Question

If a person drops a pebble in a well of $100m$ depth, after how much time will he be able to hear the sound, starting from the time he drops the pebble?

(taking $a=10m/s^2$ and speed of sound $=343m/s$)

• A. $\sqrt{20}$+0.3sec
• B. $\sqrt{20}$sec
• C. 0.3 sec
• D. None of these

Answer 1

The correct option is A

$\sqrt{20}$+0.3sec

To calculate the total time after which the sound of the pebble hitting the surface of the well reaches the person, we need to calculate two-time intervals:

i. time taken by the pebble to reach bottom;
ii. time taken by the sound wave to reach the top.

Time taken by pebble to hit the bottom is calculated as follows:

Initial speed of pebble,$u=0$

Displacement of pebble, $s=100m$

Acceleration pf pebble,$a=10m/s^2$

Using 2nd equation of motion we get,
$s=ut+\frac{1}{2}a{t}^2$

$s=\frac{1}{2}\times 10t^2$

$100=5t^2$

$t=\sqrt{20}s$ (for pebble to reach the water)

Now time for sound to reach the top = $\frac{distancecoveredbysound}{speedofsound}=\frac{100}{343}=0.3\text{(approx)}$.

Therefore, total $time=(\sqrt{20}+0.3)s$.