(Out of curiosity: I think "physical binary search" is more properly O(n^{1/3} log(n)), or maybe O(n^{1/2} log(n)). Since physical objects have sizes, and moving things (or moving between things) takes time proportional to distance).
EDIT: My earlier analysis was wrong (it assumed you never move the beeping item after the initial halving), but the conclusion was right for a different reason: Each time you move items, you move half as many as you did last time. You initially move n/2 items, and the geometric series n/2 + n/4 + n/8 + ... + 1 sums to n-1. So O(n) moves are done, and this dominates the log n term for the number of steps.
O(log n) is if you can split the collection in half in an O(1) step, like, *shoving* the whole pile together as a unit
O(n) if you're moving items one at a time. So, splitting the pile in half once is O(n)
O(n^{3/2}) if the project is way out of control and walking distances start to matter