For air take the diffusivity of sound ,

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Waves, acoustics and compressible flow

Signal Speeds in Fluids, Ch Steepening and the normal shock wave

Problem

For air take the diffusivity of sound

\delta=3.7\times10^{-5}\ \mathrm{m^2\,s^{-1}}

\beta=1.2

\rho_0c_0=(1.2)(343)\ \mathrm{kg\,m^{-2}\,s^{-1}}

and a mean free path of

68\ \mathrm{nm}

. Use the weak-shock thickness

4\delta/(\beta\Delta u)

with

\Delta u=\Delta p/\rho_0c_0

. ((a)) Estimate the thickness of a weak shock carrying a pressure jump of

5\ \mathrm{kPa}

, in metres and in mean free paths. ((b)) Estimate the pressure jump at which this thickness falls to

10

mean free paths, and say what that implies for describing such a shock with Burgers's equation.

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