Resonant frequencies with a burette

This activity is best conducted with a burette and any good spectrum analysis software. PhyPhox is one good app that works on both iPhone and Android.

Setup

Securely suspend a burette over a sink or other drainage with a stand.

You should be able to comfortably blow across the top of the bottle to produce a tone. Don't worry if you are unable to produce a very clear tone.

For a burette with a diameter of approx. 1cm, an air column of approx. 25-35cm will probably be the easiest length for producing a clear tone.

Taking readings with PhyPhox

Open Phyphox and select "audio spectrum".

Under Settings, select the maximum number of samples (for better resolution).

Go back to Spectrum

Press the "Play" button at the top-right to start collecting data. It will turn into a "pause button" (looks like this:⏸).

The graph will display a frequency spectrum corresponding to the sound being picked up by the mic. When you can see clear peaks, press the "pause button" to stop recording.

By default, PhyPhox displays the data with logarithmic axii. You can change this under "More tools".

Since resonance peaks are expected to be at integer multiples of the fundamental frequency, you should always un-select "Logarithmic x axis".
For the y axis, it doesn't matter, since we are just identifying resonant frequencies. A logarithmic y axis can help reduce the difference between peak amplitudes.

While you're still in "Pan and zoom" mode, zoom in to see the first few peaks.

Peaks at regular intervals are most likely resonant frequencies.
You can expect to see a broad "peak" at extremely low frequencies. This is likely to be background noise and you can ignore it.

Under the "pick data" mode, you can click on any point on the graph to display the frequency and amplitude.

Suggested investigations

You can investigate how these frequencies depend on the length of the air column in the burette.

By adjusting the amount of water in the burette, you can change the length of the air column and thus the resonant frequencies.

By taking data for several harmonics at different lengths, you can obtain a graph that looks like this:

Some points to consider:

What sources of uncertainty are present in this experiment?
- Consider experimental uncertainty v.s. instrument error: PhyPhox can take measurements to 6 s.f.; is this a realistic representation of the uncertainty?
How do you know the full length of the air column?
- Is there any need to adjust for boundary conditions?
How are the frequencies of each harmonic related to each other? Do they form consistent integer multiples?
- What is the standard deviation here?
What kind of relationship are you expecting to see?

Further analysis

With an appropriate transformation, you can obtain a linear graph:

Why do all extrapolated trendlines intersect at zero?
Can you determine the speed of sound in air from this data?

Produced by Nicholas Wong
Last updated Nov 2022

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