Yes, something like that. The Doppler effect among other things such as spectrometery have helped us to understand the universe. But the universe we are seeing now is just a small portion of universe since only about 5% of the universe is visible through electromagnetic emissions (the rest is dark matter and energy). The gravitational waves are produced by high energy events in universe such as supernova, black holes colliding with each other, binary stars orbiting each other and other events which will now be discovered. It is now too early to say what will be all that we will see with this new "telescope" as it was too early to speculate what we would find seeing when Galileo had invented his telescope.
Well, they have done quite marvelous engineering to detect the gravitational waves. This is how they have done it. They put a laser and split the beam of this laser, guiding it down two paths, at the end of the paths, the mirrors reflect the laser beam back and when they meet again, these beams interfere with each other (as any other wave does):
As you can see above, the photodetector, is looking at the return beams. In case, both the paths the beams are travelling on, are the same length, the interference is going to be say constructive:
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But if a small difference in length of the paths occur due to say, a gravitational wave passing by the earth, then the waves go out of sync and a destructive interference occurs, which will be detected by the photodector:
This is of course highly simplified. The difference, they are measuring for is 0.1% the diameter of a proton. And it was an engineering challenge to measure such a small difference, as even a mosquito landing on the equipment produces larger differences, so they had alot of engineering problems, isolating the system from all that is happening around it, mosquitoes, earth tremors, bugs, ants, humans, traffic, you name it.
That is why, the plan is for a gravitational wave detector be built in space, which will be much more accurate and sensitive (the reason it has not been built till now, has been because amrika khodesho loos kardeh bood, va beh oropa gofteh bood poolesho shomaha bedin vali prozheh amrikai bayad basheh, oropaya ghabol nakardan. Amrika ham goft ageh mitonin khodeton dorostesh konid. Oropa migeh bedon amrika in kar emkan pazir nist, va hala montazeran shayad amrika tasmimesho avaz koneh makhsosan alan keh LIGO javab dad.
But they did it finally. Einstein himself believed, detection of gravity waves will remain outside of human's technological capabilities. But here we are.
This how it sounded by the way (converting the signal at the photodetector to sound):
