e and f. Thanks!

An air bubble has formed inside a pneumatic pipe. A random vibration causes the bubbble to burst, sending an acoustic pulse through the pipe which is described by OP + Koar 0 at and 1 Op at - = 0 Po Ox where p is the fluid pressure perturbation and u the perturbation velocity. po is the ambient density in the fluid and Ko is the bulk modulus of the air. a.) Write the system of equations in matrix form. b.) Find the eigenvalues of the coefficient matrix. c.) Find the eienvector corresponding to each eigenvalue found above. d.) Transform the system of equations into characteristic form. e.) Solve the systems of equations in characteristic form. f.) If the initial conditions to the physical problem are 1, if lux-2 p(x, t = 0) = 10. otherwise u(x, t = 0) =0 Find the soluion to the problem in physical variables for t > 0. g.) Plot a wave diagram, e.g. an r - t diagram that shows the evolution of the pressure pulse in time. Note: the speed of sound, co is defined as co = Ko/po