William Stromberg and Moscow Symphony Orchestra.
That clip is from Visual Concept Entertainment's documentary Trinity and Beyond, aka The Atomic Bomb Movie. They have also couple other documentaries around same subject.
http://www.vce.com/about.html

Here's some more clips from those documentaries.
Cannikin with resulting "6.8 Richter shaking":
http://youtube.com/watch?v=OCb34tmX4UI
Redwing Cherokee:
http://youtube.com/watch?v=lvzpqecuB-M
Operation Dominic shots:
http://youtube.com/watch?v=joupmq4e2eM
Ivy Mike, first real two stage thermonuclear bomb:
http://youtube.com/watch?v=xEFXfMQ-vzQ
http://youtube.com/watch?v=asAkcbI2nt4
Castle Bravo, "little miscalculation". Non-inert Lithium-7 rised yield to 2.5 times greater than estimated making it largest nuclear device ever detonated by US:
http://youtube.com/watch?v=fd1IFjBNNVo
Sedan excavation test:
http://youtube.com/watch?v=VplPn52Lbm4
Nuclear artillery shell, Upshot-Knothole Grable:
http://youtube.com/watch?v=oBIYLG8XMOc