Question

The sound of a starting pistol can be heard easily from a distance of 800.0 m but the smoke can be seen much sooner than the sound is perceived. Why is the smoke seen before the sound is heard? What is the time delay for the sound of the pistol if the air temperature is 15 °C?

Answer 1

Let:

$\begin{gathered} v_s=Speed_{\text{ }}of_{\text{ }}sound=343.3m/s_{\text{ }}at_{\text{ }}20^{\circ}C_{\text{ }}and_{\text{ }}1atm \\ c=Speed_{\text{ }}of_{\text{ }}light=3\times10^8m/s \end{gathered}$

The speed of the sound decrases if the temperature is below 20. The change is 0.6m/s per ⁰C, so:

$\Delta v_s=343.4-5(0.6)=340.4$

We can write the speed in terms of the distance and the time as follows:

$v=\frac{d}{t}$

So, for the light:

$\begin{gathered} t=\frac{d}{c}=\frac{800}{3\times10^8}=2.6667\times10^{-6}s \\ \end{gathered}$

For the sound:

$t=\frac{d}{\Delta v_s}=\frac{800}{340.4}=2.35s$

Since:

$2.6667\times10^{-6}s<2.35s$

That's the reason why the smoke is seen before the sound is heard. The time delay for the sound of the pistol is 2.35 seconds