Speed of waves in a cup of coffee that spills over, help please

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SUMMARY

The discussion focuses on calculating the speed of waves in a cup of coffee with a diameter of 9 cm when it spills over due to sloshing. The primary formula mentioned for wave speed in fluids is v = √(bulk modulus / density). Participants suggest that the wave peaks created by each step amplify as they reflect back and forth within the cup. The challenge lies in determining the density of coffee and calculating the bulk modulus for accurate results.

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  • Familiarity with the properties of coffee, including its density and bulk modulus.
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Speed of waves in a cup of coffee that spills over, help please!

"When you walk with a cup of coffee (diameter 9 cm) at just the right pace of about 1 step per second, the coffee builds up its "sloshing" until eventually, after a few steps, it starts to spill over the top. What is the speed of the waves in the coffee?"

I would show my work but I have NO clue how to even approach this. Only thing I can think of to use is the longitudinal wave speed in a fluid which is v = square root ( bulk modulus / density). But I don't know density of coffee or how to calculate bulk modulus. Can someone point me in the right direction? Thanks.
 
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My first impression was that you'd use something simpler

Consider a wave peak that is created at the center due to your first step. This wave moves to the edge of the cup, gets reflected back and the peak reaches the center back again just in time for your next step which causes another peak, continually amplifying the wave with each step.

From the known diameter and and assumed waveform/wavelength, you can derive a velocity. That's my idea.
 

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