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An explosion creates a shock wave. Find the initial velocity of the wave front when the air pressure is 200 times the atmospheric pressure, assuming that the front of the shock wave may be regarded as a discontinuity in the density. Take into account that at such pressures gamma = 1.8.

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Solution :The velocity of the shock wave is `u sqrt((RHO(p - p_0))/(rho_0(rho - rho_0)))` Here `p_0= 1.01 XX 10^5 Pa, rho_0 = 1.29 kg//mg^3, p=200p_0`. The density at the front of the shock wave may be found from the Hugoniot equation. DENOTING
`a = sqrt((gamma_a P_0)/(rho_0)) , y = p/(p_0) = 200 , alpha = (gamma_0 + 1)/(gamma_0 - 1) = 3.5`
We obtain after some TRANSFORMATIONS:
`u = sqrt((alpha y + 1)/(alpha -1) cdot (a^2)/(gamma_0)) = a sqrt(280/(1.4)) = a sqrt(200)`.


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