|MadSci Network: Physics|
Hi Mike, It's very simple... Imagine a steel cup. The cup is narrower at the base than at the top. It gets broader at the top. When you tap on the bottom you start a wave which rides from the bottom to the top. To the wave, the cup is a multitidue of rings resting on top of one another, the rings get larger at the top. Each ring resonates according to its characteristic frequency, like a guitar string wrapped into a circle. The rising pitch you here is because the rings don't begin to resonate until the wave is moving back from the lip of the cup toward the bottom, having been muted by the liquid when you tapped on the bottom, the outer most ring at the lip of the cup is free to resonate when the wave reaches that point, since it is not muted by liquid. Now that it is resonating, the wave's momentum carries it back down the length of the cup, the pitch rising as the concentric rings get smaller and smaller. The rings resonate now because the wave is organised. The organization of the wave occured at the lip of the cup when it began to resonate. An organized wave can make it back and forth across the muted rings because the energy is directed. You don't hear the traveling wave in an empty steel cup because it is not muted by the liquid, all of the tones come out almost simultaneously - so it merely rings with a broad spectrum 'dong.' The viscosity of the liquid determines the speed of which the wave will travel through the rims of the cup, as the energy of the organized wave struggles against the muting liquid. I've actually though about that one breifly while consuming intoxicating beverages of various viscosities in drinking vessels made of different media, varying from glass to ceramic. For instance, a mud slide produces a significantly slower wave in a crystal goblet than does red wine. Scotch is even faster yet. As for stirring, and all of that - just try imagining the effect that the motion of the liquid has on the energy of the wave. In some cases you can actually generate a standing wave by the energy of the rotating liquid, but be careful not to let the liquid 'wobble' inside the vessel, as this will produce an additional muting effect. In general, if the liquid travels up the sides of the wall of the cup while stirring, all but the highest part of the rim will be muted, and a low pitch will result. As the liquid slows, it comes back down the inside of the cup, freeing the higher pitched rings to resonate - a resulting rise in tone should be heard.
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