When a wind blow through sharp edge, say, edge of a paper, you can see the vibration of the paper and hear the sound.
For this type of oscillation, it should be a damped oscillation with external driving force $\mathcal{F}(x)$:
$\ddot{x}+2\lambda\dot{x}+\omega_{0}^{2}x=\mathcal{F}(x,t)$
with the driving force in the form of sinusoidal $\mathcal{F}(x,t)\sim F\sin(\omega t)$ (It should be a 3D version though). However, if the air flow is really steady, the external force should be constant so there is no oscillation at all from this equation.
A simple guess is that the motion of the paper influence the streamline of air flow so that the pressure gradient provides the exact sinusoidal driving force. This mechanism is reasonable because the propagation of sound wave has the oscillation relationship between the displacement and the pressure. A question here is how the air flow sustain the energy loss due to the damping.
It is also not easy to think of the initial condition as well as external force for these oscillation. So
1) What exactly is the physical mechanism to generate sound when a 'steady' air flowing through a sharp edge?
2) Another similar question is how the driving force act in the resonance in musical instrumental such as pipe? A 'steady' flow of air is also provided somewhere to the pipe, but air oscillates inside the pipe.
Edit: From the answers, people suggest few mechanism for different situations. Few more questions:
3) For static object, Kármán vortex street can form behind the object. So is the sound frequency the same as frequency of vortex generation, or the same as the expansion of the vortex? Sound is a spherical wave propagating outward, so identify the sound frequency should locate the point of generation.
4) Where is sound generated in the situation (1)? Is the sound frequency the same as the frequency of the vibrating paper?
Fluid mechanics is a difficult topics, but there are approximation for special cases trying to explain the underlying mechanism, such as the flag fluttering cited by j.c.
Best Answer
The full description of viscous fluid flow (i.e. the Navier-Stokes equations) is non-linear and can be sensitively dependent on initial conditions. What this means in practical terms it that you can't always count on your intuition.
The evolution of the Kármán vortex streets linked by mbq from laminar flow around an obstacle are are a classic demonstration. (And easy enough for a determined middle school student to create in the garage for a science project, though things are likely to get wet...)
Any way, once the wind starts doing non-linear things, it can generate periodic stresses, and from that you get the whistling or humming noise we all know and love. Add a resonant cavity and you can amplify nice pure tones which is the short-short version of how this works in wind instruments.