The Tell-Tale Heart

The narrator hears ringing in his ears...

The ringing became more distinct -- it continued and became more distinct: I talked more freely to get rid of the feeling: but it continued and gained definitiveness -- until, at length, I found that that the noise was not within my ears.

"It was a low, dull, quick sound -- much such a sound as a watch makes when enveloped in cotton."

This above line connects the narrator's earlier description of what he thought was the old man's heartbeat.

From the text, we can infer that the sound is actually the narrator's heartbeat, which grows incrasingly louder as he becomes more and more panicked over his situation.