Building a tuned instrument: a maths EPQ idea
A title to start from
Can the mathematics of vibrating air columns be used to build an in-tune set of pipes?
Why it works as an EPQ
The artefact is an instrument; the model predicts pipe lengths, and a tuner tests them.
Scope and difficulty
Solid. Solid. Tubes cut to length, with an end correction that you estimate.
The maths
Builds on these A Level topics: Exponentials and logarithms · Algebra and functions · Sampling and data.
You would learn:
- Standing waves in pipes
- End corrections
- Equal temperament
One possible plan
- Model frequency against pipe length, including an end correction.
- Cut a test pipe and calibrate the model.
- Build a scale and measure each pipe with a tuner.
- Evaluate the accuracy and improve.
Pitfalls
- Ignoring the end correction.
- Safety when cutting: follow your school's workshop rules.
Where to start reading
- Search for: open and closed pipe resonance end correction
- Music: A Mathematical Offering (Dave Benson)
Making something? Read the artefact guide first: an artefact still needs a research-based written report.
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