Question

A stone is dropped in a well of depth 500 m and a sound is heard after 45/4 seconds. Then speed of sound is (if g = 10 m/s2):

Answer 1

The depth of well is 500 m .Let it be denoted as h.

When the stone is dropped ,it will be under free fall.Hence the acceleration of the stone will be equal to acceleration due to gravity i.e g.

The time taken by the stone to reach the bottom part of well is-

                                       $t=\sqrt{\frac{2h}{g}}$

                                               $=\sqrt{\frac{2*500}{10}}\ seconds$

                                               $10\ s$

The sound was heard 45/4 [i.e 11.25 ] seconds later. The stone will fall on the bottom surface and after that the sound is produced.

Hence the time taken by sound to reach the ear will be-

                                          t' = 11.25-10  s

 Here t' is the time taken by sound to reach the ear.

                                             = 1.25 s

Now we are asked to calculate the velocity of sound.

We know that distance = velocity × time

                                ⇒ h= v×t'     [Here v is the velocity of sound]

                                ⇒500 m= v×1.25

                                 ⇒v=400 m/s.       [ans]