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Stone dropped into a 45 m well: echo time
A stone is dropped from rest into a well 45 m deep. Sound travels at 340 m/s in air (g = 10). Find the total time from releasing the stone until the splash is heard.
Answer
Total time ≈ 3.1324 s (fall 3 s + sound 0.1324 s)
Step-by-step
- t₁ = √(2h/g) = √(2×45/10) = 3Time for the stone to free-fall to the bottom
- t₂ = h/v_sound = 45/340 = 0.1324Time for the sound to travel back up to the top
- t = t₁ + t₂ = 3.1324 sTotal time = fall time + sound travel time
Why it works
The total time has two independent parts: the stone's free fall to the water, fixed by the depth, and the steady climb of the sound back up the same depth.
Common mistakes
- Forgetting to add the time for the sound to travel back up.
- Using the speed of sound to find how long the stone takes to fall.