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December 21, 2014

December 21, 2014

Posted by **Elisa** on Monday, August 4, 2008 at 10:55pm.

A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.20 s later. Find the depth of the well if the air temperature is 12.0°C.

- Physics -
**DrBob222**, Monday, August 4, 2008 at 10:59pmHere is a site that allows one to calculate the speed of sound in air at the desired temperature.

- Physics -
**Elisa**, Monday, August 4, 2008 at 11:06pmThat is the correct speed, but I don't know how to find the depth of the well, which is what the question is asking for.

- Physics -
**DrBob222**, Monday, August 4, 2008 at 11:14pmHere is a site that allows one to calculate the speed of sound in air at the desired temperature.http://www.sengpielaudio.com/calculator-speedsound.htm

Isn't distance = rate x time.

So multiply the speed of sound x 2.2 seconds = ??

- Physics -
**Elisa**, Monday, August 4, 2008 at 11:20pmNope that doesn't give the right answer, but thanks lots for your help!

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**DrBob222**, Monday, August 4, 2008 at 11:24pmMake sure you have the right units. Do you know the answer? If speed is in meters/second then the distance will come out in meters.

- Physics -
**Count Iblis**, Tuesday, August 5, 2008 at 11:35amI think you should take into account the time it takes for the stone to hit the water. If the distance is d, then the time needed for the stone to reach the water, t1, follows from:

1/2 g t1^2 = d ------->

t1 = sqrt(2 d/g)

The time needed for the sound to reach you is:

t2 = d/v

where v = 338.82 m/s is the speed of sound.

So, the total time is:

T = t1 + t2 = d/v + sqrt(2 d/g)

It is given that T = 2.20 s, so we get the equation:

d/v + sqrt(2 d/g) = 2.20 s

You can put d = x^2 to convert this to a quadratic equation. I find

d = 157.7 m (but I haven't double checked...)

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