Question

A man fires a gun and hears an echo 2.0 seconds afterwards. How far is the reflecting surface of air temperature is 25 °C.

Answer 1

Let's first calculate the speed of sound at 25°C:

$$v=\sqrt{\dfrac{\gamma RT}{M}},$$ $$v=\sqrt{\dfrac{1.4\cdot8.314\ \dfrac{J}{K\cdot mol}\cdot298.15\ K}{0.02896\ \dfrac{kg}{mol}}}=346\ \dfrac{m}{s}.$$

Finally, we can find how far is the reflecting surface:

$$2d=vt,$$ $$d=\dfrac{vt}{2}=\dfrac{346\ \dfrac{m}{s}\cdot2\ s}{2}=346\ m.$$