The speed of sound in dry air at \(20^{\circ} \mathrm{C}\) is about \(343 \mathrm{~m} / \mathrm{s}\).

a. Calculate the average speed of individual air molecules using the Maxwell-Boltzmann velocity distribution.

b. How do the two velocities compare? What is the ratio of molecular to sonic velocity?

c. How do you think you might account for the discrepancy? What might prevent an aggregate of molecules from moving as fast as an individual molecule? (Hint: the ratio of velocities \(v_{\text {sound }} / v_{\text {molecule }}\) is proportional to \(\sqrt{C_{v} / 8 C_{p}}\) ).