500 m shaft: time until the echo is heard

A stone is dropped from rest into a mine shaft 500 m deep. Sound travels at 340 m/s in the air (g = 10 m/s²). Find the total time from releasing the stone until the splash is heard.

Step-by-step

1. t₁ = √(2h/g) = √(2×500/10) = 10
   Time for the stone to free-fall to the bottom
2. t₂ = h/v_sound = 500/340 = 1.4706
   Time for the sound to travel back up to the top
3. t = t₁ + t₂ = 11.4706 s
   Total time = fall time + sound travel time

Why it works

The stone falls freely down the shaft and the sound of the splash travels back up at a constant 340 m/s, so the answer is the falling time plus the sound time over the same 500 m.

Common mistakes

• Using the free-fall formula for the whole interval.
• Treating the sound as instantaneous and answering with only the fall time.

Related

echo-well vertical-throw free-fall-echo-well-45m