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I was reading today's announcement of the gravitational waves and was wondering about this situation where there are two orbiting black holes.
Did the wave come from the final merging or was it from each orbit as they came together? In other words was the wave frequency in sync with the orbits of the black holes? I think I read that the orbits were about 250 times per second at the end.
The gravitational wave frequency is roughly twice the orbital frequency (which is rapidly changing in a merging black hole system). Thus the orbital frequency at coalescence - roughly where the black holes are at the innermost stable orbit would be around 125 Hz.
Thus GWs are produced with increasing frequency and increasing amplitude up to coalescence. After coalescence there is a brief period of further GW emission as the merged object settles into an axially symmetric Kerr black hole.
The gravitational wave amplitudes are often expressed as a fractional strain $h$ (about $10^{-21}$ in this case).This can be thought of as the fraction by which the ratio of the perpendicular arm lengths in the detector changes as the GW passes through. There appear to be a number of more complicated definitions to cope with averaging $h$ over finite intervals for a source where $h$ is varying rapidly.
In the official LIGO announcement today they demonstrated a very useful graphic which answers your question.
The graphic was based on general relativity calculations that relate to the signal that was detected by LIGO.
From looking at this graphic, yes, the initial frequency of the wave is related directly the orbit of the two black holes around each other, and the waves propagate out in the formation of a double-armed spiral. However, this picture seems to be complicated when they merge - visually, it is more akin to a stone dropped in a pond, sending a burst of circular ripples out. This is the signal which is referred to as a 'chirp' (but you could call it a 'splash' too, if you liked.)
Important note - what I've said above is based on the official graphic. I have not done any calculations myself.
Here is the time-coded link to the relevant point of the video. Its presented in a very accesible way, I'd recommend giving the whole thing a watch :) - https://youtu.be/aEPIwEJmZyE?t=2150
