Why did the wood make you want to speak in whispers?
In Chapter 1, the narrator describes the wood as "strange," with a "sleeping, otherworld appearance that made you want to speak in whispers."
If we look for an answer only right there in the text, the best we could come up with is probably that the woods feel mysterious, like there's something magical going on in them. Maybe something about the quiet or the stillness of those woods makes you wonder if someone is listening to you as you pass by it.
But that would only be a good guess. If we look a little farther on in the chapter, we see the stream that bubbles up in the middle of the wood, and we're told that someone has tried to hide the stream with pebbles. Wow! There's a good clue. If someone is hiding the stream, it must be valuable or dangerous somehow. So the wood definitely has an eerie, magical quality to it, which emanates from the stream.
Of course, reading even further in the story, we find out that the water from the stream provides everlasting life to anyone who drinks it. Now we know for certain: people passing by the wood feel a need to be quiet out of respect and a sense of wonder, because they can sense the deep magic of the immortal water in the heart of the wood.