Question

how would an audio recording most likely convey the characters emotions during the scene

Answer 1

I used to listen to drama or a romantic story on the radio, usually, the character will say what they are feeling. Sometimes they will have a dialogue with themselves to portray a internal conversation. 

Character emotions during the scene will be conveyed not only by their dialogue but also by the tone they used in the audio recording. 

For example,
when you watch a horror movie, you'll notice a dark room with eerie lighting. On the other hand, in an audio recording, the character will say "the room is so dark, it's so eerie.. I"m scared".

Answer 2

A very common practice to convey emotions in audio version of plays is through orchestral music. A more vibrant tone is played to portray rush, anger or a thrilled semblance; A lighter tone to portray relieve, refreshed feelings; A melodramatic one for sadness, sorrow, regret, and so on...

And also the very actors' voices vary the same way. Although in normal visual plays this also applies, in their audio versions, since they can't rely on the visual resources (e.g. highlight the actors' facial expressions), they got to invest an extra effort on  the vocal aspect.