Bridge Height from Sound Delay · PhysicsBowl 2021 #30
Physics · mechanics
Problem
You drop a rock off a bridge into the river below and hear the splash 2.5 s later. How far above the river is the bridge? A) 25 m B) 27 m C) 29 m D) 31 m E) 33 mIntuitive explanation
The key insight is that your 2.5 s includes two separate journeys: the rock falling down, and the sound traveling back up. You need to split the total time between these two processes using their different speeds—gravity for the rock, and the speed of sound for the acoustic wave. Set up equations for each leg, use the constraint that the times sum to 2.5 s, and solve for the height.
Intuitive explanation
The key insight is that your 2.5 s includes two separate journeys: the rock falling down, and the sound traveling back up. You need to split the total time between these two processes using their different speeds—gravity for the rock, and the speed of sound for the acoustic wave. Set up equations for each leg, use the constraint that the times sum to 2.5 s, and solve for the height.