fluid dynamics - How does a steady wind flow generate sound?

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.

Answer

There are really two parts to your question. First, how does the wind affect the motion of the paper, and how does that motion then couple to the behavior of the wind?

For the case of a flag fluttering due to the wind (which may or may not be applicable depending on what you have in mind), the physics of the instability leading to fluttering has been worked out in a fairly celebrated paper of 2005 by Argentina and Mahadevan. They argue that:

[...] in a particular limit corresponding to a low-density fluid flowing over a soft high-density flag, the flapping instability is akin to a resonance between the mode of oscillation of a rigid pivoted airfoil in a flow and a hinged-free elastic plate vibrating in its lowest mode.

I suspect this paper and probably some of the papers that cite it would be the right place to look. As you can see, this part of the question that you've asked is of fairly high interest in current research.

Second, how does this motion generate sound? This is also an interesting question but I know less about this. I would suppose that some resonant vibrational modes of the sheet of paper that you're asking about (those involved in the flapping modes described by Argentina and Mahadevan) generate the sound. But I don't know very much about sound generation or acoustics.