Coffee cup physics

I’ve noticed that when I get a cup of coffee out of our machine, and walk with it back to my office, the small amount of froth on it can start forming patterns. A stripy one is quite common – I get alternate stripes of froth and no froth – maybe about six stripes in total. I strongly suspect that what is happening here is that as I walk, I set up a standing wave across the surface of the cup, and the froth gets pushed to those places where the water is moving the least (the nodes between the crests and the troughs of the waves).

A ‘standing wave’ is a wave that doesn’t go anywhere. A good example is a wave on a vibrating guitar string – since the string is fixed at both ends, if you create a disturbance on it by plucking it, the disturbance can’t escape – it just bounces back and forth – the resulting wave therefore goes nowhere. In the case of the guitar string, the wave’s frequency (i.e. what tone it makes) depends on the length of the string, and its tension. In the case of my cup of coffee, I would expect the diameter of the cup to be important, plus the surface tension of the coffee (which depends a lot on temperature). Would make a nice little science fair investigation, I think.

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