Sound of Cocoa

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What better way to wind down after a long hard winter’s day than by slumping into your favourite chair with your hands wrapped snugly around a nice warm mug of hot chocolate? Today we will be looking at something coined as the ‘hot chocolate effect’. And no, this is not the amazing effect it has on your taste buds and mood, although that can be considered equally as fascinating.

Just before the Christmas of 1974, a Frank Crawford was sharing a hot chocolate with a friend when they noticed something rather odd about the sounds made when they tapped their spoons on the inside of the mug. As they stirred the chocolate powder into the hot milk, the pitch of the spoon clinks became progressively higher, with no apparently relation to the speed or force of tapping. As a physicist, he decided that the most intuitive thing to do would be to conduct a formal investigation and write a paper on the effect.

Unfortunately, it seems that it is not the inherent magical nature of hot cocoa powder that contributes to this phenomena. Apart from adding a heavenly sweet flavour to your milk, stirring in hot cocoa powder also adds bubbles, which are trapped between the particles of the powder. The speed of sound in a fluid v is dependent on its mass density ρ and its bulk modulus K, which describes how compressible that substance is.

{displaystyle v={sqrt {frac {K}{rho }}}}

Although the addition of air bubbles does not change the liquid’s density by a significant amount, air is approximately 15,000 times more compressible than water, which means that the speed of sound in the liquid becomes greatly reduced. For a given volume of liquid the wavelength is constant, so the frequency of the sound decreases with the bubbles. Frequency and pitch are essentially the same thing, and therefore we hear a lower pitched sound after adding the powder.

After the initial mixing in of the air bubbles and the powder is stirred, the bubbles get released from their chocolatey trap and rise to the liquid surface. As this happens and there become fewer bubbles in the hot chocolate over time, the speed of sound in the mug increases again, causing the pitch to increase until equilibrium is reached.

The key to this effect are the bubbles that change the speed of sound in the fluid, so it turns out that similar effects can be reproduced with bubbles in cold beer for example, although the quality of sound is supposedly different. This varying sound profile for different solutes and solvents potentially allows them to be differentiated, and a technique has recently been developed in analytical chemistry known as broadband acoustic resonance dissolution spectroscopy.

The next time you fancy yourself a cuppa to warm the soul, go ahead and give this experiment a try. Of course we all know you’re doing it for the science and not for the hot chocolate… don’t forget the obligatory whipped cream and marshmallows!

Harvey

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