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I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am not sure. The wind was very light.

The sound was not the "buzz" asked about here.

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My question is: assuming the sound was generated by the wind, is it possible to estimate the speed of wind from the sound properties (i.e. its spectrogram) and the mechanical properties of the cable?

If yes, how accurate will be the estimate?

If yes, can you provide some back-of-the-envelope calculation?

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The sound by the cable is produced because of the Kármán vortex shedding.

This empirical formula from the wikipedia page relates the frequency of the vortex shedding with the Reynolds number: $$ \frac{fd}{V}=0.198\left (1-\frac{19.7}{\mathrm{Re}}\right), $$ where $f$ is the frequency, $d$ cable diameter and $V$ is the flow velocity. The Reynolds number $\mathrm{Re}$ in turn is defined for this system as $$\mathrm{Re}=\frac{Vd}{\nu},$$ where $\nu$ is the kinematic viscosity of the medium. For the air at $15\,{}^\circ \text{C}$ it is $1.48\times 10^{−5}\,\text{m}^2/\text{s}$.

So solving the equations for the velocity $V$ we obtain $$ V = 5.05 \left(f d + 3.90 \frac{\nu}{d}\right). $$

Of course, this formula implies idealized conditions, so in a more realistic situations (including for instance turbulence in the wind flow) extracting the vortex shedding frequency from the sound spectrum could be tricky.

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  • $\begingroup$ Thanks! I plugged in some number but the frequency I get is quite low compared to what I heard. For example with $d=30mm$ I get $f=183Hz$ when $V=100km/h$; I think I heard a sound with an higher frequency with a much lighter wind. $\endgroup$ – Alessandro Jacopson Jan 4 '14 at 14:52
  • $\begingroup$ Are you sure that 30mm is the only cable there? Could some thinner support cable generate the higher frequencies? (Just because something is thicker does not mean it is the loudest). $\endgroup$ – user23660 Jan 4 '14 at 15:03
  • $\begingroup$ No, I am not sure. With public available info I can say the thinner wire could have $d=11mm$. $\endgroup$ – Alessandro Jacopson Jan 4 '14 at 15:11
  • $\begingroup$ So could this be this higher frequency? Or do you have some insight about the sound from the spectorgram? (I imagine there are apps for phones that could make it) $\endgroup$ – user23660 Jan 4 '14 at 15:37
  • $\begingroup$ No, the frequency is still to low also with $d=11mm$. $\endgroup$ – Alessandro Jacopson Jan 4 '14 at 15:57
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In the design of aeolian vibration dampers the frequency of oscillation is given empirically by $$ f = 3.26 V/d $$ where $f$ is in $\rm Hz$, $V$ wind speed in $\rm mph$ and $d$ the cable diameter in $\rm in$. The problem is that beyond $15 \,{\rm mph}$ the wind is too choppy to excite one frequency and the vibration amplitude (and hence sound) drops. Only across flat terrain (sand, river crossing, snow cover) the vibration can be sustained up to about $25 {\rm mph}$.

Thus the vibration frequency can only be used for low speed, and steady winds.

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