Is there any material capable of cancelling low frequencies sounds like a thunder (60Hz)?
Acoustic foam could be used to dampen all noise and create some insulation, thunder &amp; fireworks contain broad band noise everything from low frequencies to high frequencies, 60hz is the noise you hear around transformers.

If you insulate and have a dead airspace that will also provide some shelter from the noise. I have trained hunting dogs and use a starter pistol and after the noise treat them with a cookie (dog treat like the tiny milk bones) within a few days they are not bothered by the noise and we change from food treats to toys to chase this has been great for young dogs, 

For dogs that are noise shy I have only found getting mild tranquilizers was the only thing that worked well. I had an Australian Shepard that went through several windows trying to get out of the house so we would put her in her kennel inside and give her a pill in some cheese to keep her from getting heft and breaking more windows.