Downstairs neighbour harassing for talking in the house

Hi, we are three girls moved to the third floor of a residential building last month. A lady from downstairs has been coming up since day 1 - whenever we have a conversation in the living room - because her daughter is studying. At no point, have we played any music/thumped on the floors - we are just 3-4 people having conversations. We have tried to adjust by keeping our windows closed - however, according to her - our voices travel down. We are hard working, independent girls - paying high rent to have a good home. She has turned up at our door at 1AM, 2AM... and called me at odd hours of the night the moment 2-3 people start talking in the living room. Two days back - she has walked straight into the house - and told us, that if we want to talk - we can sit in the bedroom and shut the doors. Also, while walking out - threatned us that she will get her friend: the DGP of Karnataka to "take care" of the situation. This according to me is harassment, forced entry, threatning and invasion of privacy. If there is an acoustic issue with her house - she should be getting an acoustic treatment done. We were not informed about any of these problems before taking up the house. Please help.