Besides the good advice about asking her to shh and calm her etc, I can say that this dog should get out of the house, walk, go to obedience class, be around lots of other dogs and sounds and see the world. this will often make them calmer, tireder and accept sound stimuli which causes protective or alerting barking. AND dogs that hears sounds they cannot see will usually bark. Tired dogs don't care as much - i.e. exercise and obedience train. I can honestly say in 35 years I've never seen a well trained / basic socialized dog with some of these neurotic behaviors like barking, whining, etc. Try it!
I have a dachshund who used to behave in a very similar way. Even now she still has tendencies when sirens go by or motorcylces. What I found help for my dog was whenever she began barking at a noise, to walk over to her, tell her to shhhh or quiet but you have to do it calmly and just touch her like on her back, sort of like comforting a friend, and when she quiets, praise her by saying what a good girl she is and maybe a small treat, I also found it helpful when comforting her/shh ing her to make sure she knows its an undesired behavoir by showing it with your body language but also showing her she is safe. If you kind know what I mean. You want to make sure you dont send off any negative "vibs" like anger because she may be able to sense that. Hope I was some help and that you were able to follow this