InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The fundamental expression for the speed of sound in a gas is not given by which of the following equations?(a) a^2=\(\frac {dp}{d\rho }\)(b) a=\(\sqrt {(\frac {\partial p}{\partial \rho })s}\)(c) a=\(\sqrt {\frac {\gamma p}{\rho }}\)(d) a=\(\sqrt {\gamma ^2RT}\)I had been asked this question in examination.This intriguing question comes from The Basic Normal Shock Equations topic in section Normal Shock Waves of Aerodynamics |
|
Answer» RIGHT option is (d) a=\(\sqrt {\GAMMA ^2RT}\) Easiest explanation: The flow through the sound wave is isentropic, giving a=-ρ\(\frac {da}{d\rho }\). Also, a^2=\(\frac {DP}{d\rho }\) and since the change is isentropic, subscript sis used i.e. a=\(\sqrt {(\frac {\partial p}{\partial \rho })_s}\). Moreover, using the isentropic RELATIONS for pressure and density we get a=\(\sqrt {\frac {\gamma p}{\rho }}\) and by using the EQUATION of state, we get the temperature relation with the speed of sound in medium i.e. a=\(\sqrt {\gamma RT}\). |
|