Final answer:
Linguistic anthropology is the term for studying how language changes over time within a culture and how languages travel across cultures.
Step-by-step explanation:
The term for studying how language changes over time within a culture and how languages travel across cultures is called linguistic anthropology. Linguistic anthropologists are interested in the way that language varies across cultures, reflecting different environmental, historical, and sociocultural conditions. They study language as one cultural element among many, all interwoven into the sociocultural life of a people.