The Science Behind Ripples in a Moving Cup

[bbjs]

Hello members!

I was dining at Tin Star and I noticed very fast, centralized ripples when sliding my cup across the table... is this a simple phenomenon or is there a basic law I am missing here? http://youtu.be/jmf21UBXMnk

 

[DrClaude]

Hi bbjs, wecome to PF!

You're simply exciting modes of vibration of the surface of the water. It's not much different from plucking a guitar string or, better analogy, hitting a drum.

 

[94JZA80]

notice in the video that the cup does not slide smoothly across the surface of the table. the cup is sticking to the table, then losing its grip, and then sticking again after having moved a certain distance...and this process keeps repeating itself so long as someone or something applies a continuous force to the cup (thus imparting a particular velocity to the cup as it "slides" along). increase the force applied to the cup, and its velocity across the surface of the table increases, as does the frequency of the vibrations caused by the cup's "sticking and releasing" as it slides along. it is these vibrations that make the concentric ripples on the surface of the water in the cup. b/c the entire bottom of the cup sticks and releases at the same time, the vibrations work their way through the cup symmetrically, resulting in symmetric ripples on the surface of the water in the cup.

 

[DrClaude]

b/c the entire bottom of the cup sticks and releases at the same time, the vibrations work their way through the cup symmetrically, resulting in symmetric ripples on the surface of the water in the cup.

I don't think one can assume that the vibrations are uniform in the cup.

 

[94JZA80]

I don't think one can assume that the vibrations are uniform in the cup.

quite right...i should have been more specific in my description and said that the vibrations are approximately uniform such that the ripples on the surface of the water approximately represent concentric circles.

surely there is some flex and deformation in the bottom of the cup as it "skips" along the table b/c it is far from rigid...but, as evidenced by the surface ripples themselves, the duration of the cup's deformation and journey back to equilibrium during each "skip" is small enough (and happens quickly enough) that the individual vibrations imparted by each skip travel up the sides of the cup approximately in sync, causing ripples on the surface to approximate the appearance of concentric rings. I'm sure if we could decrease the frequency of the skips and slow down the vibrations enough, we could more easily track the movement of the surface ripples with the naked eye...and perhaps we could see some parts of each ring reach the center sooner than other parts - a giveaway that, as you pointed out, the vibrations aren't truly uniform.