Resonant tubes and the speed of sound

October 13, 2022

The laboratory for week nine is usually the speed of sound done by timing the delay from seeing boards clap together and hearing the clap. The laboratory is done along the entrance which provides up to 500 meters of straight line visual acquisition of the boards.

This fall, however, has been wetter than usual, and this morning was no exception. Rain was still falling as I drove in to campus. As a further complication, I knew that some of the eight o'clock section students had shifted to attending the eleven o'clock section. Attendance in the morning is usually students trickling in one by one.

Realizing I needed another plan, I thought about the tuning forks that I knew were still tucked away in the physical science supply cabinets. I was thinking about trying to use an oscilloscope app with the tuning forks, but by the time I reached Sekere I realized that the oscilloscope would be only reporting frequency data, not wavelength, and that I needed wavelength. I thought about what relationship, if any, might exist between the tuning fork length and the wavelength, but realized that was probably also only a proxy measure for frequency. Failure is always an option.

Once I got to the college I ran a search for tuning fork speed of sound experiments and an image popped up of a tuning fork over a tube of water. I had forgotten all about resonance tube approaches to obtaining wavelength. But I did not have the typical variable height resonance tube rig. I did have tubes, however. Large tubes at that.

Notes if this were to be run again: The concepts of resonant frequencies, nodes, and antinodes should have been introduced on Wednesday with visual demonstrations of these concepts. Plus perhaps springs, chains, and toy spring coils to illustrate some of the concepts at play. Even perhaps some sort of pan pipe or tubed intrument might be helpful. Light chain is really useful for showing nodes and antinodes on the lab table.

Myena came in as I was setting up the equipment, so I had her tap the tuning fork while I poured water from one tube to the other tube. There was a weak resonance with the water still down low in the tube, weak enough that I was not convinced that the location was a resonance point. I continued to fill the tube. Further up a second and surprisingly strong resonance occurred. I was surprised at the volume the resonance was producing as the tuning fork was not as clearly audible. At that moment I realized I had a viable experiment, failure would remain an option, but success would also be possible.

I then outlined the theory on the board, armed now with the knowledge that the first and weaker resonance was at three-quarters of a wavelength, with the fundamental quarter wavelength at the 24 cm air gap - a 96 cm wavelength. Myena and I continued with other forks.

Kamaloni "Kai" came in and took over the water pouring duties. Myena continued to strike the tuning fork.

The only complication with this rig is that a resonance sometimes occurs off of the pouring tube. I had plant watering pitchers in the lab, but did not think to use them. They would not have generated spurious resonances.

In keeping with the backwards ordered nature of the laboratory, I wrapped up with the introduction and equipment list.

The relationship is that the wave velocity is equal to the wavelength times the frequency. But the relationship v₁ ~ λ₁f₁ does not produce a regression line in Desmos. Curiously enough, the relationship does not fail and generate an error as I expected. The result is a list stored in v₁ that has length equal to the sample size. One can then take the mean value of the list to recover a numeric value for v₁. I knew that would be mysterious for the students and did not take that route.

Instead I solved for the frequency f₁ which yields a function that is graphed by Desmos.

Myena and Kai would produce data that appeared to be more consistent than a pair that arrived later in the morning.

At 26℃ the speed of sound is up around 34500 cm/s, so the experimental result is roughly 21% low. Most of the groups for the rest of the day would come in below the sound speed, so either there is an experimental bias or perhaps the antinode not exactly at the top of the tube.

Sanjay and then Jasmine would arrive after Myena and Kai had finished gathering data.

The board with data from Jasmin and Sanjay.

Left board at end of the 8:00 section. At 11:00 I cleared the right board and the right side of this left board to try to lay the physics out slightly more clearly.