Not an Expert / And not using studies to back this up but as a whitetail hunter who has rattled in many deer and love watching deer behavior, deer can here my beard scratch on my merino neck gaiter from 30 yards, "I'm sure I can't here that good" their hearing compared to ours has a different range and is way more directional like a parabolic microphone.
I have had deer respond and hear my rattling from over 1 mile away in the best situation, I beleive 400-800 meters would be easy for then on a good day and 100-250 on a bad day. Rattling (tinkling)is a high frequency like an elk call so it better carries in open country, but the low tones, banging etc. carry very much further in the bush like a red deer roar. I tinkle to start into an area, once I have waited for 20 min. of longer I try to change it up to lower tones Banging and crashing the antlers together. Rattling is always worth it, give it a whirl and don't be discouraged if not response, when it happens and one comes worth several days of rattling. Really listen between rattles and if you hear anything out of place don't rattle you'll give yourself away let the deer (does and buck both will come)try to find you that will help and create your best success.