One thing to keep in mind is to not try to comfort your pet.
If you secure your pet by using a gentle voice to calm him, it confirms his fear! You are actually telling your dog that it is normal to be scared.
The best thing to do is act normal, completely ignore his fear, talk to him normally, play with him as you would normally do and do not allow him to do things you normally don’t like sitting on the couch or similar.
Your idea of using music to help the dog calm down is good, but do not use it to cover up the sound.
Also, you’d want to give him some help to calm down and you can, but don’t do it because he is afraid. Basically, distract him first like stated above, once he forgets about the storm you can put him in his crate.
He will feel comfortable there, as usual, and hopefully calm down on his own. He will then learn by himself to go there when he is scared, but all this should make him less nervous as well.
Ignoring a puppy might be harder than a big dog, but do keep in mind that comforting a puppy will also have a bigger and more negative impact.
You will want to work on your dog’s sensitivity to noises.
You can buy CDs online that have fireworks and other noises specifically to help desensitize your dogs, but you’ll probably find plenty of the requisite noises on YouTube as well.
The idea is to play the noise at a volume that your dog is comfortable with and then reward him every time the noise is played and he doesn’t show signs of fear or distress.
When you’re confident that your dog is comfortable with the noise at a certain volume and doesn’t mind it at all, slowly increase the volume.
Be very careful about going slowly and not increasing the volume too quickly as your dog might considerably regress when you turn it up it too loud too fast as he will become scared and anxious.
You can also use calming/anxiety aids while practicing these exercises. You can learn more about that topic in this article here: The 6 Best calming and anxiety aids for dogs/puppies.
You can simply do a search on amazon or google for hemp calming aids, and oils which will give you many different options on extremely effective products where this is concerned.
Keep repeating until your dog gets thoroughly desensitized to the noise and even starts associating it with good things happening. You’ll have to put in quite a bit of time but it’ll make you and your dogs life a lot easier in the long run.