Page:Threeshockwaves.pdf/4



where $$c_1$$ and $$c_2$$ denote the velocities of sound in the two regions respectively and the rest of the symbols have their usual meanings. Finally

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In other words, if we measure the velocities in units of the velocity of sound in region $$1$$ then all the relevant physical quantities (including the velocity of sound in region $$2$$) can be expressed parametrically in terms of $$\sigma_\perp^{(1,2)}$$. As we have already stated, we shall measure the intensity of a shock wave by the ratio of the pressures on either side of the shock front, i.e., $$\zeta_{1,2}$$. We may note that if in a fixed frame of reference the shock is moving in the direction $$2\rightarrow 1$$, $$\zeta_{1,2}>1$$ and $$\sigma_\perp^{(1,2)}>1$$; conversely the direction of motion of a shock front can be inferred from whether $$\sigma_\perp^{(1,2)}$$ is greater than or less than unity.