The Wire That Sings
Air will not stay attached to the back of a wire. It peels off alternate sides, kicks the wire as it goes, and the rate it does that at barely changes across four decades of flow.
What it is
A 6 mm wire, seen end on, with air going past it. Click or drag to change the wind.
The wake is two staggered rows of vortices, shed from alternate sides, and every one that leaves kicks the wire sideways. The trace along the bottom is that kick. The note is the trace.
Wind it up and the note goes up with it, in strict proportion. Wind it down far enough and the shedding stops altogether and there is nothing but the wind.
The wake is shown at a fortieth of real speed, and that isn’t a shortcut. It’s the finding, and it’s in the notes below.
How it works
The rate is f = St v / d. Speed over thickness, times a dimensionless number.
That number is the whole day. St is about 0.2, and it stays about 0.2 whatever you do:
| wind | Reynolds | St | note |
|---|---|---|---|
| 0.6 m/s | 240 | 0.190 | 19 Hz |
| 2 m/s | 800 | 0.202 | 67 Hz |
| 5 m/s | 2,000 | 0.202 | 168 Hz |
| 8 m/s | 3,200 | 0.201 | 268 Hz |
| 14 m/s | 5,600 | 0.200 | 467 Hz |
| 26 m/s | 10,400 | 0.199 | 862 Hz |
Across four decades of Reynolds number, from 300 to 100,000, the tabulated Strouhal number runs 0.196, 0.201, 0.198, 0.196. A spread of 2.6 per cent. A telephone wire, a chimney and a bridge cable all shed by the same rule, and the rule doesn’t care how fast, how big, or what the fluid is.
The wake is a point vortex model: one leaves each side per period, drifts downstream a little slower than the free stream, and the rows pull apart as they go. Nothing about the note is put in by hand. The page records the sideways force on the wire, reads its frequency back by autocorrelation, and prints that next to what the flow says it should be.
There is a second number in the picture. A staggered street only holds together at one ratio of row spacing to along-row spacing, which Kármán worked out is 0.2806, and it comes out of asking which arrangement doesn’t tear itself apart rather than out of any measurement.
What surprised me
You can’t see and hear the same vortex street. A 6 mm wire in a breeze sings at 467 Hz, which means it’s shedding 934 vortices a second. There is nothing to watch there. Slow it down until you can see the rows and the note is below hearing.
That isn’t a limitation of the page, it’s a fact about the object. The thing that makes the sound is too fast to look at, and the thing you can look at is too slow to hear. So the wake runs at a fortieth speed and the note plays at its real frequency, and the page says which is which, because a slowed picture presented as if it were the real thing is a lie about the scale of the phenomenon.
Reading the frequency back needed sub-sample resolution. The force trace is sampled at 240 Hz, and autocorrelation gives you whole-sample lags. For a 40 Hz signal that’s lag 15 or lag 14, which read as 40.0 Hz and 42.9 Hz with nothing available in between. The measurement was landing on 42.9 and the test was correctly failing.
Fitting a parabola to the correlation peak and its two neighbours recovers the fraction. It is three lines and it took the error from seven per cent to under one, and I wouldn’t have noticed at all if the test had asked for the answer to within ten per cent instead of within half a hertz.
Shedding was a branch where it needed a loop. One vortex per animation frame is fine at
40 Hz and hopelessly wrong at 934, so the first wake was a thin dotted line rather than a
street. The fix is a while, which is the sort of thing that’s obvious in hindsight and
invisible while the numbers are small enough to hide it.
What I would do next
Let the wire move. A real aeolian tone does something this page cannot: when the shedding frequency wanders close to the wire’s own natural frequency, the shedding locks on to it and stays locked over a band of wind speeds, rather than sliding smoothly past. The wire stops being a thing the flow pushes and becomes part of the oscillator.
That lock-in is why a fence hums at one pitch over a range of gusts instead of sliding about, and it needs the wire to have a mass and a stiffness that the vortices can talk back to. Same model with one more equation in it, and a much better sound.