Vocal Tract Resonance and Formant Shift Modeling

ISEF Category: Physics and Astronomy

Subcategory: Biological Physics  ·  Difficulty: Advanced  ·  Setup: University Lab  ·  Time: Full Year

The Hook

Your voice changes when your throat swells, and physics can measure that change. The vocal tract acts like a flexible tube that boosts some sound frequencies and weakens others. If you model that tube well, you can predict how edema shifts formants, the resonance peaks that shape speech. That gives you a real link between biology, sound, and math.

What Is It?

The human vocal tract works like a resonance tube, or a horn. When you speak, air from your lungs vibrates the vocal folds, then the shape of your throat, mouth, and lips filters that sound. Some frequencies get amplified. Others get damped. Those boosted frequencies are called formants. They help make vowels sound different from one another.

A Webster-horn model treats the vocal tract like a tube whose width changes along its length. The Webster equation is a differential equation that describes how sound pressure travels through that changing shape. If you build the model from MRI-based geometry, you can estimate where the resonance peaks should land for different vowel shapes. If you then change the tube shape to mimic swelling, such as edema, the resonances should shift. That gives you a physics-based way to predict how voice quality changes when tissues are inflamed.

In plain terms, you are turning a body part into a sound model. Think of it like modeling a flute with dents and bends, then asking how the note changes when one section gets narrower. The math gives you a prediction, and phone recordings give you a real-world check.

Why This Is a Good Topic

This is a strong science fair topic because it mixes clear physics, measurable outputs, and real biology. You can test how geometry changes resonance, compare prediction to recording data, and study a problem tied to speech, illness, and voice disorders. You also get to work with real datasets and build a model, which makes the project more original than a simple experiment with a home-made tube.

Research Questions

• How does adding simulated edema to the vocal tract geometry shift the first three formant frequencies?
• What is the effect of different vowel shapes on the match between Webster-horn predictions and phone-recorded formants?
• Does a subject's before-and-after gargle recording show a measurable change in formant spacing?
• To what extent do MRI-derived vocal tract geometries improve formant predictions compared with generic tube shapes?
• Which segment of the vocal tract geometry has the largest effect on predicted resonance shifts when its cross-sectional area changes?
• How does the amount of smoothing or mesh resolution in the geometry model affect the predicted formants?

Basic Materials

• Smartphone with voice recording app and manual exposure controls if possible.
• Quiet room with consistent background noise.
• Computer with Python or MATLAB access.
• Free vocal tract or MRI geometry datasets from a university or NIH source.
• Headphones for checking recording quality.
• Spreadsheet software for organizing formant measurements.
• Basic microphone stand or phone tripod to keep distance fixed.

Advanced Materials

• MRI-derived vocal tract geometry files from open datasets.
• Computer with Python, MATLAB, or COMSOL access.
• Numerical solvers for ordinary differential equations.
• ImageJ or 3D Slicer for geometry cleanup and measurement.
• Audio analysis software for formant extraction.
• High-quality external microphone.
• Optional acoustic calibration source for comparing recording setups.

Software & Tools

• Python: Solves the Webster-horn equation, runs parameter sweeps, and compares predicted formants across geometries.
• Praat: Measures formant frequencies from your recordings and helps you compare speech before and after swelling.
• ImageJ: Measures cross-sectional areas from image slices or exported geometry plots.
• 3D Slicer: Views and edits MRI-derived anatomy files before you turn them into a tract model.
• Jupyter Notebook: Keeps your code, plots, and analysis in one place.

Experiment Steps

1. Define the exact vowel sounds, geometry source, and swelling model you will compare.
2. Convert the vocal tract geometry into a one-dimensional area function that the Webster equation can use.
3. Build a baseline resonance model and check whether it reproduces known formant patterns for normal speech.
4. Add a swelling profile to the geometry and predict how the resonance peaks move.
5. Plan a recording protocol that keeps speaking style, phone position, and room conditions as steady as possible.
6. Compare predicted formants with measured formants, then test where the model agrees and where it breaks down.

Common Pitfalls

• Using a geometry file that is too coarse, which blurs narrow constrictions that strongly affect resonance.
• Comparing predictions to casual speech recordings, which mixes vowel shape changes with voice pitch and loudness changes.
• Ignoring microphone position, which changes the spectral balance and weakens formant measurements.
• Modeling edema as a uniform swelling everywhere, which can hide the effect of a localized airway narrowing.
• Treating one person's recording as universal, which makes the model look better or worse than it really is.

What Makes This Competitive

A competitive version of this project would go beyond a simple before-and-after comparison. You would test multiple vocal tract shapes, compare different swelling patterns, and quantify how well the model predicts each vowel. Strong analysis would include error bars, sensitivity testing, and a clear reason for every modeling choice. If you also compare generic tube models against MRI-derived models, you can show why the anatomy-based version matters.

Project Variations

• Model vowel formants for several speakers and compare how anatomy alone changes the resonance peaks.
• Test how localized swelling in different regions of the vocal tract shifts the first formant more than the second or third.
• Compare Webster-horn predictions with a simpler uniform-tube model to see when geometry details matter most.

Learn More

• MIT OpenCourseWare: Search for acoustics or speech signal processing lecture notes and problem sets that cover resonance and wave behavior.
• NIH PubMed: Search review articles on vocal tract acoustics, formants, and speech production.
• NCBI PMC: Find full-text papers on speech acoustics and anatomy-based vocal tract modeling.
• NASA ADS: Search for papers on Webster horn equations and wave propagation in variable-area tubes.
• Praat manual: Read the built-in documentation for measuring formants and inspecting voice spectra.