It wasn’t that Frodo did not hear Gollum’s tormented back and forth forces with himself. It spooked Frodo out that he did not sleep for several nights forward.

He knew of Sam’s glances at him and he knew that Sam did not approve of the plan to use Gollum’s shortcut.

But over the course of the Quest, Frodo had learned more about Gollum.

“You were not always called Gollum.”

“Why does Master care, we do not care that you care, do we preciousss,” Gollum replied looking away.

“You were one of us, in the past.  Gandalf told me your sad story,” continued Frodo looking at him with pity.

“Go away, you do not know what we wants and why we wants it.”

“You were called Smeagol at one time… the Ring brought you to how you are now, didn’t it?”

Gollum jerked at Frodo calling It so obviously, leaned forward. “You gots it don’t you?”

Frodo recoiled at his reaction but kept his calm.  “Why don’t we both resolve to keep it away from Him and you help me do that? That will be your ultimate sacrifice.  This isn’t something for us to have, Smeagol.  You’ve done your share of harm. Why don’t you help and turn it into a good action, instead?”

Gollum started weeping, “But we wants the precioussss, we needs it.”

“You don’t need anything and do not have to be controlled by anything,” Frodo replied sternly.  “Promise me by the Ring that you won’t succumb to It and will do as I say.  Sacrifice yourself.”

Frodo’s voice thundered and he seemed to have grown in height and power.

Smeagol shrunk and withdrew to what he was already, a former shell of his own self and he could do nothing but oblige.

“We will turn into dussst…”