The caster can recreate the natural sounds of any creature. Ones they know well, i.e. having both seen and heard multiple times, can be mimicked easily. Recreating unfamiliar creature sounds requires the caster to have heard the sound recently. (Recently being within the last 24 hrs, or whatever time period the DM considers appropriate.) 

DM Tip: If the sound that the caster is trying to mimic is very memorable, unique, and/or caused them to receive a condition (i.e. fear or charmed), consider letting them recall the sound clearly (even if the event happened long ago).

Likewise, sounds that were mixed with heavy background noise (like a raging storm or the cries from an angry mob), or were distorted (i.e. heard underwater or in a echoey cave) should be harder to reproduce even if heard recently. History checks and/or perception checks can make these events reasonably challenging, without punishing player creativity.

Limitations and Detection

• The volume of mimicked sounds are limited to what the caster can produce naturally UNLESS magic or an ability says otherwise. For example, an unassisted caster can mimic the unique sound of a Tarrasque's cry, but not how ear-shatteringly loud it is.
• The sounds the caster can mimic are limited to the natural sounds the creature can make (i.e. chirps, cries, hums, generic speech, etc). It CANNOT reproduce specific voices. Likewise it cannot recreate footfalls, clattering weapons, or other similar noises.
• Any sounds meant to mimic a creature's language are heard as indistinct speech or meaningless gibberish UNLESS the caster can speak that language.
• If any creature that hears the mimicry takes a Study action to examine the sound, they can attempt to determine the spell's deception with a successful Intelligence (Investigation) check against the casters spell save DC. If a creature discerns the mimicry for what it is, the creature becomes aware that the sound is not genuine. However the creature does not automatically know what is making the sound.