Raptor, a couple of additional considerations:
First, in order to arm itself, the torpedo must travel several hundred yards before impact. Given the closing speed of the DD and torpedo, the torpedo must be launched at least 700 yards from the target (Dick O'Kane's figure. No reason to think he's wrong, although you can work through the numbers if you'd like. "The proof is left as an exercise for the reader.") So, starting at 1000 yards, that only gives the sub 300 yards to reach firing position.
Second, if the sub remains at periscope depth and the vessels stay on converging courses, the DD will certainly impact the sub's conning tower, probably with loss of hull integrity for the sub. (For the DD, too!) So, after firing at range GTE 700 yards, the sub must either go deeper or shear off to one side. And going deeper is not a great option, since the DD will continue forward (and down) even if its bow is blown off. IIRC, Wahoo turned off.
O'Kane's account of Wahoo's shot (he was XO) is pretty gripping. Although they were already at PD, the DD had sighted their scope and they had to keep it extended to observe the DD right to the firing point. (They fired at 800 yards.) Bottom in Wewak harbor was less than 100 feet, so there was no room to maneuver vertically. AND, they had already fired 5 of the 6 bow tubes, so they couldn't launch a spread. VERY high pucker factor!
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