physics -using sound to calculate depth

[seethrusoul]

you toss a stone into a well and hear a splash in 2.5 seconds. the speed of sound is 340 meters/second. how deep is the well?

[bird_81]

i think it is speed multiplied by time

[ugly_bob]

thing is though, the sound will travel much faster than the stone. To the point where you'd need to calculate how far the stone would fall in 2.5 seconds, rather than how far the sound has travelled in that time.
You'd need to know the speed you released the stone at for that too. If the stone is stationary when you release it, it'll be approx 31m deep

[jake-the-peg]

This is newtons laws of motion:

S=ut +�at�

S is the distance t the time and u the initial speed

the acceleration due to gravity is usually taken to be 9.8m/s�

so as u=0

S=� 9.8 (2.5)�

Which I'll leave you to key in - Now what about the speed of sound. Look at your answer - roughly how long would the sound take to reach you? - is that significant given that there are other factors that you've ignored like air resistance and the shape of the stone and timing errors? I'd suggest not .

I think the fact that you have been given the speed of sound is a red herring designed to make you think

[jake-the-peg]

Of course if you want to show off and take it into consideration:

there is a time t1 for the stone to fall and a time t 2for the sound to travel back up

you know

t1+t2=2.5 seconds

you also know

S=�a(t1)�

and you know that S=(speed of sound) multiplied by t2

so you have 3 equations and 3 unknowns t1, t2 and S

Solve them simultaneously to get S.

You should find you get an answer very close to the one you got earlier

[knobbynonuts]

ah but the stone might have hit the well wall on its way down causing its velocity speed to slow down so you will have to put that into your calculations

[reman2893]

stone is dropped into a deep well and is heard to hit the water in 3.4 seconds after being dropped. determine the depth of the wall