An audio engineer deals with the mechanics of recorded sounds. In other words, they work on recorded sound to make it sound a specific way. In the music industry, you may work with a music producer to mix, master, and reproduce music. Outside of the music industry, you can find audio engineers engineering sound for video games, live events, or recorded audiobooks, among others.
Above everything, this position requires experience and natural talent. Including as much as you can of the former, and showing evidence of the latter, should be your aim for your resume. Take a look at this resume sample.
