Find the depth of the well if the air temperature is 10 degrees Celsius?

Question

A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.00 seconds later. Find the depth of the well if the air temperature is 10 degrees Celsius.

Answer 1

speed of sound (m/s) = 331.5 + 0.60 T(°C) = 337.5 m/s @ 10°C

d = (1/2)(9.80665)t1^2 = 337.5t2

t1 + t2 = 2.00

(9.80665)t1^2 + 675t1 - 1350 = 0

t1 = [- 675 ± √(675^2 + 4(9.80665)(1350)]/[2(9.80665)]

t1 ≈ 1.945037 s

t2 ≈ 2 - 1.945037 ≈ 0.05496326 s

d ≈ (337.5 m/s)(0.05496326 s)

d ≈ 18.550 m