Pride and superiority
According to a Huffingtonpost article, many Americans speak loud in foreign countries as a result of feeling proud and sometimes superior. The fact that those citizens are proud of being Americans motivates them to speak loudly. (See Why do people strive for superiority?)
They want to be heard
Because the culture of the US encourages individualism, the typical American develops the need of developing his unique thoughts and ideas. This motivates some Americans to be loud in order to get heard.
Introversion is considered a weakness
In the American culture, introversion and humility are considered to be signs of weakness. As a result, Americans became extroverted by nature.
They occupy larger personal space
According to a Quora thread, the fact that Americans live in large uncrowded areas conditioned them to acquire a larger personal space. The larger personal space can usually lead to a louder voice and a louder behavior.
The rebels theory
According to one theory, Americans are rebels and they might take pride in being unyielding to authority. This could have motivated some Americans to become loud.
The culture is loud
Americans are generally loud but friendly people. The American culture is considered a relatively loud culture and this is one reason why many Americans never notice that they are being loud unless someone points their attention to it. (See Why are Egyptians loud?)
Wanting to get noticed
According to one theory, the pride an American has, because of believing that they belong to a great nation, motivates them to try to get noticed, especially when they travel abroad.
Living in open space
According to one theory, Americans who lived in agricultural-dominated areas needed to be loud in order to be heard by the people around them.