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The same feedback causes dangerous combustion instability in rocket engines and gas turbines.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ef ≈ c \/ 2L   (loudest with the gauze at about L\/4 from the bottom)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ef: tone frequency (Hz)\u003c\/li\u003e\n\u003cli\u003ec: speed of sound in the warm air (m\/s)\u003c\/li\u003e\n\u003cli\u003eL: tube length (m)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eRijke, Ann. Phys. 183, 339 (1859); Rayleigh, “The explanation of certain acoustical phenomena”, Nature 18, 319 (1878).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e c is the warm-gas value, so the pitch depends on how hot the air is. Rijke used a hot gauze, not a flame; flame versions are variants.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Rijka, the pixel-art character, with “SINGING HEAT”. 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The pitch is set by its radius, which is why streams babble.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ef = (1 \/ 2πa) √(3γp \/ ρ)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ef: resonant frequency, Hz\u003c\/li\u003e\n\u003cli\u003ea: bubble radius, m\u003c\/li\u003e\n\u003cli\u003eγ: heat capacity ratio (air 1.4), dimensionless\u003c\/li\u003e\n\u003cli\u003ep: ambient pressure, Pa\u003c\/li\u003e\n\u003cli\u003eρ: water density, kg m⁻³\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eAir in water at 1 atm: f·a ≈ 3.3 m\/s. A 1 mm radius bubble sings near 3.3 kHz.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Small bubbles are closer to isothermal and surface tension matters, so the formula is best for millimetre-size bubbles.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\u003cli\u003eM. Minnaert, Phil. Mag. 16, 235 (1933).\u003c\/li\u003e\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 090, “Minnaert's Bubble”: the pixel-art plate with its slogan “Every bubble sings at a pitch set by its size.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50962700075111,"sku":"32400206308754389700","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50962700107879,"sku":"81979924227408173038","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50962700140647,"sku":"20939112476611483081","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50962700173415,"sku":"18427593086877483084","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50962700206183,"sku":"30799939780649391523","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50962700238951,"sku":"27624214185059955563","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50962700271719,"sku":"86420850020081416618","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50962700304487,"sku":"25739408951159654763","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50962700337255,"sku":"25235784745846826793","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/5798398100366943536_2048.jpg?v=1793734582"},{"product_id":"the-shadow-zone-plate-092-physics-poster","title":"The Shadow Zone – Plate 092 Physics Poster","description":"\u003cp\u003ePlate 92 speaks for itself: \u003cem\u003e“Earth's centre was found in the waves that weren't supposed to arrive.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eSeismic waves bend at the boundary of Earth's liquid outer core, leaving a shadow zone. Lehmann noticed faint waves inside it in 1936 and deduced a solid inner core.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003en₁ sin θ₁ = n₂ sin θ₂\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003en₁, n₂: slowness (1\/wave speed) in each layer, s m⁻¹\u003c\/li\u003e\n\u003cli\u003eθ₁, θ₂: angles to the boundary normal, rad\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe liquid outer core leaves a shadow ≈ 104°–140°. Inner core ≈ 1220 km; outer core ≈ 3480 km.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eI. Lehmann, Publ. Bur. Cent. Séismol. Int. A14, 87 (1936).\u003c\/li\u003e\n\u003cli\u003eA. M. Dziewonski, D. L. Anderson, PREM, Phys. Earth Planet. Inter. 25, 297 (1981).\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 092, “The Shadow Zone”: the pixel-art plate with its slogan “Earth's centre was found in the waves that weren't supposed to arrive.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50962701942887,"sku":"23706910525057674688","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50962701975655,"sku":"10759199212023109654","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50962702008423,"sku":"10928014650579276737","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50962702041191,"sku":"20975987660686889096","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50962702073959,"sku":"21680478506027920660","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50962702106727,"sku":"25055280941296365037","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50962702139495,"sku":"27583910969000639543","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50962702172263,"sku":"83633472131909275643","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50962702205031,"sku":"30213284813350226826","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/4986255583241389074_2048.jpg?v=1793734711"}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/collections\/waves-and-optics.png?v=1793678032","url":"https:\/\/pixelatedphysics.com\/pt\/collections\/waves-and-optics\/domain:quantum.oembed?page=2","provider":"Pixelated Physics","version":"1.0","type":"link"}