributed to the error in your experiment).  A good thing to keep in mind is to think of this report as a report you are submitting as part of your job responsibilities.   If you do not think your boss would accept what you have to say, it is a safe bet that I will not like it either.

The asterisks indicate the sections that I will pay closest attention to.

Modified March 27, 2013 by Galen C. Duree Jr.