When Will You Hear a Stone Dropped in a 240m Deep Mine Shaft?

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To determine when a stone dropped in a 240m deep mine shaft will be heard hitting the bottom, the speed of sound at 23.5°C is calculated to be 345.1 m/s. The time for the stone to fall is calculated using the formula D = (1/2)gt², resulting in approximately 6.93 seconds. The time for the sound to travel back up the shaft is calculated using T = D/V, yielding about 0.695 seconds. Adding both times together gives a total of approximately 7.623 seconds. This combined time is deemed reasonable for the scenario presented.
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Homework Statement


one last problem..
IF you dropped a stone into a mine shaft that is 240 m deep. HOw soon after you drop the stone do you hear it hit the bottom of the shaft? Assume that temperature for this situation is 23.5 celcius



Homework Equations



So.. in order to get the wave speed i plug in
V= 331 m/s +(.6(23.5 C))
V= 345.1 m/s

I know that T is equal to the inverse of the frequency.. however i don't know how to get the frequency. Does anyone have a clue?


The Attempt at a Solution

 
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You don't need the frequency for this. You know the speed of sound, and the distance it travels. From that, you can work out the time it took for the sound to get back up the shaft.

You must also consider the time it took the stone to drop to the bottom of the shaft. That is important in your answer.
 
so i have D= (1/2)gt^2... i solved for t and i got 6.93 second it took for the stone to get up. Then I used V = D/T .. so T = D/V.. hence.. afterward i got .695.. so i add the two answers i got together ...and got 7.623s. Does this answer sound resonable?
 
It looks OK to me.
 
well.. it looks reasonable to me too? thx! ^_^
 

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