Is the speed of gravitational waves non- dispersive?

[shadishacker]

Dear all,
In a recent talk, I have heard that speed of gravitational waves is non-dispersive.
How is it proved "observationally" in LIGO detections that all the frequencies travel with the same speed, so one can say the speed is non-dispersive?

 

[.Scott]

If you received a gravitational signal that followed a sine wave slowly increasing in amplitude and then slowly decaying, then as far as frequency dispersion is concerned, there would little you could conclude from it. That is because such a wave would have little more than a single frequency component - so there would be nothing to disperse.

On the other hand, if you are watching two black holes spiraling towards each other, frequency dispersion would distort the signal. For example, the higher frequency components would arrive first followed by lower and lower frequency components. Since what they "hear" of these gravitational waves is what they would expect from the phenomenon that created them, the observations show no frequency distortion. Since the source of these wave is many light years away, and not distortion is seen ever across time periods of several milliseconds, an upper limit can be placed on the amount of frequency dispersion.