Many times I see confusion regarding chest voice, as if it is a specific timbre or tone quality. This is largely due to either no standardization of nomenclature or to misunderstanding of the terminology.
Chest voice got its name because vibrations from the vocal folds at lower frequencies have sound waves at a size to where they cause sympathetic vibrations in the thorax, or chest.
Head voice got its name because vibrations from the vocal folds at higher frequencies have sound waves at a size to where they cause sympathetic vibrations in the head.
Technically, chest voice is not a sound, but instead is a range in the voice and is usually where mots people “live” in their speaking voices. More technically, above chest voice is low middle voice. Above that is high middle voice, then head voice then the whistle tone register, also called flageolet or superhead voice.
The direction in which the sound waves travel is something which may be interesting. In chest voice range, the sound travels mostly straight out through the mouth. As the frequency of vibration raises, so do the sound waves in direction, to where on high notes, they travel up and on the highest notes, the sound waves are traveling to the back of the head. These things are measurable and also are not something controllable to a large extent. It is possible to force the sound forward at the top end of chest voice or the low middle voice but it may not sound musical. It might sound like yelling or screaming.
There is a term called full voice. Full voice can be achieved when the vocal folds are vibrating in close enough proximity to where an excess of air does not escape, as it would with a breathy sound. When a singer can sing in full voice in all ranges, it sounds as if there is one “voice”, not 3 or 4. It is possible for it all to blend and not change tone quality. Additionally, this can be done at all dynamic levels from very soft to very loud.
When properly trained, a tenor should be able to sing a C5 in full voice. It will sound clear and loud, as if it were in the chest voice register. A properly trained tenor will also be able to sing any tone with a lighter tone production or even with a breathy quality, should he choose to do so.