Most films of nuclear explosions got dubbed. If they do contain an actual audio recording of the test blast itself (something I'm often suspicious of -- I suspect many were filmed silently and have a stock blast sound effect), it's almost always shifted in time so that the explosion and the sound of the blast wave are simultaneous.
This is, of course, quite false: the speed of light is much faster than the speed of sound, and the cameras are kept a very healthy distance from the test itself, so in reality the blast wave comes half a minute or so after the explosion. Basic physics that even a non-technical guy like me can understand.
Me included. So it is that the U.S. National Archives has digitized footage of an atomic blast which took place at Yucca Flat, Nev., on March 17, 1953.
Listen to an atomic bomb explosion (WMV file download. May load slowly.)
Listen closely in the aftermath of the sharp bang that accompanied the blast and you can hear the excited reactions of the soldiers -- and civilians invited to attend -- as they watched the blast from 11 kilometers away. This was part of a bigger program underway to calm public fears about about weapons testing. In this case, troops soon moved into the blast area on maneuvers.
Halfway through the video, you can watch General John R. Hodge offer this post-mortem:
This test, I think, went very well. I was quite interested in how the troops reacted. I didn't find any soldier there who was afraid. They were all - the ones who hadn't seen the bomb before were a little apprehensive. but there was no sigh of relief when the thing went off and no great exuberance which comes from being scared. In other words, as far as the soldier reaction to the thing, I'd say they took it in their stride as American soldiers take all things of danger or things that they've been told about and oriented on. The troops moved out just as soon as the safety officers pronounced it safe -- went out in good formation. The last I saw of them, they were pretty well up toward Ground Zero. The reaction of the troops in the trenches -- they did exactly what they were told to do. They showed good discipline, which was good sense in this case. Any man who stuck his head up there was trouble in store for him...they moved out very promptly and in good formation. It'll be beneficial to them and also to their buddies when they go back to their units so they can tell them about this thing...we need the solider to understand this weapon so we can use it intelligently.