No, linguistic anthropology is not the study of dead languages (that’s classics). No, it’s not the study of the mechanics of language (that’s linguistics). No, it’s not the study of the language of dinosaurs (that’s linguistic paleontology and it doesn’t exist). Yes, I’ve met people before that assumed those were the definitions of linguistic anthropology.
Linguistic anthropology is a discipline that uses the microanalysis of linguistic form to shed light on macro-scale sociocultural processes. Did I loose you yet? If we liken linguistic anthropologists to chemists, we would say that linguistic anthropologists look at things similar to protons, electrons, and neutrons that make up the chemical composition of language (microanalysis). They use this microanalysis to better understand larger phenomenon such as how people interact within a society or culture (macro-scale sociocultural processes).
Basically, linguistic anthropologists study MODERN DAY LANGUAGE phenomenon in order to ask the same questions as sociocultural anthropologists. In fact, I would even take a step further and say we are basically sociocultural anthropologists with one additional tool in our kit: language.
Sociocultural anthropologists study groups of people using ethnographic methods (surveys, interviews, focus-groups, and participant-observation among others). My sociocultural anthropologist friends have studied Tongan villages, American elementary schools, Karate classes, and health clinics. They ask questions about cultural identities, gender roles, perceptions of mental health, and so on.
Linguistic anthropologists ask the same questions and use the same methods plus they record conversations and other speech events as well as collect written documents. They take those recorded speech events and written documents and analyze them to address those same questions. My linguistic anthropology friends have studied bathroom graffiti, conversations between couples expecting babies, and lament (crying while singing) classes in Finland.