PASCO WA-9867 Sine Wave Generator - Manual (Page 20)

Sine Wave Generator Standing Waves In Strings
20 ®
Procedure
1. Clamp the String Vibrator about 120 cm from the pulley. Hang about 50 g from the string over
the pulley. Measure from the knot at the vibrating blade to the top of the pulley. This is the
distance L. (Note that L is not the total length of the string, only the part that is vibrating.)
2. Record the total hanging mass, including the mass hanger.
3. Adjust the frequency of the Sine Wave Generator so that the string vibrates in four segments.
As before, adjust the driving amplitude and frequency to obtain a large-amplitude wave, and
clean nodes, including the node at the end of the blade. Record the frequency.
4. Add 50 g to the hanging mass and repeat steps 2 and 3.
5. Repeat at intervals of 50 g up to at least 250 g. Record your data in a table.
6. Make a graph of Frequency-squared, f
2
, versus hanging mass, m. (The units will be easier to
work with later if you graph the mass in kilograms.) Is the graph linear?
7. Find the slope (including uncertainty) of the best-fit line through this data.
8. As you can determine from Equation 3, the slope of the f
2
vs. m graph is:
From the slope of your graph, calculate the density (
µ) of the string. What is the uncertainty?
9. Determine the actual density of the string by measuring the mass of a known length. If you do
not have a balance readable to 0.01 g, use several meters of string.
10. Compare the density that you measured in step 8 to the actual density that you determined in
step 9. Calculate the percent deviation.
Further Investigations
1. Repeat the procedure using the yellow cord. Put the data from the string and cord on the same
graph to show the difference in their densities.
2. Repeat the procedure with elastic cord. The density is much larger, so put the data on a
separate graph. Look carefully at the graph. Is it linear like the first two? Calculate the density
using both the minimum and maximum slopes.
3. Measure how much the elastic cord stretches when you place the maximum mass on the
hanger. Based on the unstretched density of the cord, and the amount that it stretches, estimate
the “stretched” density of the cord. Compare this value to the densities that you calculated
from your graph.
slope
4g
µL 2
---------- =
% Deviation
Measured Actual –
Actual
--------------------------------------------- 100%
Ч
=