was the beating of the old man's heart. It increased my fury, as the beating of a drum stimulates the soldier into courage.

There is simply no way that the narrator would be able to hear the old man's heartbeat from across the room. It is only logical to assume that the heartbeat he hears is his own, beating harder and faster because of his growing "fury."  

Furthermore, the narrator hears this same sound even after he has killed and dismembered the old man. There is, again, simply no way that the sound could be coming from someone who has been murdered and cut apart. While the police officers sit just on top of the spot where the narrator buried his victim, he again hears

a low, dull, quick sound -- much such a sound as a watch makes when enveloped in cotton. [He] gasped for breath -- and yet the officers heard it not.

The narrator is growing more and more nervous that the officers will find him out (he says "[his] head ached, and [he] fancied a ringing in [his] ears"), and so his heart begins to beat loudly and more quickly once again. He describes the sound in precisely the same way as before -- a watch wrapped in cotton -- and as he gasps for breath, the sound will only increase like it did before. Further, the officers cannot hear it, and so we must assume that it is actually the narrator's own heart that he hears.

Those of us readers who are not madmen must realize that it could not be the old man's heart the narrator is hearing. This is why:

First of all I dismembered the corpse. I cut off the head and the arms and the legs.

Poe has his narrator include these words in his description of how he concealed the body because Poe wants the reader to be quite sure the old man is dead. After all, the narrator has cut off the head. He also refers to the victim as a "corpse." If we take it for granted that the old man is totally dead, then it could not be his heart that the narrator imagines he is hearing.

However, since the murderer is mad, it is not impossible that he should imagine it is the old man's heart he keeps hearing. The answer seems to be that he thinks he is hearing the victim's heart and we know he is hearing his own heart. His agitated behavior towards the end of the story strongly suggests that his heart must be pulsating abnormally.

I arose and argued about trifles, in a high key and with violent gesticulations; but the noise steadily increased. Why would they not be gone? I paced the floor to and fro with heavy strides, as if excited to fury by the observations of the men—but the noise steadily increased. Oh God! what could I do? I foamed—I raved—I swore! I swung the chair upon which I had been sitting, and grated it upon the boards, but the noise arose over all and continually increased.

Obviously he is increasing his own blood pressure, his own heartbeat, his own pulse, and the flow of his own adrenaline with his exertions and his hallucinations. He is giving himself away. We have all experienced such feelings--though not as strongly, and we have not had dismembered bodies buried under our floors. The fact is that other people can't read our feelings as well as we think they can. The three police officers are not "dissembling." They are not "making a mockery" of the narrator. And the narrator is probably not behaving as wildly as he seems to imagine. Just moments earlier he had described the officers as follows:

The officers were satisfied. My manner had convinced them. I was singularly at ease. They sat, and while I answered cheerily, they chatted of familiar things.

So the title of the story, "The Tell-Tale Heart," probably refers both the narrator's heart and the old man's tell-tale heartbeat which he imagines. 

There are several possibilities. Either the narrator hears, or thinks he hears, the heart of the old man he has murdered; or it is his own heart, or his own pulse, he hears beating in his ears; or thirdly there is nothing at all to hear and he only imagines he is hearing a heart beating.

He cannot be hearing the old man's heart because the old man is dead. Poe makes it clear in the following paragraph that the old man could not possibly be alive.

If still you think me mad, you will think so no longer when I describe the wise precautions I took for the concealment of the body. The night waned, and I worked hastily, but in silence. First of all I dismembered the corpse. I cut off the head and the arms and the legs.

And if the victim cannot be alive, his heart cannot be beating. It would seem that Poe does not want his reader to get the impression that his narrator really hears the victim's heart, even though Poe has his narrator say that it is the old man's heartbeat he is hearing up to the time he confesses to the murder.

So the narrator must either be hearing his own pulse beating in his ears and imagining that it is the victim's heartbeat, or else there is nothing in the nature of a heartbeat to be heard, and the narrator is just imagining he hears the pulsating sounds he describes. 

The opening sentences of the story seem intended to create the impression that it is his own pulse that finally drives the narrator to break down and confess.

TRUE!—NERVOUS—VERY, very dreadfully nervous I had been and am; but why will you say that I am mad? The disease had sharpened my senses—not destroyed—not dulled them. Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. 

He is VERY NERVOUS, but he is trying to act perfectly calm. The fact that the heartbeat keeps growing louder and faster strongly suggests that it must be his own pulse he is hearing. If the sound were completely imaginary and had no source in reality, then it seems most likely that he would imagine the volume and tempo to remain the same. The sound can only keep increasing in volume and tempo if it is his own heartbeat stimulated by guilt and fear that is causing the tell-tale sound. It must be the narrator's own heart.