On the Shock Wave in the Elastic Medium

As the result of the four conservation laws i. e. those of the conservation of mass momentum, energy and the area of the section of the tube of flow, we have obtained following conclusions for the shock wave induced in the elastic medium. 1 . When the wedge moved with the supersonic speed z , the angle between the shock wave and the direction of undisturbed velocity denoted by α is {aligned} α=Sin⁻¹(M⁻¹)+θ {aligned} {aligned} where\ θ=3λ+2μ/λ+2μ {M⁴α²βδ²}{4C₀(M²-1)2/3}\ and\ M=z/a. {aligned} α, β, c 0 , λ and µ, and δ denote the speed of sound, the coefficient of the linear expansion, the specific heat, Lames constants of the elastic medium, and the half vertex angle of the wedge resp.. 2. The plane shock wave is reflected by the plane rigid wall. α and α ′ denoting the angles included between the incident or reflected waves and the wall, we have {aligned} x^{}={{η}x(1+η²x²)-x(1-η²)\{1+η²x²(η²-1)\}1/2}{(1+η²x²)\{1+η²x²(η²-1)\}1/2+{η}x²(1-η²)} , {aligned} {aligned} where\ x={tan}α\ x^{}={tan}{α}^{},\ and\ (1-η²) {aligned} represents the strength of shock.