In this thesis we solve and compare two tri and penta furcated waveguide problems having rigid and soft lining by using mode matching technique. We also study the phenomenon of extraordinary acoustic transmission (EAT) in Helmholtz resonator. It is shown that combination of a single propagating mode and symmetry orthogonal to direction of propagation leads to EAT. This is accomplished by decomposing the problem using symmetry, the Blaschke product and the properties of functions of a single complex variable which have modulus one on the real axis. A detailed numerical study has been presented to analyze reflection and transmission behaviour to probe the acoustic radiated energy. These results can be used in noise reduction devices and theory of acoustics.