It's a matter of scatter. You don't want it. Scatter comes from irregularities in the surface, so you can try to minimize those by sanding to the approximate limit of 20/20 resolution - CAMI 320 or P 400 - along the grain. If you sand across, you'll see the contrast even a small particle can give. Some people LOVE to sand. I am not one of them. If you want the wood to feel and glow satin, burnish it.
http://i35.photobucket.com/albums/d160/GoodOnesGone/Ten-By-Interior.jpg That's 320 and then a paper (not plastic) grocery bag. Still scatters light because the wood is porous. Light comes back from different angles.
Put some oil on the surface, and it will bridge over small pores and drape itself over minor irregularities to give a smoother surface. That's when people say they've "popped" the grain. They seem to forget what happens after the oil is absorbed. If you put on more coats of a finish you will come to a consolidated and permanent smooth surface. While you're doing it, ask yourself how much sense it makes to sand to 4000 when you use 400 to smooth and tooth for the next coat.
The best surface you can get is the finish itself, second is a polished one. For ease of use, look-through, and the ability to go as shiny as I care to, I like shellac. French Polish technique of a thousand thin coats a minute is an easy finish, but it is shellac, and vulnerable to alcohol and alkali in cleaners. Second best is a wiping varnish. Oil base is my preference. Wiping varnish have resin (solids) content between brushing varnish and Danish oil. On with a rag, drag for smooth, and by coat three on most woods you have enough to make a continuous surface. If I didn't like the first two so much I'd spray lacquer, but it's picky and stinky.
I don't like satin finishes where there's scatter within the coat. If I want some scatter I use the old method of steel wool or buff with tripoli to destroy the flowed surface. Some people like to buff for bright with rouges. Never has quite the shine of a flow surface, though.
Varnish
http://i35.photobucket.com/albums/d160/GoodOnesGone/Cultivated-Birch.jpg
Shellac shallow
http://i35.photobucket.com/albums/d160/GoodOnesGone/ShellacLongSide.jpg