Standing Waves in a Column of Air Experiment

For this experiment, I looked at the sound produced by different PVC pipes when hit differently so that they would be open or closed tubes. I aimed to look at how the length of tube affected the pitch of the sound and how sound differs in an open vs. closed tube. I used five PVC pipes of different length with a constant diameter of 2 cm and a constant thickness. They were numbered as follows:

Tube #9	15.6cm
Tube #1	25.6cm
Tube #7	46.0cm
Tube #3	50.9cm
Tube #5	61.0cm

I recorded the fundamental frequency produced by hitting the top each pipe with my finger. For each length of pipe, I recorded the resulting frequency three different times. I plotted the average frequency for each length and calculated a best fit curve. I repeated this process by treating the pipe like a closed tube and hitting it with my palm. The data is plotted here:

What is interesting about this plot, is that the ratio between of the best fit curve of the open pipe to the best fit curve of the closed pipe is .52. In order to understand why this makes sense, you need to understand how a sound wave travels in a column. For a pipe that is open at both ends, the fundamental wave looks like this: 

source: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/opecol.html

For a pipe that is closed at one end and open at the other, the fundamental wave looks like this:

source: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/clocol.html

As you can see, 2L is the wavelength for an open tube's fundamental frequency, while 4L is the wavelength for a closed tube's fundamental frequency. The ratio between these two is .50. The value in practice was .52, however. Why is this larger value still accurate? In the real world, the nodes and anti-notes of a sound wave traveling through a pipe exist outside of the pipe's open ends. For the pipe open at one end, the effective tube length is the length of the tube + a third of the diameter. For the pipe that is open at both ends, two thirds of the diameter must be added to the tube length to find the effective tube length.

Using the same data set for the open pipe, one can create an estimate for the speed of sound. I plotted the wavelength and period for each pipe length. The slope of the line of best fit provides the approximate speed of sound:

The slope is 331.2 meters/sec which is the nearly the exact speed of sound at 0 degrees Celsius. The temperature in the room during the experiment was 24.6 degrees Celsius, however, which predicts an actual speed of sound of 345.76 degrees Celsius. This makes the percentage error 4.2%. This can be attributed the lack of precision in retrieving the information about the sound waves from the Logger Pro software and to potential fluctuation in the temperature of the room during the experiment, as this temperature was not monitored after data collection began.