An azimuthally symmetric wave (0,t) on a sphere is governed by the wave equation 8²u at² c²a R² sin 800 where k is a constant. sin 8 მო. where t is the time, is the spherical polar angle, c = constant is the speed of the wave and R = constant is the radius of the sphere. (a) Using the separable solution u(e,t) = F(8)G(t), show that F(0) and G(t) obey the following pair of ordinary differential equations: 1 d (sin 6df)+kF = 0, sin e de d²G c²k dt² + R2G=0,
An azimuthally symmetric wave (0,t) on a sphere is governed by the wave equation 8²u at² c²a R² sin 800 where k is a constant. sin 8 მო. where t is the time, is the spherical polar angle, c = constant is the speed of the wave and R = constant is the radius of the sphere. (a) Using the separable solution u(e,t) = F(8)G(t), show that F(0) and G(t) obey the following pair of ordinary differential equations: 1 d (sin 6df)+kF = 0, sin e de d²G c²k dt² + R2G=0,
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