Answer to Question #178660 in Physics for katniss

Question

While leaving the movie theatre after a great show, your friend comments on how cold it is outside and asks you if you have any idea how cold it actually is. You know that you are standing 70.0 m away from the high exterior walls of the theatre. You clap your hands loudly and hear the echo of your clap 0.55 s later; you were timing this with an extremely accurate stopwatch. Calculate the temperature and impress your curious friend.

Answer 1

Let's first find the speed of sound in the air:

$$v=\dfrac{2d}{t}=\dfrac{2\cdot70\ m}{0.55\ s}=254.5\ \dfrac{m}{s}.$$

We can find the temperature of the air from the formula:

$$v=331.3+0.606T,$$ $$T=\dfrac{v-331.3}{0.606}=\dfrac{254.5\ \dfrac{m}{s}-331.3\ \dfrac{m}{s}}{0.606\ ^{\circ}C^{-1}}=-127^{\circ}C.$$