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 deswrihed by and . + ' = [l where p is the fluid pressure. perturbation and u the perturbation velocity. p" is the ambient delu-iitjtr in the uid and If\" is the bulk modulus of the air. 6.) Solve the systems of equations in characteristic form. f.) If the initial conditions to the physical problem are 1, if 1 E .r.' 5 2 [1, otherwise p(.-r,t = ) = { \"(ext = 0] = U