Calculate the speed of sound with a Coke bottle...

As Wales gears up to implement Successful Futures, I'm in the process of collecting as many examples of "real world" science that can be undertaken in Primary and Secondary classrooms - things that don't require specialist equipment AND are relateable to by our learners. It's Bank Holiday here in the UK, so what else am I doing, but measuring the speed of sound with a Coke bottle.

Here is said 330ml bottle - which required a special trip to the supermarket to procure (had to buy x6 - so the kids are happy)

Physics bit - blow across the top of a bottle like this and you have a resonating cavity. Add some liquid to the cavity and you can change the resonant frequency - more liquid, less space in the cavity and the higher the frequency of the note produced. Eventually, as you add more and more liquid, the resonance breaks down and it becomes impossible to actually produce a distinct note. This happens some where above the red label, at the point that the "neck" of the bottle appears.

A quick mosey over to Hyperphysics shows that this has been done before, with the resonant frequency being given by a simple formula:

Where A is the opening in the top of the bottle (internal cross sectional area), V is the volume of the cavity and L is the length of the opening (the neck). A is easy to measure (in cm2), V can be deduced by measuring the total bottle volume, tipping the liquid out and adding a known volume back again - the volume V is then the difference between these values. L is some what tricky to measure as it depends how far down the "neck" you go as the neck is a curve. v is the speed of sound - what we are trying to find.

In the case of this 330ml glass Coke Classic bottle, I took A to be 3.14cm2 and L to be 5cm.

The equation is of the form y=mx+c, so if we plot:
(x-axis) against the frequency (y-axis) we should get a straight line whose gradient is , which we can rearrange to get an expression for the speed of sound:

The process is easy - add water to the bottle, measure the resonant frequency - repeat and plot the graph.

Measuring resonant frequency
Using the excellent Physics Toolbox Suite from (Android and iOS versions available) you are able to turn your smartphone into a sensor suite - one of the functions of which is to measure the frequency with the most energy - ie the resonant frequency of any sound it hears...


Using the value of the gradient as 4219 and the above equation gives me v=334m/s - not bad for 1hrs work (including finding and installing the app to measure resontant frequency)

I'll be using Physics Toolbox Suite again and their website gives a number of sensor related experiments that are suitable for use in the classroom.

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