Mine sounds exactly like that stereotypical "Bawk Bawk BAGAAAAWWWK!!" that you might hear in a cartoon. It's loud enough that I could hear it in my house with its 18 inch thick stone walls. The coop is at least 50 feet from the house. At first I thought I was hearing a flock of geese flying by. Standing right in front of her when she does it is pretty loud but not ear-drum ripping. But then, loud noises don't usually bother me. =)
My Buff Orpington sings the egg song AFTER she layed her egg....to proudly announce the news, I guess! She will also sing the egg song if she's out in the tractor and needs brought in to the coop and nest box. What is amazing is that she's only been laying a little over a week. I'm glad she can coummunicate herself so well---and loudly. Another interesting thing is when our Rhode Island Red (not yet laying) watches over the BO in the nesting box and sings the egg-song with her after it's laid.
They stop squaking when we get the egg or acknowledge her accomplishment. Usually they get to go back out to the tractor, where they like to be best.
It can be fairly loud, but it's fun to hear. I wish at least one of my girls would sing it for me. I only have one frequent layer right now (my BR) and the only noises she makes are soft little, "aaaawk awwk, awwwwww" noises while she's fussing around with the nest before laying. It makes me smile when I can hear a hen belting out a song after they've deposited an egg!