Why are the wires humming?

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Even the ancient Greeks noticed that a string stretched in the wind sometimes begins to sound young - to sing. Perhaps the Elov harp was already known then, called so by the name of the wind god Eolla. The Aeolian harp consists of a frame on which several strings are stretched; it is placed in a place where the strings are set in motion by the wind. Even if you limit yourself to one string, you can get a whole range of different tones. Something similar, but with less variety of tones, will pass through when the wind moves telegraph wires.

For quite a long time, this phenomenon and many others associated with the flow of air and water around bodies were not explained. Only Newton, the founder of modern mechanics, provided the first scientific approach to solving such problems.

According to the law of resistance to the motion of bodies in a liquid or gas, discovered by Newoton, the resistance force is proportional to the square of the speed: $F = k\rho v^2S$.

Here $v$ is the speed of the body, $S$ is the area of ​​its cross-section perpendicular to the direction of the speed, $\rho$ is the density of the liquid.

Later we found out that Newton’s formula is not always correct. In the case when the speed of motion of a body is small compared to the speed of the tellan motion of molecules, Newton’s law of resistance is no longer valid. When moving slowly, the resistance force is proportional to the speed of the body, and not its square, as with fast movement. Such a situation will arise, for example, when small drops of rain move in an area or when sediment settles in a glass. However, in modern technology with its rapid speeds, Newton’s law of resistance is usually valid.

It would seem that since the laws of resistance are known, the humming of wires or the singing of an el harp can be explained. But that’s not true. After all, if the strength of resistance was constant, then the wind would simply stretch the string, and not excite its sound.

What’s the matter? To explain the sound of a string, those simple ideas about the force of resistance that we have just discussed will not be enough. Let’s discuss in more detail some types of fluid flow around a stationary body (this is more convenient than considering the movement of a body in a stationary fluid, and the answer, of course, will be the same).

Look at figure 1. This is a case of low fluid velocity. The streamlines follow the cylinder (a section is shown at figure) and smoothly continue behind it. This resistance flow is laminar. The resistance force in this case owes its transmission to internal friction in the fluid - gravity and is proportional to $V$. The speed of the fluid at any place, as well as the resistance, does not depend on time (stationary flow). This case is of no interest to us.