How do I appease a sensitive neighbor?

A few of us just moved into a new house and introduced ourselves to the neighbors. Passed the neighbor my phone number if she had any issues (she's around 45-50 years of age).

A few days on, she's been texting me at night, threatening to call the police. This is because one of our rooms is adjacent to her room, about a 30-40 feet gap between the houses, and whenever there is any noise in the room, she is able to hear it. So if my friend makes a phone call in his bedroom, she hears it and is sensitive to the noise. Our windows are closed, and I'm guessing her window isn't, but this is getting quite ridiculous. We have been patient with her complaints, but it is starting to be a big inconvenience to us.

We would like to meet with her and discuss about this issue, but are unsure of what to say and how to approach this. If you have any advice, we would greatly appreciate it. We want to deal with this as cordially as possible, as we're not here for a negative environment, but at the same time, need her to understand that we have to work together on this issue. We also need her to understand that we do have social lives, and may gather a few friends for barbeques or dinner parties at times. Thanks!