Question

In a sports meet the timing of a $200m$ straight dash is recorded at the finish point by starting an accurate stop watch on hearing the sound of 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

Answer: (B)

In summer

The velocity of sound is directly proportional to the square root of absolute temperature.
The formula for velocity of sound in a gas is
$v=\sqrt{\frac{\gamma p}{\rho }}$
According to standard gas equation
$pV=RT$
or $p=\frac{RT}{V}$
$\therefore v=\sqrt{\frac{\gamma RT}{\rho \times V}}=\sqrt{\frac{\gamma RT}{M}}$
where $\rho \times V=M$, the molecular weight of the gas
$\therefore v\propto \sqrt{T}$
Hence, the sound of the gun fired at the starting point will reach the finishing point quicker in summer than in winter. The lapse of time due to the time taken by the sound in reaching the finish point will be less in summer and, hence the time recorded will be more accurate in summer than in winter.