Question

A stone is dropped into a well 44.1 m deep. The sound of the splash is heard 3.13 seconds after the stone is dropped. Find the velocity of sound in air. (g = 9.8 m/s²).

Answer 1

The speed of sound = 339.23m/s

Answer 2

The velocity of sound in air is 339.23 m/s.

Explanation:

The initial speed of the stone is 0 because it was at rest initially. A stone is dropped into a well 44.1 m deep. It will move under the action of gravity.

Let the t the time taken by the stone to reach the bottom. It can find out using second equation of motion.

$s=ut+\dfrac{1}{2}gt^2\\\\s=\dfrac{1}{2}gt^2\\\\t=\sqrt{\dfrac{2s}{g}} \\\\t=\sqrt{\dfrac{2\times 44.1}{9.8}} \\\\t=3\ s$

So, the time taken by the stone to listen the splash of sound will be, 3.13 - 3 s = 0.13 seconds

Now finding the speed pf sound suing total distance divided by total time taken.  

$v=\dfrac{d}{t}\\\\v=\dfrac{44.1\ m}{0.13\ s}\\\\v=339.23\ m/s$

So, the velocity of sound in air is 339.23 m/s.

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