Timing question

[Moshiner1345]

2nd quarter :12 seconds remaining. 3rd and 4 from the B42 yard line.Team A snaps the ball and goes for a long run (past the first down markers) and is downed on the 2 yard line. The sequence of events are this: player downed, official's whistle is sounded, then mechanical horn goes off from scoreboard indicating the period is over. Bam, Bam, Bam. very sequential.... but very close to one another. As a crew we got together and came to a consensus that the whistle had sounded prior to the mechanical horn sounding. Do you put time on the clock? and if so how much?

According to Rule 3.5.7 The referee shall have the authority to correct obvious errors in timing if discovery is prior to the second live ball following the error, unless the period has officially ended as in 3.3.5

What do you do? and what explanation do you give to coach B