Physics AP - Singing Rob Lab (#19)

Background:
A wave is made up of two humps.  Half a wave is from node to node,
and half a wave is the first harmonic.  If one end of the wave is
closed and the other side is open you have to multiple the length by
4 to get the wavelength.

To find the velocity you can use the equation v=8f or the equation
v= bulk modulus/density.  Bulk modulus of aluminum is 7.0 x 1010 (pa)
and the density is 2.7 x 103Kg/cm3.  In order to find the period you
can use the oscilloscope and then the equation f=1/period.   

Problem:
Find the velocity and the frequency of the rod.

Materials:
aluminum rod, and oscilloscope

Procedure:
1. Measure the rod from end to end and then to find the wavelength,
   double the length.
2. In order to find the velocity use the equation v= bulk density/
   density.
3) To find the frequency you can use the equation v=8f, f=v/8 or you
   can figure out the frequency by experiment.
4) Pick a rod and then find the center of the rod with your index
   finger and thumb.
5. Then with you other index finger and thumb pull across the rod.
6. Once the rod is singing bring it over to the oscilloscope's
   speaker.  7) Then read the period off the oscilloscope.
8. You can then use the equation f=1/period to find the frequency. 

Data:
Wave-
length  Velocity               Frequency    Period        Exp. Freq.
8=2L    v=buld density/density f=v/8        4.4 humps×    f=1/per
8=2×117 v=7.0×10^10/2.7×10³    f=5091.8/234 .7×10-³sec    f=1/.44×10-³
8=234cm v=5091.8/s²            f=2175Hz     T=.44×10-³sec f=2273Hz

Analysis/Conclusion:
As the data shows the experiment frequency is a little high then the
actual frequency.   This can be accounted for by human error, maybe
the placement of the tree sap on the rod.  Also the reading of the
period could have been off because the vibrations of the rod would
have been getting slower making the period also slower.