I guess the question is, how much of the ambient noise is truly ambient?
There are also ways to mask noise, some of them fairly inexpensive.
One mental exercise you may wish to do is take some time, as much as you desire, to just listen to every noise and identify it. Do nothing else but listen and identify. Thunder storms are difficult because, like a cat pouncing on your head, the sudden KA-BOOM! is a surprise. Sure, it clears all conscious thought for a second or so, but it also clears your mind of the Password, the Intention, and your call to the Master.
As long as you have a good grasp at a preconscious level of what the noises are, and a reasonable expectation of them, they should not intrude. They are simply the sounds of the city.