### Transverse Waves on a String

The speed v of a wave is related to the frequency f and the wavelength l by

v = f * l.

The speed v of a wave on a stretched string depends upon the tension T and the linear mass density m according to

We will study wave behavior using standing waves produced by stretching a string between a vibrator (oscillating at a constant frequency f of 120 Hz) and a pulley. Weights attached to the free end of the string are used to vary the tension T. The arrangement is shown below.  The length of the string should be about 1 m. You may log onto the computer using your davidson account. Use an Excel spreadsheet to record and analyze the data.  Create a spreadsheet with the title of the experiment, your name, your partner's name and the date.  Label 4 columns "Wavelength", "Velocity", and "Velocity Squared", and "Tension".

The pattern shown here is composed of three antinodes.   The distance between the nodes in these standing waves is one half of the wavelength.  Measure this distance and calculate the wave speed v for each value of the tension.  Find the values of the tension which will give standing waves of 2, 3, 4 and 5 antinodes.

Make an X-Y scatter plot of Velocity vs. Tension and another graph of Velocity Squared vs. Tension.  Label the horizontal axis as "Tension [N]" and the vertical axis as is appropriate.  Be sure to include the units in the axis label.  Do not connect the data points with line segments.  Just use symbols.  Right-click on a data point and "Add a trendline". Which of the two plots is closer to being a straight line?

• For the Velocity vs. Tension graph, remove the linear trendline and add a power trendline.  Go to the options menu of the trendline and display the equation on the graph.  What power relation does your data indicate?

• Obtain a copy of the two plots and the spreadsheet.  Write a paragraph containing an interpretation of your results and comments you have about the exercise.  Turn them in by 5:00, February, 1.

If you need help with Excel or getting into the room, please contact Tom Lipinski tolipinski@davidson.edu or Dan Boye daboye@davidson.edu .