Hot chocolate effect

The Hot Chocolate Effect is a phenomenon of wave mechanics first documented in 1982 by Frank Crawford, where the pitch heard from tapping a cup of hot liquid rises after the addition of a soluble powder. It typically arises in the making of hot chocolate or instant coffee, but also occurs in other situations such as adding salt to supersaturated hot water or cold beer.

It can be observed by pouring hot milk into a mug, stirring in chocolate powder, and tapping the bottom of the mug with a spoon while the milk is still in motion. The pitch of the taps will increase progressively with no relation to the speed or force of tapping. Subsequent stirring will gradually decrease the pitch again.

The phenomenon is explained by the effect of bubble density on the speed of sound in the liquid. The note heard is the frequency of a standing wave where a quarter wavelength is the distance between the base of the mug and the liquid surface.

This frequency f is equal to the speed v of the wave divided by four times the height of the water column h:

f = 0.25\frac{v}{h}

Upon initial stirring, entrained gas bubbles reduce the speed of sound in the liquid, lowering the frequency. As the bubbles clear, sound travels faster in the liquid and the frequency increases.

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