# What are the wave characteristics for the detected gravitational wave?

I'm curious to know what the amplitude and wavelength of the detected gravitational waves are? The paper mentions some characteristics of the detection event, but not what that means for the wave itself.

Additionally, I'm curious what the theoretical limit of this detection technique as it relates to the gravitational wave characteristics. How short does the wavelength need to be? How large the amplitude?

• What units do you propose to use for the amplitude? Wavelength can be derived from frequency and speed (of light). I bellies the Mac frequency was 7 kHz – Floris Feb 14 '16 at 3:27
• I thought gravity waves traveled within 10% of the speed of light, that seems like a huge margin. Could the amplitude be measured in time difference? – brysgo Feb 14 '16 at 3:29
• I think they use "strain" - the relative distortion of space-time. According to this the sensitivity is about $10^{-22}$ although the wave detected was quite a bit bigger than that. But when the frequency was < 7 kHz it is hardly surprising the wave speed has considerable uncertainty on it! – Floris Feb 14 '16 at 3:39
• Wow, that's incredible, thanks for sharing that link. It is no wonder the findings need to be confirmed by multiple stations. – brysgo Feb 14 '16 at 3:43

As reported in the article in PRL, the detected gravitational waves swept up in frequency from around 35 to 250 Hz. Since GWs propagate at the speed of light, the corresponding wavelength ($\lambda = c / f$) is $8.6 \cdot 10^{6}$ to $1.2 \cdot 10^{6}$ meter.

Note that the frequency did not increase any further (since the black holes merged at some point), so the wavelength did not get any shorter than this. There is however no upper limit to the wavelength, since the two black holes were initially orbiting each other at huge distances with periods measured in micro-Hertz. It might have taken a billion years before they lost enough energy due to GW and could finally merge! Most of this was however outside the sensitive detection band of LIGO, so it could only observe the last 0.2 second.

Some day, they hope to measure the earlier part of the inspirals with space-based detectors like the LISA mission, which are sensitive to lower frequencies. In the best case, you could see an inspiral slowly sweeping through the LISA frequencies for a few months, disappear for some time (since there is a gap in sensitivity) and finally see it reappear in the LIGO band to witness the final few seconds and the merger!

The peak amplitude of the gravitational strain was $1.0 \cdot 10^{-21}$ when the frequency was around 150 Hz.

• Welcome to the site! That's some good stuff, we hope you'll stick around ;-). – Emilio Pisanty Feb 14 '16 at 14:01
• @EmilioPisanty thanks! We had to be be quiet about the detection for 5 months, it is good we can finally discuss it in public ... – Bas Swinckels Feb 14 '16 at 14:07
• @BasSwinckels Were you by any chance associated with the LIGO project? – tatan Feb 16 '16 at 8:55
• @tatan I am not working on LIGO myself, but I am part of the wider community. I was lucky to be one of the 1000 authors of the paper ... – Bas Swinckels Feb 16 '16 at 9:05
• @BasSwinckels Can you please specify...which paper you are referring to,please? – tatan Feb 16 '16 at 9:23