Any suggestions on how to cope with a mother who makes constant verbal sounds?

Sometimes, not sure with your mother, certain medications can cause them to have verbal tics, a phrase, or even a constant clearing of the throat. You might want to ask the doctor.

I haven't had the experience of one constant sound, but my mom does repeat herself. I find that music of her teens and 20's gets her out of the loop. Luckily, my mom has a beautiful voice, so it is a pleasure to hear her sing along. We actually get connected sometimes when we are both singing along. She doesn't seem to mind, I can't sing a lick. If this doesn't work, you can try using an IPOD with something soothing for you or maybe an audio book. If she is just repeating the same sounds, she probably isn't expecting your participation in the conversation. If you NEED quiet they do have awesome sound reduction headphones today. I'm not saying to use these 24/7, but its a way for you to rest your nerves.
Hope this helps,

Making the sounds must comfort her in some way (though I can see why it's anything but comforting to you!). Aside from learning to ignore the sounds, all I can suggest is that you call the doctor and see if he or she have an idea. Generally, a diversion of some kind will help, but if she just goes back to making the sound, you'll need more help. If you find something that works, please let us know. You aren't the only one coping with this.
Best,
Carol