• Black Drum Mode physics hoodie, pixel-art circular membrane vibration design, worn by a model, front close-up
  • Black Drum Mode physics hoodie, pixel-art circular membrane vibration design, worn by a model, back close-up
  • Black Drum Mode physics hoodie, pixel-art circular membrane vibration design, front view
  • Black Drum Mode physics hoodie, pixel-art circular membrane vibration design, back view
  • Black Drum Mode physics hoodie, pixel-art circular membrane vibration design, turning on a model
  • Black Drum Mode physics hoodie, ΨP Pixelated Physics neck label
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Drum Mode HoodieSOME DRUMS SOUND IDENTICAL | Pixelated Physics

Drum Mode Hoodie – SOME DRUMS SOUND IDENTICAL | Pixelated Physics

$54.99 USD
$54.99 USD
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Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
Black
Size
S–5XL
Made
To order · shipping times

A drumhead fixed at its rim can only vibrate in certain shapes. Each one is a Bessel function in radius times a cosine in angle. Mode (3,2) of a circular drumhead, u = J₃(kr) cos 3θ: twelve lobes, three nodal diameters and one nodal ring, exactly. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

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.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

Delivery times & where we ship

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.

Full refund & replacement policy

The physics

A drumhead fixed at its rim can only vibrate in certain shapes. Each one is a Bessel function in radius times a cosine in angle.

This is mode (3,2): cos 3θ gives three nodal diameters, and J₃(kr) with the rim at its second zero, kR = 9.7610, gives one nodal circle inside. The amber and cyan lobes move in opposite directions; the dark lines never move.

In 1966 Mark Kac asked whether you could hear the shape of a drum, that is, whether its set of frequencies fixes its shape. In 1992 Gordon, Webb and Wolpert showed you cannot: two differently shaped drums can have exactly the same frequencies.

A circle is not one of those shapes. Some drums sound identical; this one only sounds like itself.

Rings and spokes of silence.

Equations

\[\nabla^2 u = \frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}\]
\[u(r,\theta,t) = J_3(kr)\cos 3\theta\cos\omega t\]
\[kR = j_{3,2} = 9.7610\]
SymbolMeaningUnit
\(u\) transverse displacement of the membrane \(\mathrm{m}\)
\(c\) wave speed on the membrane \(\mathrm{m/s}\)
\(J_3\) Bessel function of the first kind, order 3 \(\mathrm{1}\)
\(k\) wavenumber \(\mathrm{m^{-1}}\)
\(r, \theta\) polar coordinates on the drumhead \(\mathrm{m, rad}\)
\(R\) drum radius \(\mathrm{m}\)
\(\omega\) angular frequency, ck \(\mathrm{rad/s}\)
\(j_{3,2}\) second zero of J_3 \(\mathrm{1}\)

Sources

  1. Poisson (1829) Mémoire sur l’équilibre et le mouvement des corps élastiques, Mém. Acad. Sci. Paris 8, 357
  2. Rayleigh, The Theory of Sound, Vol. 1 (1877), Ch. IX: Vibrations of Membranes
  3. Kac (1966) Can One Hear the Shape of a Drum?, Am. Math. Monthly 73, 1
  4. Gordon, Webb & Wolpert (1992) One cannot hear the shape of a drum, Bull. Am. Math. Soc. 27, 134
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