Question

The isentropic compressibility, in terms of speed of sound in any medium is given by ________

(a) τs=ρa^2

(b) τs=\(\frac {1}{\rho a^2}\)

(c) τs=\(\frac {\rho }{a^2}\)

(d) τs=\(\frac {1}{\rho a}\)

I got this question in class test.

Enquiry is from The Basic Normal Shock Equations topic in portion Normal Shock Waves of Aerodynamics

Answer 1

Correct choice is (b) τs=\(\frac {1}{\rho a^2}\)

To explain: The speed of sound in any medium is given by a^2=\(\frac {dp}{d\rho }\) and the isentropic compressibility is related to the speed of sound as τs=\(\frac {1}{\rho a^2}\). To derive this, v=\(\frac {1}{\rho }\) has been used. The higher is the compressibility, the lower the speed of sound.