Question

Two border check posts are $4.8km$ apart. A gun is fired from one check post. The time difference between seeing the flash of gun and its sound at the second check post is $14sec$. Find the speed of sound in air.

Answer 1

Step 1 Given data

1. Distance between Two border check posts $\left(d\right)$$=4.8km$
2. The time difference between seeing a flash of a gun and its sound at the second check post $\left(t\right)$ $=14sec$

Step 2 Concept used:

1. Since the speed of light is much greater than the speed of sound, the flash is seen almost instantaneously as the gun is fired.
2. Therefore, the time difference between the flash and the sound is equal to the time taken by the sound to travel the distance between the check-posts.

Step 3 Formula used:

Distance travelled = Speed of sound × Time taken.

$\Rightarrow$Speed of sound = Distance travelled / Time taken .

$\Rightarrow v=d/t$

Step 4 Finding speed:

$$\begin{gathered} \Rightarrow v=4.8km/14sec \\ \Rightarrow v=4800m/14sec \\ v=342.86m/sec. \end{gathered}$$

Hence, the speed of sound is $342.86m/sec.$