# Why does a minor vertical vibration cause my coffee to spill?

When I walk my kid sometimes I put a cut of coffee in a cupholder attached to the stroller. When I push the stroller over a brick pavement it seems to vibrate vertically. That is enough for the coffee to spill, even if the cup is only 3/4 full. It looked like waves were forming in the cup, beating its forward and backward sides, and they quickly grew large enough to spill.

Thus the question: is it possible to quantitively estimate the size of the waves caused by the vibration, so that one could figure out the level one can safely fill the cup to?

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Have you tried different speeds? I ask because it could provide a hint. If changing speeds helps it may well be a resonance effect. – dmckee Jul 20 '14 at 3:14
You could always get a cup with a lid. – LDC3 Jul 20 '14 at 3:15
@LDC3: The cup did have a lid; the coffee spilled through the sipping hole. Regardless of that, I am curious about the physics related to the waves that form inside the cup, even if the answer wouldn't have a practical application. – Michael Jul 20 '14 at 3:34
@dmckee: I did; the spillage occurs even at slow stroller speed. I think it has to do with the hardness of vertical movement, such as a momentary acceleration on the order of g when passing the seem between the bricks, more than the frequency of those vertical movements, and only their frequency depends on stroller speed. – Michael Jul 20 '14 at 3:37