Cara woke to the sound of drums. Rhythmic, strong, like the drums that led the rowing of a ship, or a march to war. She lay for a moment, wrapped in half-sleep, and then rubbed her eyes, shook herself free of the tatters of her dreams.
Still she heard the drums, just behind and beneath the humming of the refrigerator, the rattling of windows in the wind, water from a neighbor's apartment running through the pipes.
She got up, shrugged into a robe, went to the window in the pre-dawn darkness. She was intimate with the drums' rhythm, had heard them, woken with them in her head and chest, since she was small enough to cry in the night with the force of their pounding. Just a dream, her mother had always said. The drums aren't real. They're only a dream.

Thanks!

Your prose is fine but the presentation makes it miss the hook.
Dream beginnings are done way too much but this idea of constant drumming, like a constant ringing in the ear, is a very good idea. One thing that isn't clear is how long she has been experiencing it. Is it just this morning all has been going on for awhile? Does it come and go or is it there all the time? Is the rhythm always the same? The pitch? The volume?

Try focusing on these aspects in your opening. I liked how she noted it was there as she tried going about her morning, makes me think she's been living with it for a long time. I suggest you open this with her walkiing to the refridgerator while the drumming is pounding. Show a person trying to live with this affliction.

I'll agree with Skadder by and large; the drums are a good idea and worth developing. From my reading, the drumming sound is one she experiences louder at night, but she always hears them softly during the day. In that case, I can't see that her mother would dismiss them as "simply a dream". There's a few details you'll have to work out there, but it was enough to get me reading.

The "just woken up" start is a cliche and almost always a sign that you've started the story too early. The rule I try to stick to (although I frequently fail) is to open the story just as the protagonist's life is going to change. I presume that Cara's life is going to change in some way, small or large; start the story just at that point and have her react to it.

Unfortuantely, I'm leaving for a long holiday tomorrow, so I can't comment on the rest.

Regards and good luck,

Nick

As for the opening 13: I think it has potential but could tighten. I like the description of the drums, but you have it split over two paragraphs. Why not cut out the part about laying in bed, half-asleep, and condense your drum description to the first paragraph. If you really feel the need to make clear she's in bed (which you already accomplish just by saying she woke up), you can do "She got out of bed, shrugged into a robe ..."