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Mach Cone Hoodie

IT ARRIVES BEFORE ITS NOISE | Pixelated Physics

\[\sin\mu = \frac{c}{v} = \frac{1}{M}\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

What happens when something outruns its own sound? The Mach Cone stands for the shock cone around anything supersonic. Each sound wave spreads as a sphere, but the source keeps moving past them, so the wavefronts pile up on one cone whose half-angle satisfies sin µ = 1/M, exactly 30° at Mach 2. This is a black pixel-art hoodie from Pixelated Physics.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

An object moving faster than sound outruns its own sound waves, and they pile up into a cone. The cone's half-angle satisfies sin μ = 1/M, so the faster the object, the narrower the cone; at Mach 2 it is 30 degrees.

Anything that moves faster than sound gets ahead of its own noise.

Each moment the source sends out a sound wave that spreads as a sphere at the speed of sound c. The source itself moves on at v. When v is bigger than c, it keeps leaving its old wavefronts behind, and they all end up touching one cone that trails from its nose.

The half-angle of that cone is the Mach angle: sin µ = c/v = 1/M. In the art the source flies at M = 2, so every disc touches the same two edges at exactly 30°. The discs are drawn at equal time steps, newest and brightest at the front.

Ernst Mach and Peter Salcher photographed this cone around a supersonic bullet in 1887. Nothing is heard before the cone arrives. When it sweeps past you, that is the boom.

It arrives before its noise.

Equations

\[\sin\mu = \frac{c}{v} = \frac{1}{M}\]
\[M = 2 \;\Rightarrow\; \mu = 30^\circ\]
\[r_n = c\,(t - t_n),\qquad x_n = v\,t_n\]
SymbolMeaningUnit
\(\mu\) Mach angle, half-angle of the cone \(\mathrm{rad}\)
\(c\) speed of sound in the medium \(\mathrm{m/s}\)
\(v\) speed of the source \(\mathrm{m/s}\)
\(M\) Mach number, v/c (here 2) \(\mathrm{1}\)
\(r_n\) radius at time t of the wavefront sent at time t_n \(\mathrm{m}\)
\(x_n\) position of the source when it sent that wavefront \(\mathrm{m}\)

Sources

  1. Mach & Salcher (1887) Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge, Sitzungsber. Akad. Wiss. Wien 95 (II), 764
  2. Mach & Salcher (1887) same paper, Ann. Phys. 268, 277

Source Mach, E.; Salcher, P. (1887). Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge. Annalen der Physik 268, 277–291.doi.org/10.1002/andp.18872681008

Field notes

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