What sound does the narrator hear at the end of the story that causes him to confess to the murder?

The narrator invites the officers who have come to investigate the cry his neighbors heard to sit directly over the spot where he has buried the corpse of the old man, his victim.  Before long, however, he says, his ears began to ring.  Then,

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...

The narrator invites the officers who have come to investigate the cry his neighbors heard to sit directly over the spot where he has buried the corpse of the old man, his victim.  Before long, however, he says, his ears began to ring.  Then,

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.

The narrator believes that he must have begun to grow pale as he heard this sound that he now believes is coming from outside his own body, and he continues to speak effortlessly so as to distract the officers.  As he talks, he becomes more and more aware of the sound, increasing in volume, saying, "It was a low, dull, quick sound -- much such a sound as a watch makes when enveloped in cotton."  This line reiterates the narrator's earlier description of the sound he believed the old man's heartbeat made when he was scared; right before the narrator killed the old man, he said, "there came to my ears a low, dull, quick sound, such as a watch makes when enveloped in cotton [....].  It was the beating of the old man's heart."  Thus, he believes that the sound he hears beneath the floorboards is the sound of the old man's heart, somehow beating again even though he'd confirmed the man to be dead. 

However, it isn't the old man's heart.  It can't be.  It turns out that the hellish tattoo the narrator hears is actually his own heartbeat, growing louder and stronger and faster the more excited the narrator gets.  This explains why, as his adrenaline began to flow just prior to committing murder, he could hear his own heart, but he interpreted it as the old man's.  Now, nervous in the presence of the police officers, his heart begins to race again, and he hears it.  He has said several times, throughout the story that he is "nervous," and anxiety tends to increase one's heart rate.  Therefore, in the end, it is actually the narrator's own heart that he hears, but the fear that it is really the old man's is what causes him to confess.