---
title: "Stellar Oscillation Modes Interactive Lab | Sandbox Physics"
description: "How can a flickering point of light reveal a star’s interior? Waves cross a star and return at preferred rhythms."
canonical_url: "https://sandboxphysics.com/labs/stellar-oscillation-modes/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/stellar-oscillation-modes/"
last_modified: "2026-11-04"
---

AC26 · Waves inside a star

# Stellar Oscillation Modes

**How can a flickering point of light reveal a star’s interior?** Waves cross a star and return at preferred rhythms. Their frequency spacing reveals the sound travel time; waves that also feel buoyancy can probe the core. Interpreting those rhythms requires a model of the star and of the observations.

Drag an internal boundary and change its sound speed. Watch radial waves combine, then read their rhythms from the saved noisy signal.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The controllable model is a constant-density spherical radial acoustic cavity with a pressure-release boundary. It includes no buoyancy, self-gravity or nonadiabatic stellar photometry. Its nonzero boundary-displacement proxy is driven by independent stationary damped modes with white acceleration and exact joint finite-exposure noise. The spectrum uses the saved noisy, gapped record; model frequencies are a separate reference. Spectral peaks and spacing alternatives are diagnostics without precision posteriors. Real TESS/Kepler observations and licensed MESA structures are separate fixed data. Solar-scaled, acoustic-integral, published GYRE and measured spacings retain distinct labels. The single HD128279 track gives conditional model properties, not a reproduced age posterior. Apparent displacement, radial scale and playback speed are schematic.

## One saved signal, two ways to see its rhythms

Blue comes from the saved displacement proxy in thousandths of the radius; orange marks separate model modes. Folding uses a measured candidate when available, otherwise a labeled exploratory spacing.

Noisy displacement proxy and actual gaps

Power spectrum of the saved observation

Fold the measured candidate into an échelle diagram

The default noisy observation is already saved and analyzed. Spectral peaks are finite-window diagnostics.

Real TESS / Kepler observations and stellar structures

These fixed observations keep their own time stamps and source versions. Cavity controls change the synthetic experiment above.

Real lightcurve periodogram; published mode markers

Licensed HD128279 model sound speed

TESS sectors38/65 are short observations separated by about two years. Their average periodogram is a discovery view; published frequencies remain external references.

[Open the reproducible real-data tutorial](https://sandboxphysics.com/stories/stellar-seismology/tess-red-giant-model/)

Physics tutorial

## Read the rhythms of a layered sphere

**Background** A star can support many waves at once. Each mode has its own radial shape and natural frequency. Their combined surface motion leaves repeated rhythms in a time series.

**Why it matters** The surface is visible; the interior is hidden. Frequency patterns connect the two.

Start with the essentials

- **Focus question**: Which part of the frequency ladder changes when the core sound speed changes?
- **One-sentence intuition**: Different modes sample a layer differently. A frequency pattern contains more structural information than one pitch.

### Core mathematical model

#### Uniform radial cavity

$$
\nu_n=\frac{nc}{2R}
$$

A regular center and pressure-release outer boundary select a discrete ladder. The boundary pressure is zero, while its displacement can be nonzero.

#### Acoustic travel time

$$
\tau=\int_0^R\frac{dr}{c(r)},\qquad\Delta\nu_{\rm asym}\simeq\frac{1}{2\tau}
$$

This high-order estimate uses the travel time. Low-order frequencies and a real star’s atmosphere can shift the actual spacings.

#### Saved measurement

$$
y_i=\frac{1}{\Delta t}\int_{t_i-\Delta t/2}^{t_i+\Delta t/2}q(t)\,dt+\epsilon_i
$$

Exposure averages the stochastic boundary-displacement proxy; measurement noise is added afterward. Missing samples keep their actual positions.

### Common difficulties

#### A spectral maximum is noisy

**Typical misconception** The tallest frequency bin is the exact natural frequency.

**Better mental model** Random excitation, finite duration and gaps move the local maximum. The orange reference and blue saved-data peaks answer different questions.

#### A spacing does not give a unique age

**Typical misconception** One measured spacing determines a unique stellar age.

**Better mental model** Mass, composition and outer layers also change frequencies. The real-model exercise compares one fixed track conditionally.

### Run the experiment

1. 01

   #### Start with an even ladder

   Choose An even frequency ladder, then inspect the separate spectrum.

   **What to observe:** Uniform sound speed gives evenly spaced model modes, with noisy observed peaks nearby.

2. 02

   #### Move the internal boundary

   Drag the highlighted internal ring, then drag the core sound-speed handle vertically.

   **What to observe:** The node pattern and frequency ladder respond continuously to the same structure.

3. 03

   #### Shorten the mode lifetime

   Choose Short-lived rhythms blur, keeping the saved record in view.

   **What to observe:** Rapidly changing mode phases broaden peaks. A finer frequency grid would not restore a longer coherent observation.

Physical conclusion

Frequency patterns probe wave travel through the interior, while the saved observation determines how precisely those patterns can be read.

## Related experiments and articles

Read a star through its vibrations · Reading path

### Read a star through its vibrations

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why stars ring**](https://sandboxphysics.com/stories/stellar-seismology/why-stars-ring/)
2. [Article **Standing waves inside a sphere**](https://sandboxphysics.com/stories/stellar-seismology/radial-standing-waves/)
3. [Article **Sound crossing a layered star**](https://sandboxphysics.com/stories/stellar-seismology/layered-acoustic-interiors/)
4. [Article **From a light curve to stellar modes**](https://sandboxphysics.com/stories/stellar-seismology/lightcurves-modes-and-windows/)
5. [Article **Test a red giant model with TESS data**](https://sandboxphysics.com/stories/stellar-seismology/tess-red-giant-model/)
6. [Article **Read core rotation from mixed modes**](https://sandboxphysics.com/stories/stellar-seismology/mixed-modes-core-rotation/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)