Why do a flute and a violin sound different on the same note?

AA SLAA HLAI SLAI HL Solid Also in: Modelling

Research question

Can the waveform of a note played on [two instruments] be modelled as a sum of sine waves at integer multiples of the fundamental, and how do the relative amplitudes of the harmonics differ?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Timbre — the colour of a sound — comes from the mix of harmonics. Recording instruments with your phone and modelling their waveforms with sums of sinusoids links trigonometry to something you can hear.

The mathematics you'll need

Sinusoidal functions and superposition
Period and frequency
Fitting amplitudes (reading a spectrum; explain Fourier ideas simply)
Comparing models with residuals

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Record notes with phyphox's audio oscilloscope and spectrum tools; export data.

phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.
Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain sound as pressure waves.
Record the same note on two instruments.
Read harmonic amplitudes from the spectrum.
Rebuild each waveform from sinusoids and compare.
Reflect on phase, room acoustics and microphone response.

Pitfalls that cost marks

Presenting spectra without explanation.
Ignoring phase in reconstruction.
Too many harmonics to discuss meaningfully.

Showing personal engagement

Record your own instrument.
Synthesise a sound from your model and compare by ear.
Test how harmonics change with loudness.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Compare odd-harmonic-dominated instruments (clarinet) with others and explain the physics.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).