2007 Toyota Yaris 3dr manual, had brakes replaced and now I'm hearing (not feeling) a rhythmic pulsing sound when braking. Garage is at a loss. Any help would be greatly appreciated.

I'd like to preface all of this with the fact that I'm not, nor have I ever been, a "car guy."I have a 2007 Toyota Yaris, 3dr, with 89,352 miles. I recently, April 19th to be specific, had new brakes installed (front pads, front rotors, rear shoes, and rear drums). I also had the tires rotated and balanced. Within a month and a half I started hearing an intermittent rhythmic noise while braking. The sound seemed to be coming from the rear passenger side of the car. After taking it to the same shop that did the brake job, a shop I've been going to for years, it was determined that a crack in my exhaust, just before the catalytic converter, was the initial culprit. When braking the exhaust apparently shifted forward enough resulting in the exhaust being directed through the wheel.Within a day of getting the exhaust patched I started hearing a new, albeit quieter, instance of the sound. This time the sound seemed to be coming from the driver side of the car, I'm still not entirely sure if it's coming from the front or the rear. I took the car back to the shop that did the brakes and they were unable to locate the source of the sound I described, nor were they able to hear the sound for themselves. I was also told that the pads were not wearing unevenly and that the rotors and drums both looked fine. The sound came back on the ride home from the shop.So, after another week of trying not to worry about the sound, thinking maybe it was just the brakes needing to be "worn in." After dealing with the sound for two more weeks, it seemed to get louder, than quieter, than go away for a day or so, then come back... I finally got sick of it and got an audio recording of the sound, HERE. I took the car back to the shop and they were still unable to find anything that could be causing that sound.So, I'm about at my wit's end with all of this. Does anybody here have any suggestions as to what could be the culprit so when I take it back to the shop next week I can point them in a specific direction?TL;DR - 2007 Toyota Yaris 3dr manual. Brakes completely redone. New rhythmic sound when braking, turned out to be exhaust being directed through wheel from crack in line. Got exhaust fixed. Sound came back on other side of car less than a day later. Garage that did brake replacement can't figure out what's causing the sound. Here's the sound. via /r/cars http://ift.tt/2tQhOEU