## 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.**