What was the sound which the murderer heared in "The Tell-Tale Heart"?I mean can we suppose that he forgot his watch near the corpse because of fear?

Nice try, and full marks for creative thinking. However,
there are a few problems that you need to be aware of with your line of reasoning. The
first is the way in which that the only person who can hear this strange noise at the
end of this grim and gruesome story is the narrator himself. The men who are with him
and investigating the scream that was heard continue to "chat pleasantly" and smile in
spite of the deafening sound that drives the narrator to such paroxysms of rage and
frustration. If it was a watch that he had left in the room, these men would have heard
it too.

Secondly, let us remember that Poe gives us every
reason in this narrative to doubt the sanity of the narrator. He is presented as being
profoundly unreliable, from the grandiose claims that open the story as he claims to
hear "all things in heaven and on earth" and "many things in hell." His obsession with
the old man's eye and the subsequent way in which only he is shown to be able to hear
the sound indicates that this is yet another symptom of the narrator's madness, as he
concludes that the sound he hears is "the beating of his hideous heart." However we
interpret this sound, whether it is some remnant of the narrator's conscience that
causes him to confess, we can definitely assume that this sound is imagined in the
narrator's head.