Yes, there is a formula that can be used to estimate the amplitude of air oscillations in a Helmholtz resonator. The Helmholtz resonator is a type of acoustic resonator that consists of a cavity with a small neck or opening. When a sound wave at the resonant frequency of the cavity is incident upon the opening, it can cause the air in the cavity to resonate.
The formula to calculate the amplitude of the air oscillations in a Helmholtz resonator is as follows:
A = P / (ρcAv)
where: A is the amplitude of air oscillations, P is the sound pressure at the opening of the resonator, ρ is the density of the air, c is the speed of sound in the air, and A is the cross-sectional area of the neck or opening of the resonator.
In this formula, the amplitude is directly proportional to the sound pressure and inversely proportional to the density of the air, the speed of sound, and the cross-sectional area of the neck or opening.
It's important to note that this formula provides an estimation and assumes ideal conditions. In reality, various factors such as losses due to viscosity and heat conduction, radiation losses, and non-linear effects can affect the actual behavior of the Helmholtz resonator.