How deep is the well?
Drop a stone and start a timer. The splash you hear has made two journeys: the stone fell down, then its sound climbed back up.
Equation in use√(2h/g)stone falling
h/csound returning
Ready at the rim.timer 0.00 s
Time until you hear the splash tlonger wait → deeper well
0.5 s12 s
Air temperaturechanges sound speed c
−10°C35°C
Solved for depth
h=(√(c² + 2gct) − c)²2g
The measured total time t contains both journeys; c is adjusted for the selected air temperature.
Try
The stopwatch includes both the fall and the returning sound. The stone is treated as starting from rest and falling in vacuum under constant g = 9.81 m/s², so fall time is √(2h/g). Sound speed is approximated as c = 331.3 + 0.606T m/s for dry air at temperature T in °C, and return time is h/c. The page solves their sum for h. Air drag would make a real stone fall more slowly, while echoes, reaction time, wind, humidity and an uncertain release instant add measurement error; those effects are omitted. For a deep shaft or a light stone, ignoring drag can overestimate depth. The motion equations follow standard constant-acceleration kinematics; the temperature dependence of sound speed is summarized by Engineering ToolBox.
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