## 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

(2)

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? **