320 m well: time until the echo is heard

A stone is dropped from rest into a well 320 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 sound comes back.

Step-by-step

1. t₁ = √(2h/g) = √(2×320/10) = 8
   Time for the stone to free-fall to the bottom
2. t₂ = h/v_sound = 320/340 = 0.9412
   Time for the sound to travel back up to the top
3. t = t₁ + t₂ = 8.9412 s
   Total time = fall time + sound travel time

Why it works

The stone falls freely so its time follows from h = ½gt², while the sound rises at a constant speed so its time is the depth divided by that speed; the total is the sum of the two.

Common mistakes

• Computing the fall time as 320 ÷ 10 = 32 s.
• Using twice the depth as the distance the sound travels.

Related

echo-well projectile-motion free-fall-echo-well-245m