## II. Procedure: Transverse Waves on a String

The speed v of a wave on a stretched string depends upon the tension F and the linear mass density μ (mass/length) according to

(2)

We will study wave behavior using standing waves produced by stretching a string between a mechanical oscillator and a pulley. Frequencies can be varied using DataStudio. The arrangement is shown below. The overall length of the string should be a little over 2 m. Use your spreadsheet to record and analyze the data.

1.  The pattern shown here is composed of three loops. Place a 200-g mass (maximum) on the hanger and find the values of the frequency that will maximize the amplitude of the standing waves for 2, 3, 4, and 5 loops. The distance between the nodes in these standing waves is one half of the wavelength. Measure this distance.  Use equation (1) to find the wave speed v by plotting frequency vs. (wavelength)-1.

2.  Now consider equation (2). A plot of the tension versus the square of the speed should give a straight line whose intercept is 0 and whose slope is μ. Use masses of 100, 150, ..., 300 gms.  Keep the number of nodes equal to 3.  Use your spreadsheet to obtain this plot; a linear regression for the slope and intercept (the linest command in Excel), to 90% confidence; and the best fit line for the data. Obtain a copy of the plot and the spreadsheet for your notebook.  How linear is the data plotted in this manner?  Explain.

Your instructor will give you a 3-meter length of string to weigh.  To 90% confidence, how well does the slope of your graph agree with the value of μ obtained by finding the actual mass per unit length?   Explain any discrepancies.