Question

A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.30 s later. Find the depth of the well if the air temperature is 12.0°C.

Answer 1

we know, velocity of sound at temperature T,

v = vo + 0.6*T

= 331 + 0.6*12

= 338.2 m/s

let h is the depth of the well.

let t1 is the time taken for the stone to hit the water.

use, h = voy*t1 + 0.5*g*t1^2

h = 0.5*g*t1^2

t1 = sqrt(2*h/g)

time taken for the sound to reach top of the well,

t2 = h/v

= h/338.2

given t1 + t2 = 2.30 s

sqrt(2*h/g) + h/338.2 = 2.3

sqrt(2*h/9.8) + h/338.2 = 2.3

on solving the above equation we get

h = 24.3 m <<<<<<<<<<-------------------Answer