I think you should use a tool called
It's easier using the
Clipping Mask tool where the letter (A) act like a mask for all objects underneath.
For doing that, make sure to put your letter (A) over the group of wavy strokes and select all artworks, then go to
Object > Clipping Mask > Make or just Click CTRL + 7 ... That's it.
as you can see Illustrator will hide the mask strokes and keep it's content only, so you don't have to delete the stroke of the letter (A).
The advantage of this methods is you can change the content of that mask with any other content, in our case the waves could be changes by going to
Object > Clipping Mask > Edit Content or released in anytime by going to
Object > Clipping Mask > Release or click CTRL + ALT + 7