What is the chirp mass and why does it matter most?

The chirp mass 𝓜 = (m₁m₂)^{3/5}/(m₁+m₂)^{1/5} is the combination of the two masses that sets how fast the frequency sweeps up: at leading order df/dt depends on 𝓜 alone. That is why detectors measure it first and most precisely. Separating m₁ and m₂ needs higher post-Newtonian terms and the merger itself, and those estimates carry much larger errors.

How much did the wave change LIGO’s arms?

Strain h is a fractional length change. GW150914 peaked at h ≈ 10⁻²¹ at Earth. With 4 km arms the difference in arm length was ΔL = hL ≈ 4×10⁻¹⁸ m, a few hundredths of a proton diameter. LIGO reaches this with Fabry–Pérot cavities that bounce the light about 300 times, power recycling and squeezed light.

Why "chirp", and is the sound real?

As the bodies spiral in they orbit faster and closer, so the wave’s frequency and amplitude rise together, like a bird’s chirp. Gravitational waves are not sound, but GW150914 swept from 35 to 250 Hz, inside human hearing, so the strain played as audio sounds like a short chirp. The tool synthesizes audio with the frequency and amplitude of h(t), and you can stretch it in time or shift it up in pitch.

How accurate is the waveform?

The inspiral uses the leading post-Newtonian (Newtonian quadrupole) formulas, which are accurate at low frequency and drift near merger. The tool cuts the inspiral at the Schwarzschild ISCO and adds a ringdown sketch whose frequency and damping follow the Berti fits. Real searches use templates calibrated to numerical relativity, such as IMRPhenom and SEOBNR, and include spins, precession and cosmological redshift.

Why do LISA and LIGO see different sources?

Wave frequency scales roughly as one over the total mass. Black holes of tens of solar masses merge at tens to hundreds of hertz, in the band of ground-based detectors. Million-solar-mass pairs merge at millihertz, where seismic and gravity-gradient noise swamp any ground detector, so they need the space interferometer LISA with 2.5-million-km arms. Even heavier supermassive binaries emit at nanohertz and are found with pulsar timing arrays.

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🌀Gravitational Wave Simulator - Black Hole Merger Chirp, Strain, LIGO

This tool models a binary inspiral with the leading post-Newtonian (quadrupole) formulas. From the two masses and the distance it computes the chirp mass, the rising frequency of the chirp, the cycles left, the strain at Earth and the LIGO arm-length change, compared with the size of a proton. An animation shows the pair spiralling faster while a ring of test particles is stretched and squeezed in the + and × polarizations. You can play the waveform as sound and compare the signal with LIGO, Einstein Telescope and LISA on a log–log sensitivity plot.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Gravitational Wave Simulator (Binary Inspiral & Chirp)

1Pick a preset such as GW150914 or GW170817, or enter the masses, distance and inclination
2In "Waveform & frequency", choose how many cycles before merger to show h(t) and f(t)
3Open "Orbit & ring of particles", press Play and switch between + and × polarization
4Press "Play sound" to hear the chirp; on phone speakers try "Two octaves up"
5Use "Detector sensitivity" to compare the signal with each detector and read the SNR

FAQ

What is the chirp mass and why does it matter most?: The chirp mass 𝓜 = (m₁m₂)^{3/5}/(m₁+m₂)^{1/5} is the combination of the two masses that sets how fast the frequency sweeps up: at leading order df/dt depends on 𝓜 alone. That is why detectors measure it first and most precisely. Separating m₁ and m₂ needs higher post-Newtonian terms and the merger itself, and those estimates carry much larger errors.
How much did the wave change LIGO’s arms?: Strain h is a fractional length change. GW150914 peaked at h ≈ 10⁻²¹ at Earth. With 4 km arms the difference in arm length was ΔL = hL ≈ 4×10⁻¹⁸ m, a few hundredths of a proton diameter. LIGO reaches this with Fabry–Pérot cavities that bounce the light about 300 times, power recycling and squeezed light.
Why "chirp", and is the sound real?: As the bodies spiral in they orbit faster and closer, so the wave’s frequency and amplitude rise together, like a bird’s chirp. Gravitational waves are not sound, but GW150914 swept from 35 to 250 Hz, inside human hearing, so the strain played as audio sounds like a short chirp. The tool synthesizes audio with the frequency and amplitude of h(t), and you can stretch it in time or shift it up in pitch.
How accurate is the waveform?: The inspiral uses the leading post-Newtonian (Newtonian quadrupole) formulas, which are accurate at low frequency and drift near merger. The tool cuts the inspiral at the Schwarzschild ISCO and adds a ringdown sketch whose frequency and damping follow the Berti fits. Real searches use templates calibrated to numerical relativity, such as IMRPhenom and SEOBNR, and include spins, precession and cosmological redshift.
Why do LISA and LIGO see different sources?: Wave frequency scales roughly as one over the total mass. Black holes of tens of solar masses merge at tens to hundreds of hertz, in the band of ground-based detectors. Million-solar-mass pairs merge at millihertz, where seismic and gravity-gradient noise swamp any ground detector, so they need the space interferometer LISA with 2.5-million-km arms. Even heavier supermassive binaries emit at nanohertz and are found with pulsar timing arrays.

Features

Chirp mass, ISCO frequency, time to merger and cycle count at once
h₊ and h× waveforms and the frequency sweep, with a ringdown sketch
Orbit animation plus + / × deformation of a ring of test particles
Playable chirp: real time, stretched, pitched up or sped-up tape
LIGO arm change ΔL = hL compared with a proton diameter
Approximate aLIGO, ET, LISA and PTA sensitivity curves with SNR estimates

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