## Speed of Sound Lab – Another Update

Two years ago, I wrote about how I took tuning forks out of the standard resonance tube lab for measuring the speed of sound.

My students all have phones and make a modest effort to keep them put away. I decided to get them to take them out for the lab today.

I found this free function generator app that generates clean sine, square, triangle, and sawtooth waves across a pretty good range. Above 1 kilohertz, harmonics are visible on a software frequency analyzer, so I didn’t have students go quite that high. The frequency can be set across this range by entering the frequency manually, or by using preset buttons on the app. By playing the waveform, plugging in earphones, and hanging them on top of the tube, finding the fundamental vibration frequency is pretty straight forward.

Collecting data in this lab has, in my experience, been a pretty slow process. Today though, my students were able to collect 15-20 frequency and height pairs in less than half an hour. I took all of their data and graphed it together. I’m pretty impressed with how consistently the data sits in a line:

The slope of the best fit of L vs. 1/(4f) forced through the origin is 320 m/s, which is probably the closest result to theoretical that I’ve ever gotten. The precision of the data is the big winner here. It was a simple task to ask students to cycle back through their range of frequencies and check that their new measurements meshed well with the old.

## Speed of sound lab, 21st century version

I love the standard lab used to measure the speed of sound using standing waves. I love the fact that it’s possible to measure physical quantities that are too fast to really visualize effectively.

This image from the 1995 Physics B exam describes the basic set-up:

The general procedure involves holding a tuning fork at the opening of the top of the tube and then raising and lowering the tube in the graduated cylinder of water until the tube ‘sings’ at the frequency of the tuning fork. The shortest height at which this occurs is the fundamental frequency of vibration of the air in the tube, and this can be used to find the speed of sound waves in the air.

The problem is in the execution. A quick Google search for speed of sound labs for high school and university settings all use tuning forks as the frequency source. I have always found the same problems come up every time I have tried to do this experiment with tuning forks:

• Not having enough tuning forks for the whole group. Sharing tuning forks is fine, but raises the lower limit required for the whole group to complete the experiment.
• Not enough tuning forks at different frequencies for each group to measure. At one of my schools, we had tuning forks of four different frequencies available. My current school has five. Five data points for making a measurement is not the ideal, particularly for showing a linear (or other functional) relationship.
• The challenge of simultaneously keeping the tuning fork vibrating, raising and lowering the tube, and making height measurements is frustrating. This (together with sharing tuning forks) is why this lab can take so long just to get five data points. I’m all for giving students the realistic experience of the frustration of real world data collection, but this is made arbitrarily difficult by the equipment.

So what’s the solution? Obviously we don’t all have access to a lab quality function generator, let alone one for every group in the classroom. I have noticed an abundance of earphones in the pockets of students during the day. Earphones that can easily play a whole bunch of frequencies through them, if only a 3.5 millimeter jack could somehow be configured to play a specific frequency waveform. Where might we get a device that has the capacity to play specific (and known) frequencies of sound?

I visited this website and generated a bunch of WAV files, which I then converted into MP3s. Here is the bundle of sound files we used:
SpeedOfSoundFrequencies

I showed the students the basics of the lab and was holding the earphone close to the top of the tube with one hand while raising the tube with the other. After getting started on their own, the students quickly found an additional improvement to the technique by using the hook shape of their earphones:

Data collection took around 20 minutes for all students, not counting students retaking data for some of the cases at the extremes. The frequencies I used kept the heights of the tubes measurable given the rulers we had around to measure the heights. This is the plot of our data, linearized as frequency vs. 1/4L with an length correction factor of 0.4*diameter added on to the student data:

The slope of this line is approximately 300 m/s with the best fit line allowed to have any intercept it wants, and would have a slightly higher value if the regression is constrained to pass through the origin. I’m less concerned with that, and more excited with how smoothly data collection was to make this lab much less of a headache than it has been in the past.