In view of applications in the design of mufflers the transmission and reflection of sound is investigated for cylindrical ducts with area changes and with or without spherical obstacles inside. Using the transmission and reflection matrices of simple acoustical components the scattering-matrix technique is employed to construct solutions for more complex systems in a building-block fashion. The solutions for the simple element of a bifurcation, i.e. a semi-infinite open cylinder in an infinite cylinder, is outlined in the present paper. The pertinent formulae of all other simple muffler elements used have been published previously and are only summarized. The building-block method is illustrated by computing the transmission and reflection coefficients for several muffler configurations. In particular the case of a sound-hard or lossy spherical obstacle inside an expansion chamber with or without extended inlets is treated and constitutes the main new result of this paper. Nonlinear and mean-flow effects are neglected.