To understand how a rooster makes that magnificent {or annoying depending upon you point of view} sound you need to understand a little about the structure of the chicken's anatomy, and exactly HOW the bird makes the sound.
Firstly, birds have a much higher metabolic rate than people, which means they burn energy at a higher level, and therefore they require more oxygen. Puzzlingly, their lungs are quite small, but they have a complex system of air sacs throughout their body, 9 altogether, and the flapping of wings actually helps move the air through these sacs and hence the body. The next three diagrams show the distribution of the air sacs throughout the chicken's body.
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Hopefully too from these diagrams it can be seen why respiratory illnesses are so crippling for poultry, as all the air sacs potentially become infected, and can become congested with phlegm.
In terms of the roosters' crow, the important structure to note on the top diagram is the trachea. Notice how it branches into two, and each branch, called the bronchi, goes into the lungs. Now, just before it branches, there is an area of slight thickness, called the syrinx. It can be seen in the photograph below just before the bronchi pass behind the heart. On the right of the heart, the reddish bubbly bit you can see under the probe is one of the chicken's lungs.

Now you all will have noticed that as a rooster gets ready to crow he usually seems to take in a couple of deep breathes and flaps around his wings. What he is doing is filling up his air sacs.
When he finally lets rip he is blasting out through the syrinx like those tediously annoying blow out paper party whistles..........that is how he makes his crow

If you watch and listen carefully, the noise is usually only on exhalation, with sometimes a funny little catch at the end. This is also why baby cockerels sound sooooo hilarious when they are learning to crow, as they have not yet learnt to control the vibrations of this cartilaginous structure.
Now all the clucky noises the rooster and the hens make come from the larynx up near the mouth. The crow comes from this structure buried way down deep in his chest.
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