# Acoustic resonance

## Main Question or Discussion Point

I am trying to understand the physics of resonance phenomenon. One can find the resonant modes of a water filled spherical cavity either analytically or by using the FEM eigenvalue analysis (K-ω2n M = 0, with K and M being the usual stiffness ans mass matrices in FEM). For the later, we usually set u=0 (Dirichlet bc) or du/dn=0 (Neumann bc) and depending on the boundary condition, the mode shapes and modal frequencies will change.

Let the set of natural frequencies of water filled balloon obtained by this process be denoted as ωn. Now, consider the water balloon to be placed in air and assume I have an acoustic source outside balloon that emits acoustic waves of a frequency that matches with one of the frequencies from the set ωn.

Would this cause the water inside the balloon to resonate at the applied frequency (since it matches with one of its natural frequencies)? My understanding is, once you place the water filled balloon in air, the boundary condition at the interface is no longer u=0 or du/dn=0. So the natural frequencies obtained earlier are no longer correct in this situation.

Alternatively, how can one find the natural frequencies of fluid filled cavities that are embedded inside another fluid with different density and sound speed? Appreciate any comments or answers.

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I am trying to understand the physics of resonance phenomenon. One can find the resonant modes of a water filled spherical cavity either analytically or by using the FEM eigenvalue analysis (K-ω2n M = 0, with K and M being the usual stiffness ans mass matrices in FEM). For the later, we usually set u=0 (Dirichlet bc) or du/dn=0 (Neumann bc) and depending on the boundary condition, the mode shapes and modal frequencies will change.

Let the set of natural frequencies of water filled balloon obtained by this process be denoted as ωn. Now, consider the water balloon to be placed in air and assume I have an acoustic source outside balloon that emits acoustic waves of a frequency that matches with one of the frequencies from the set ωn.

Would this cause the water inside the balloon to resonate at the applied frequency (since it matches with one of its natural frequencies)? My understanding is, once you place the water filled balloon in air, the boundary condition at the interface is no longer u=0 or du/dn=0. So the natural frequencies obtained earlier are no longer correct in this situation.

Alternatively, how can one find the natural frequencies of fluid filled cavities that are embedded inside another fluid with different density and sound speed? Appreciate any comments or answers.
To find resonance frequencies for external excitation (maximal amplitude at boundary), you basically should replace 0-th order spherical Bessel function j0(r) for 1st order j1(r)