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

[confusedbyphysics]

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.

 

[mezarashi]

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.

 

[quicknote]

I would start by gathering more information about the coffee and the cup. This would include the density of the coffee, the material and shape of the cup, and the amount of coffee in the cup. I would also consider the temperature and viscosity of the coffee, as these factors can affect the speed of waves in a fluid.

Once I have all of this information, I would use the formula for wave speed in a fluid that you mentioned (v = √(bulk modulus/density)) to calculate the speed of the waves in the coffee. The bulk modulus is a measure of how resistant a substance is to compression, and can be calculated using the Young's modulus (a measure of stiffness) and the Poisson's ratio (a measure of how a material deforms under stress).

However, it is important to note that this formula assumes small, uniform waves in a homogeneous fluid. In the case of a sloshing cup of coffee, the waves may be larger and more complex, and the coffee may not be completely homogeneous. This could affect the accuracy of the calculation.

Another approach could be to use high-speed video footage of the coffee spilling over to measure the distance and time it takes for the waves to travel from one side of the cup to the other. This could give a more precise measurement of the wave speed in this specific scenario.

In any case, it is important to remember that the speed of the waves in a cup of coffee spilling over is not a constant value, as it can vary depending on the factors mentioned above. It is also worth noting that the speed of the waves may not have a significant impact on the overall spilling process, as the motion of the cup and the viscosity of the coffee are likely more important factors.