# Gravitational waves

> Listen to two black holes merge: the chirp LIGO heard in 2015, from the masses up. Choose the masses and distance, see the wave, and play it.

Page: https://sciencehub.sh/sciencehub-team/gravitational-waves

- Project: [sciencehub-team/gravitational-waves](https://sciencehub.sh/sciencehub-team/gravitational-waves.md)
- Authors: ScienceHub
- Subjects: astronomy-and-astrophysics, mathematical-physics
- Topics: gravitational-waves, ligo, black-holes, sonification
- 0 stars, 0 forks
- DOI: https://doi.org/10.83371/sh.2610.6h4rx
- Source: https://sciencehub.sh/sciencehub-team/gravitational-waves/source
- Updated 13 Oct 2026

## Notebook

Text the notebook's authors wrote, its cells as Python, and the outputs it produced when it last ran in a browser and was saved.

The script header: the dependencies the notebook declares (PEP 723) and the app it defines.

```python
# /// script
# requires-python = ">=3.12"
# dependencies = ["marimo>=0.25.1", "numpy", "matplotlib"]
# ///

import marimo

__generated_with = "0.25.1"
app = marimo.App(width="medium")
```

### Listen to two black holes merge

On 14 September 2015 the two LIGO detectors recorded a signal that
rose in pitch and loudness for a fifth of a second and stopped: two
black holes, about 36 and 29 times the mass of the Sun, spiralling
into each other 1.3 billion light years away. It was the first direct
detection of gravitational waves.

Long before the merger, an orbiting pair loses energy to gravitational
waves at a rate set by one combination of the masses, the chirp mass
$\mathcal{M} = (m_1 m_2)^{3/5} / (m_1 + m_2)^{1/5}$. To leading order
the wave's frequency $\tau$ seconds before the merger is

$$f(\tau) = \frac{1}{\pi}\left(\frac{5}{256\,\tau}\right)^{3/8}
\left(\frac{G\mathcal{M}}{c^3}\right)^{-5/8}.$$

Choose the masses and the distance, look at the wave, and play it.

```python
import io
import wave

import marimo as mo
import numpy as np
import matplotlib.pyplot as plt
```

```python
m1 = mo.ui.slider(1.4, 80, step=0.1, value=36, label="Mass 1 (Suns)")
m2 = mo.ui.slider(1.4, 80, step=0.1, value=29, label="Mass 2 (Suns)")
distance = mo.ui.slider(40, 3000, step=10, value=410, label="Distance (megaparsecs)")
mo.vstack([m1, m2, distance])
```

```python
G, C = 6.674e-11, 2.998e8
M_SUN, MPC = 1.989e30, 3.086e22

def chirp(m1, m2, distance_mpc, f_low=20.0, rate=4096):
    """Leading-order inspiral from f_low up to the innermost stable orbit.

    Returns time (s, zero at the end), strain h(t) for a face-on source,
    frequency f(t), and the stopping frequency.
    """
    total = (m1 + m2) * M_SUN
    mc = (m1 * m2) ** 0.6 / (m1 + m2) ** 0.2 * M_SUN
    tc = G * mc / C**3
    f_isco = C**3 / (6**1.5 * np.pi * G * total)
    tau_low = 5 / 256 * tc ** (-5 / 3) * (np.pi * f_low) ** (-8 / 3)
    tau_end = 5 / 256 * tc ** (-5 / 3) * (np.pi * f_isco) ** (-8 / 3)
    tau = np.arange(tau_low, tau_end, -1 / rate)
    f = (5 / (256 * tau)) ** 0.375 * tc ** (-0.625) / np.pi
    phase = -2 * (5 * tc) ** (-0.625) * tau**0.625
    amplitude = 4 / (distance_mpc * MPC) * (G * mc / C**2) ** (5 / 3) * (np.pi * f / C) ** (2 / 3)
    return -(tau - tau_end), amplitude * np.cos(phase), f, f_isco
```

```python
t, h, f, f_isco = chirp(m1.value, m2.value, distance.value)
cycles = np.sum(f) / 4096
last = t > -min(0.5, -t.min())

fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(7.2, 5), sharex=True)
ax1.plot(t[last], h[last] * 1e21, color="#0072B2", lw=1)
ax1.set_ylabel("strain h (10⁻²¹)")
ax2.plot(t[last], f[last], color="#D55E00", lw=2)
ax2.set(xlabel="seconds before the end of the inspiral", ylabel="frequency (Hz)")
fig.tight_layout()

mo.vstack(
    [
        fig,
        mo.md(
            f"From 20 Hz, where LIGO starts to hear it, the pair has **{-t.min():.2f} s** and "
            f"**{cycles:,.0f} wave cycles** left. The inspiral ends near **{f_isco:.0f} Hz**, "
            f"where the orbit can no longer stay stable. The peak strain here is "
            f"**{np.abs(h).max():.1e}**: a 4 km detector arm changes length by "
            f"{np.abs(h).max() * 4000:.1e} m, about 1/{1.7e-15 / (np.abs(h).max() * 4000):,.0f} "
            "of the width of a proton."
        ),
    ]
)
```

Output:

```text
From 20 Hz, where LIGO starts to hear it, the pair has 0.81 s and 23 wave cycles left. The inspiral ends near 68 Hz, where the orbit can no longer stay stable. The peak strain here is 1.2e-21: a 4 km detector arm changes length by 4.8e-18 m, about 1/357 of the width of a proton.
```

```python
speed = mo.ui.dropdown({"real time": 1, "4 × faster, two octaves higher": 4}, value="real time", label="Playback")
speed
```

```python
rate = 4096 * speed.value
pcm = (h / np.abs(h).max() * 0.9 * 32767).astype(np.int16)
pcm = np.concatenate([np.zeros(rate // 4, np.int16), pcm, np.zeros(rate // 4, np.int16)])
buffer = io.BytesIO()
with wave.open(buffer, "wb") as out:
    out.setnchannels(1)
    out.setsampwidth(2)
    out.setframerate(rate)
    out.writeframes(pcm.tobytes())
mo.vstack(
    [
        mo.audio(buffer.getvalue()),
        mo.md(
            "The sound is the strain itself, scaled to full volume. Heavy pairs chirp "
            "low, below what laptop speakers play well; try the faster playback or "
            "two neutron stars (1.4 and 1.4 Suns), whose chirp lasts much longer."
        ),
    ]
)
```

Output:

```text
The sound is the strain itself, scaled to full volume. Heavy pairs chirp low, below what laptop speakers play well; try the faster playback or two neutron stars (1.4 and 1.4 Suns), whose chirp lasts much longer.
```

---
**Model and limits.** Leading (quadrupole, Newtonian) order in the
orbital speed, circular orbits, a face-on source, and no detector
response. The waveform stops at the innermost stable circular orbit;
the merger and ringdown that follow need numerical relativity, and the
real GW150914 signal peaked near 150 Hz. Masses here are as measured
at the source, without the redshift correction.
**References.** B. P. Abbott et al. (LIGO and Virgo), *Phys. Rev. Lett.*
116 (2016) 061102; P. C. Peters and J. Mathews, *Phys. Rev.* 131 (1963)
435; M. Maggiore, *Gravitational Waves*, vol. 1 (2008), ch. 4.
Fork it to add the next post-Newtonian term or a detector's noise curve.

## Versions

- [ver_01M4SH2BM7GZKD1N7GWVT91941](https://sciencehub.sh/sciencehub-team/gravitational-waves/history/ver_01M4SH2BM7GZKD1N7GWVT91941), 13 Oct 2026: Edited (current)
- [ver_01M4SGE9E62RE74B2B2SQ9WX15](https://sciencehub.sh/sciencehub-team/gravitational-waves/history/ver_01M4SGE9E62RE74B2B2SQ9WX15), 13 Oct 2026: Created

## Cite

ScienceHub (2026). Gravitational waves \[Computer software\]. ScienceHub. https://doi.org/10.83371/sh.2610.6h4rx

```bibtex
@software{gravitational_waves_2026,
  author = {ScienceHub},
  title = {Gravitational waves},
  year = {2026},
  publisher = {ScienceHub},
  doi = {10.83371/sh.2610.6h4rx}
}
```