IE9 definitely does support .m4a. All our existing games use it and play audio in IE9. Here's a demo of your arm.m4a file which plays in IE9:http://www.scirra.com/labs/ie9m4a/
I would guess your .m4a file is using a different encoding. .m4a is just a wrapper for other codecs, and it has to be the right kind (AAC) inside the file for it to play. If you encoded it using Construct 2's importer, it should play fine too.