Can you stall array animation?

I have these electromagnetic waves that I want to animate emanating outwards. I’ve done it by creating duplicates and moving the keyframes back more and more for each duplicate, but I’m trying to find a more efficient way to get this effect. The top example is what I want it to look like and what I did with the duplicates. I have the bottom example on a cycles modifier for the keyframes. I was thinking maybe I could use an array modifier, but the array copies would be in exact same place as the original. I need a way to either stall the animation for the array copies, or make the copies offset inside the original like the top example. Anyway I can do this with or without the array mod?