steaming milk

The hot chocolate effect

hot chocolate effect, Raphas

A ready prepared hot chocolate

This is an effect that reveals how sound travels in liquids. It enables us to understand the milk steaming process involved in making lattes and yet, it can be studied in your kitchen. It has an alternative name, “The instant coffee effect”, but we won’t mention that on this website any further. To study it you will need,

1) a mug (cylindrical is preferable),
2) some hot chocolate powder (no, instant coffee really will not do even if it does work)
3) a teaspoon
4) a wooden chopstick (optional, you can use your knuckle)

Make the hot chocolate as you usually would and stir. Then, remove the spoon and repeatedly tap on the bottom of the mug with the wooden chopstick (you could instead use your knuckle). Over the course of about a minute, you will hear the note made by the chopstick rise (not having a musical ear, I will have to trust that this can be by as much as three octaves).

resonator, mouth organ

The length of the pipes in this mouth organ determine the note heard. Photo © The Trustees of the British Museum

What is happening? Well, just like an organ pipe, the hot chocolate mug acts as a resonator. As the bottom surface of the hot chocolate is fixed in the mug and the top surface is open to the air, the lowest frequency of sound wave that the hot chocolate resonator sustains is a quarter wavelength. The note that you hear depends not just on the wavelength, but also on the speed of sound in the hot chocolate, and it is this last bit that is changing. When you put in the water and stir, you introduce air bubbles into the drink. With time (and with tapping the bottom surface), the air bubbles leave the hot chocolate. The speed of sound in a hot chocolate/air bubble mixture is lower than the speed of sound in hot chocolate without air bubbles. Consequently, the frequency of the note you hear is higher in the hot chocolate without bubbles than in the former case.

Let’s use this to make a prediction about what happens when a barista steams milk ready for a latte. At first, the steam wand introduces air and bubbles into the mixture but it is not yet warming the milk considerably. From above, we expect that the speed of sound will decrease as the bubbles are introduced. This will have the effect of making the ‘note’ that you hear on steaming the milk, lower. At the same time the resonator size is increasing (as the new bubbles push the liquid up the sides of the pitcher). This too will act to decrease the note that is heard as you steam (though the froth will also act to damp the vibration, we’ll neglect this effect for the first approximation). At a certain point, the steam wand will start to heat the milk. The speed of sound increases with the temperature of the milk and so the note will get higher as the milk gets warmer.

So this is my prediction, musically inclined baristas can tell me if there is any truth in this:

1) On initially putting the steam wand into the cold milk, the tone of the note heard as the milk is steamed, will decrease.
2) This decrease will continue for some time until the milk starts to get warm when the note increases again.
3) Towards the end of the process, the note heard on steaming the milk will continue to increase until you stop frothing.
4) It should be possible, by listening to the milk being steamed, to know when the milk is ready for your latte just by listening to it (if you are experienced and always use similar amounts of milk per latte drink).

So, let me know if this is right and, if it is wrong, why not let me know what you think is happening instead. I’d be interested to know your insights into the hot chocolate effect in a milk pitcher.