Final answer:
The Swing dance, particularly the Charleston, was the dance associated with the big band era of the 1930s and 1940s. Jazz bands, like the King and Carter Jazzing Orchestra, played a great role in the vibrant atmosphere of the Jazz Age, where the Charleston flourished in popularity among the younger, modern audiences.
Step-by-step explanation:
The dance that was closely associated with the big band era of the 1930s and 1940s is the Swing dance. This era of music is often referred to as the "Roaring Twenties" or the "Jazz Age." Alongside the energetic and improvisational music played by jazz bands, people took to nightclubs and dance halls to enjoy dances like the Charleston and the Lindy Hop, a style of swing dance. The Charleston, in particular, became famous due to its lively, flapper-driven culture which promoted a sense of freedom and rebellion during this time. Jazz bands such as the King and Carter Jazzing Orchestra played a significant role in this cultural shift, offering a soundtrack to the dance craze that was sweeping the nation.
During the Jazz Age, venues like the Cotton Club became hotspots where white flappers and sheiks would gather to watch Black entertainers play jazz. This was a period where young, hip audiences could experience new forms of entertainment and social expression through music and dance, which were considered modern and thrilling. The immersion in jazz and dance during this time fostered a sense of cultural and social growth, reflecting the changing attitudes towards race, gender, and class in the American society of the 1920s.