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I am trying to understand the behavior of air when a large, planar object hits a parallel surface at a high velocity, thus forcing the initially static air outwards, and creating a sound wave. This is a simplified version of hands clapping, or of a flip flop hitting the ground.

I'm struggling with finding literature online about this, or how to even properly formulate the problem. Here is my current attempt at describing the setup.

Consider a cylinder with radius $R$ and thickness $h$, with $R>>h$. let the cylinder hit the ground parallel to it at a speed $v >>$ (some characteristic speed, which I would eventually find through an appropriate non-dimensionalization of the problem). Let the space between the cylinder and the ground initially be filled with a gas of density $\rho$ and viscosity $\mu$.

Questions:

  1. What is the mechanism by which the cylinder produces a sound wave?

  2. What is the asymptotic dependence of the amplitude and frequency distribution of sound waves on the radius of the cylinder as $R \rightarrow \infty$?

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  • $\begingroup$ Mildly related: physics.stackexchange.com/q/612624/59023 (i.e., You can do this using just the continuity equation and kinematics if you assume the cylinder is dense enough and heavy enough to ignore air resistance prior to the outflowing air generating a sonic boom) $\endgroup$ Jun 7, 2022 at 13:04

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The basic idea is simply that you need to expel air of volume $\pi h R^2$ through the periphery of area $2 \pi h R$, implying that for a given $\dot{h}$ there's an outflow proportional to $R$ and a corresponding dynamic pressure. In this simple picture, you don't really have a frequency but a single pressure wave emitted whose amplitude is proportional to $R$.

Among limitations of this is that $\dot{h}$ is not independent of $R$. If the surfaces are perfectly no-slip, you would even have a paradox that the cylinder should never touch ground, a paradox which is lifted if you consider a small slip-length.

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