thank you Anja Ruß .

but according to two voice theory, birds in general (even without double trachea) are capable of producing two totally independent carrier waves because of presence of two independently vibrating membranes in syrinx.

http://www.acoustics.hut.fi/research/avesound/pubs/akusem04.pdf

i was trying to understand the physiological function of double trachea and also its phylogenetic significance.

It would be surprising if penguins did not perform their phonation by means of the syrinx, the unpaired vocal organ that is situated at the bifurcation of the trachea. Therefore, the penguin's ability to "speak with two voices" is obviously limited by only one available voice-producing organ (sorry Anja!). Additionally, the term "double trachea" sounds a bit exaggerated, as it refers only to a tracheal septum which divides the tracheal lumen in its caudal part, just a few centimeters before it reaches the syrinx. The cranial and middle part of the trachea, at least three quarters of its length form a normal bird trachea with unpaired lumen. However, the presence of similar structures in other aquatic/diving species suggests a function within the complex of respiratory regulation.

I worked as medical officer on Antarctic base many years ago. Noted double lumen trachea in Gentoo penguin. A likely advantage related to gas exchange and diving. Once a dive has started there is a fixed mass of air in the space between beak and alveolus. A proportion of this space allows blood/gas exchange a proportion does not. As the partial pressure rises nitrogen narcosis and other adverse effects can occur. If however with a decreasing overall volume gas is squeezed from mobile gas exchange areas such as the lung to structurally sound and volume protected structures eg a double lumen trachea there is less exchange. On resurfacing the gas expands from the protected areas to re-inflate the lung and allow exchange to begin at safer partial pressures. There are pictures of whales and dolphins at depth with collapsed thoraces conststant with this theory  

The double lumen is a structurally efficient way of providing the required strength and stability.