Question

In a sports meet the timing of a 200 m straight dash is recorded at the finish point by starting an accurate stopwatch on hearing the sound of the starting gun fired at the starting point. The time recorded will be more accurate
A In winter
B In summer
C In all seasons
D None of these

Answer 1

Hint: This question is based on the theory of gases. In this question we use the concept of velocity of sound of a particle. We see the effect of environment temperature of the speed of sound of a particle. We can use the relation of velocity of sound and ideal gas equation to conclude the answer of this question.

Complete step by step answer:
We know that to study about the gas particle we follow the kinetic theory of gases. The kinetic theory of gases used to study the properties and its behavior.
The expression of velocity of sound is given as,
\[v = \sqrt {\dfrac{{\gamma p}}{\rho }} ........\left( {\rm{i}} \right)\]
Here, $\rho $ is the density of a gas, $p$ is the pressure of the gas and $\gamma $ is the adiabatic index.

We know that there is a standard equation for gas that is known as ideal gas equation. The idea gas equation is given as,
$\begin{array}{l}
pV = nRT\\
\Rightarrow p = \dfrac{{RT}}{V}
\end{array}$
Here, $R$ is the gas constant, $T$ is the temperature of the gas and $V$ is the volume of the gas
Substitute the values in equation (i) we get,
\[v = \sqrt {\dfrac{{\gamma RT}}{{\rho \times V}}} \]
Therefore, we see that the velocity of sound is proportional to the temperature.
\[v\propto \sqrt T \]
From the above relation, we can conclude that the speed of the sound is depends on the square root of temperature.
So, if the gun is fired at the starting point will reach the finishing point quicker in summer. As the temperature in the summer is more, so the velocity of sound also becomes more. The time taken by the sound of a gun is less. Therefore, the recorded in the summer season is more accurate than all other seasons.

So, the correct answer is “Option B”.

Note:
In this question, students must have the knowledge about the kinetic theory of gases. We use the expression of the ideal gas equation for $n = 1$ and then put it into the expression of speed of sound.