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180 m well: time until the echo is heard
A stone is dropped from rest into a well 180 m deep. Sound travels at 340 m/s in the air (g = 10 m/s²). Find the total time from letting the stone go until the splash is heard.
Answer
Total time ≈ 6.5294 s (fall 6 s + sound 0.5294 s)
Step-by-step
- t₁ = √(2h/g) = √(2×180/10) = 6Time for the stone to free-fall to the bottom
- t₂ = h/v_sound = 180/340 = 0.5294Time for the sound to travel back up to the top
- t = t₁ + t₂ = 6.5294 sTotal time = fall time + sound travel time
Why it works
The falling stage is set by the depth and by g, while the sound stage runs at a steady 340 m/s over the same depth, so the total time is the sum of the two stages.
Common mistakes
- Using the depth divided by the speed of sound as the falling time.
- Answering with only the sound's travel time and dropping the 6 s fall.