Question

The sound produced by a thunderstorm is heard $10\;s$ after the lightning is seen. The approximate distance of the thunder cloud:
Given speed of sound$= 340\;m{s^{ - 1}}$
(A) $3.4\;Km$
(B) $340\;m$
(C) $3.4\;m$
(D) None of these

Answer 1

We know during a thunderstorm we first see the lightning and then we hear the sound of the thunderstorm. Here we hear the sound of the thunderstorm $10\;s$ after the lightning is seen. We are given the time and the velocity of the thunderstorm. We have to calculate the approximate distance travelled by the thunderstorm.

Complete step by step solution:
Though the thunder and lightning are produced at the same time, we see the lightning first and then we hear the thunder. This is because light travels faster than sound through air.
We know that the speed of light $c = 3 \times {10^8}m/s$
The speed of sound through air is given as, $v = 340m{s^{ - 1}}$
Therefore, the time $10\;s$ is taken by the sound to travel the distance between the origin of the thunderstorm and the observer.
We can calculate the distance travelled by the sound in the following steps,
Let the distance travelled by the sound be $s = vt$
The velocity of sound$v = 340m{s^{ - 1}}$
The time taken by the sound to travel the distance $t = 10s$
Substituting these values in the above equation, we get
$s = 340m/s \times 10s = 3400m = 3.4Km$

Therefore, the answer is: Option (A): $3.4\;Km$

Additional Information:
The sound waves will be propagating through gases only if the gas molecules collide with each other. These collisions will give rise to condensations and rarefactions. . Since the molecules in the liquid are more tightly packed than that of gases, the sound wave will travel at a much faster speed than through gases. The maximum speed of sound is attained when it travels through a solid.

Note:
Sound is propagated as transverse waves. Sound requires a medium to travel. The velocity of sound in a solid medium will be greater than that of the velocity of sound in the air. Sound travels faster in solids than through air. Another factor that affects the speed of sound through air is the temperature.