{"product_id":"minnaerts-bubble-plate-090-physics-poster","title":"Minnaert's Bubble – Plate 090 Physics Poster","description":"\u003cp\u003ePlate 90 speaks for itself: \u003cem\u003e“Every bubble sings at a pitch set by its size.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eA gas bubble in water rings like a spring: the gas is the spring and the surrounding water is the mass. 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\/843575811133691644_2048.jpg?v=1793637829","url":"https:\/\/pixelatedphysics.com\/products\/minnaerts-bubble-plate-090-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}