A microscopic modeling of the instant coffee effect

So-called the instant coffee effect is well known in the field of the physics education. The effect is explained that the sound yielded by touching the cup with a spoon is shifted to low-pitched by adulterating bubble owing to putting a spoon of instant coffee into hot water. The phenomenon has been interpreted with the averaged density and compressibility of the fluid in the macroscopic relation for the sound velocity, ν = √(κρ)^-1. We introduce the linear coupled oscillator model with finite oscillators including the impurity air-mass oscillator. The model may well reproduce the increase in the shift of the eigen frequency accompanying with the amount of bubble.