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 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 F. The arrangement is shown below. The length of the string should be about 1 m. Use your spreadsheet to record and analyze the data.





The pattern shown here is composed of three loops.  Find the values of the tension which will give standing waves of 2, 3, 4 and 5 loops.  The distance between the nodes in these standing waves is one half of the wavelength.  Measure this distance and use it in equation (1) to calculate the wave speed v for each value of the tension. 

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 m.  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.

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