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

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The discussion centers on calculating the speed of waves in a cup of coffee that spills over when walked with at a specific pace. A participant suggests using the formula for longitudinal wave speed in fluids, v = square root (bulk modulus / density), but struggles with determining the density and bulk modulus of coffee. Another contributor proposes that the wave peaks created by each step reflect back and amplify with each subsequent step, indicating a relationship between the cup's diameter and wave velocity. The conversation emphasizes the need for a simplified approach to derive the wave speed based on the cup's dimensions and wave behavior. Understanding these dynamics can help in calculating the spilling point of the coffee.
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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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