Cavity resonances between two long parallel plates

[nawidgc]

Consider two rigid and infinitely long parallel plates (say they are of infinite length in X direction, so running from -inf to +inf in X axis) separated by a distance d (say measured in Y-direction). Let the space between the plates be filled up with a fluid that supports acoustic waves. If we somehow setup the resonance of acoustic wave, the wavelengths corresponding to successive resonant modes are:

λ1 = 2d/1
λ2 = 2d/2
λ3 = 2d/3
and so on.

How does the wavelength change when the plates are no longer of infinite extent in X-direction? If the dimension in X-direction is of the same order as d, what effect would this have on the resonant frequencies/wavelengths?

 

[Paul Colby]

The boundary conditions will be changed. There are now edges or interfaces normal to x. What are these boundary conditions on these surfaces?

 

[nawidgc]

The surfaces normal to the x-direction are open to air outside whereas the plates themselves are rigid (normal component of particle velocity = 0).

 

[BvU]

And that air is a different fluid than the fluid between the plates ?

 

[nawidgc]

No - the medium between the plates and outside is the same, i.e., air.

 

[nawidgc]

And that air is a different fluid than the fluid between the plates ?

i suppose a normal mode analysis would not be useful as the cavity is not completely enclosed.

 

[nawidgc]

And that air is a different fluid than the fluid between the plates ?

 

[Paul Colby]

You will have radiation losses.

 

[nawidgc]

You will have radiation losses.

Of course. So in that case, i would need to assume appropriate boundary condition at the exit surfaces of domain and compute the normal modes.

 

[Paul Colby]

Of course. So in that case, i would need to assume appropriate boundary condition at the exit surfaces of domain and compute the normal modes.

Depending on what accuracy you wish, yes. I would expect the geometry shown will have strong coupling to the outside world which will wash out the resonances. You might get some indication by assuming a perfectly absorbing x-boundary.