There's a common (almost clichéd) claim that you can only hear some distant sound "depending on the wind direction".
Here are some random examples.
- The local population does not have to expect any noise emissions because the test pile is situated about 2.3 km from the coast. Depending on the wind direction, dull thuds at the most may be heard on the cliff coast. 
- depending on the wind’s direction you began to smell the smoke of the wood fire or hear the sounds of Ethan’s delicately constructed music. 
- Depending on the wind direction i'll probably be able to hear most of the arctic monkeys gig from my back garden... 
- you can hear cows or horses and, depending on the wind direction the milk machine in the morning (5.30) and afternoon (5.30).
My intuition (which I naturally don't trust) suggests that the amount of distance that the sound is advanced by a small wind in the time it takes to travel to the ear is irrelevant.
Using my first example, travelling at 343 metres per second, the sound is going to take about 6.7 seconds to reach the coast, 2.3km away. If the air is moving at, say, 3 metres per second (which is enough to cause leaves to rustle, but not enough to cause waves to break [Ref], it means the sound could, at most, be heard an additional 20 metres further (compared to still air), or 40 metres further (compared to the same wind heading away from you). Over a distance of 2300 metres, the difference in loudness caused by an additional 40 metres seems like it should be imperceptible.
Yes, the wind might be faster, but again my intuition suggests this would break-up and/or cover the sound more than it would assist the sound.
Does this expression have a basis in truth? Is it ascribing the fact that one can only sometimes notice the sound to the wrong cause?