A friend just asked me how does wind affect the propagation of sound and I am ashamed to say I do not exactly know. It is experienced that when the wind blows from different directions, you would hear a distant sound differently. Obviously changes in pressure will affect some characteristics of the sound wave, but I cannot think of a model. Any ideas?

This is pretty well established. The speed of sound in a wind is greater than the speed of sound in still air by the component of the wind velocity along the direction of propagation.

 

This effect will Doppler Shift the frequency of the sound, just as a moving observer would.

 

[math]f(wind~blowing~toward~you)=f(no~wind) \frac {c+c_w} {c} [/math]

 

[math]f(wind~blowing~away~from~you)=f(no~wind) \frac {c-c_w} {c} [/math]

so, it's just doppler shift. I thought of that, but seemed too simple to be true. how about wind blowing perpendicular?

how about wind blowing perpendicular?

It's the component of the wind velocity along the direction of interest that you want [imath]c_w cos \theta [/imath]. For a perpendicular wind, there should be no effect, according to this simplistic theory. There may be lower order effects, and also, winds are never in laminar flow, so the provided expression is only an approximation.