Question

a) Helium is a monatomic ideal gas ( = 5/3) with a molecular mass of 4.0026 u. Find the speed of sound in helium, at normal human body temperature (37.0 °C).

b) Sulfur hexafluoride consists of one sulfur atom and six fluorine atoms, giving it a molecular mass of 146.06 u; meanwhile its geometry gives it an adiabatic ratio of  ≈ 1.11. Find the speed of sound in SF6, again at body temperature.

c) Consider three tubes of length L, each representing the human trachea. One is filled with helium, one with sulfur hexafluoride, and one with ordinary air. Calculate the ratio of the nth natural frequency of the He- and SF6-filled tubes to their corresponding frequencies in the air-filled tube. Comment on the result.

Answer 1

(a) Assuming helium as an ideal monatomic gas, with = 5 / 3, and molecular mass m = 4.0026 u = 4.0026 x 1.66 x 10^-27 kg = 6.644 x 10^-27 kg, the speed of sound in this gas at a temperature T = 37^o C = ( 37 + 273 ) K = 310 K is : v = ( KT / M ), where, K = 1.38 x 10^-23 J / K is the Boltzmann constant.

So, v = { ( 5 x 1.38 x 10^-23 x 310 ) / ( 3 x 6.644 x 10^-27 ) } m / s = 1036 m / s.

Hence, the speed of sound in helium, at normal human body temperature is 1036 m / s.