RE: Deer can hear arrow first? Not!
Though I agree with the sound situation as presented here there is one factor that has not been mentioned. There is an intangible curiosity in every game animal we hunt.
I believe the animal hears the bow and release first then perhjaps the arrow, sometimes they even hear us drawing the bow, but generally, before they react, they try to identify the source then react. With the exception of bears, most animals will duck or drop their whole body as they are springing into action allowing us the displeasure of seeing our arrow flying just over the animals back.
Even driving an automobile it takes a period of time for us to react; so too game animals. I believe their reaction time is slower than ours and this allows for the clean, quick killing shots that we all pray for.