• Murmura Whispering Gallery pixel-art physics T-shirt, white tee, front view

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Murmura

The Whispering Gallery Physics

\[2\pi R \approx m\lambda \qquad (m \text{ large})\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Murmura whispers into the wall, and her voice runs all the way round to the far side.

The Physics

In a round gallery, sound clings to the curved wall and travels around it rather than spreading through the space, so a whisper can be heard on the far side. A wave fits around the circle when a whole number of wavelengths matches the circumference. Light does the same in tiny glass rings and spheres.

2πR ≈ m λ

  • R: radius (m)
  • m: whole number of wavelengths (dimensionless)
  • λ: wavelength (m)

Lord Rayleigh explained the whispering gallery of St Paul's Cathedral in 1910; optical whispering-gallery resonators reach Q > 10¹¹.

Honest caveat: It is not an echo: the sound hugs the wall.

On the shirt

Front: Murmura, the pixel-art character, with the title. Back: the resonance condition, the St Paul's story, the optical resonators and Rayleigh's 1910 paper. Printed on a unisex tee.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

पैमाने के लिए: साइज़ M की चौड़ाई 20 in (50.80 cm) है, यानी लगभग 3.143 × 1034 प्लांक लंबाई (lP = 1.616255 × 10−35 m)। इंच-टेप ज़्यादा जल्दी काम करेगा।

Measurements in inches, ±1.5 in tolerance.

ShippingBy destination

Shipping calculated at checkout by destination. Printed to order for you.

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

Whisper into the wall of St Paul's Cathedral and I carry your voice all the way round the gallery to the far side.

It is not an echo bouncing across the dome. The sound clings to the curved wall and creeps along it, so it hardly spreads out and stays loud. Lord Rayleigh explained it in 1910. A wave fits round the circle when a whole number of wavelengths matches the circumference: 2πR ≈ mλ, with m large.

Light does the same trick. Tiny polished rings, discs and spheres of glass or crystal trap light circling just inside their rim, and the best crystalline whispering-gallery resonators reach quality factors above 10¹¹. My gallery is just the big, audible version.

Equations

\[2\pi R \approx m\lambda \qquad (m \text{ large})\]
SymbolMeaningUnit
\(R\) radius of the curved wall \(\mathrm{m}\)
\(\lambda\) wavelength \(\mathrm{m}\)
\(m\) number of wavelengths around the circumference \(\mathrm{1}\)
\(Q\) quality factor of an optical resonator \(\mathrm{1}\)

Sources

  1. Rayleigh (1910) The Problem of the Whispering Gallery, Phil. Mag. 20, 1001
  2. Savchenkov, Matsko, Ilchenko & Maleki (2007) Optical resonators with ten million finesse, Opt. Express 15, 6768
  3. Vahala (2003) Optical microcavities, Nature 424, 839

Field notes

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