Bessel functions, acoustics circular room

[erwinscat]

Hi everybody !

Maybe this post should go under partial differential equations but I'm not sure...

I have the following problem and I would like to know if someone could give me some hints or something to read related to this.

I'm studying multiple reflections of acoustics waves in a circular room and I'm trying to find the modes of this system. I know (but still have to fully understand how and why) that the solution of this problem is given by the Bessel functions.

I would like to be able to plot these functions in Matlab or actually have a plot of the modes pattern in the room .

Any ideas of how I could do this ? Any help would be very much appreciated!

Thanks a lot in advance !
Erwin

 

[Born2bwire]

If you solve the scalar wave equation due to an infinite line source, you'll find that the solution is a Bessel function (or more generally a Hankel function). A Bessel function represents a traveling cylindrical wave. It is just like as if you solved for the traveling wave due to a sheet source (plane wave) or a point source (spherical wave). So with a circular room, using a Bessel function will make it easier to match the boundary conditions because it will probably be dependent upon \rho (or in the case of a traveling wave, the product of the wave number and \rho). Thus, a Bessel function is a natural basis to work with because it represents a traveling wave and it will uniformly satisfy the boundary conditions in the room. Of course the specific Bessel functions and modes will be dependent upon the actual differential wave equation that you have.

Matlab has a family of functions for calculating the Bessel functions. Take a look at the help, besselj is for Bessel functions, besselh is for Hankel functions, and I think maybe it's bessely for Neuman functions. You can find a brief discussion of the differential equation that the Bessel functions solve in Abramowitz and Stegun as well as plots and ways to calculate them (but use Matlab).

 

[erwinscat]

Hi Born2bwire,

thanks a lot for the explanation it does clear my mind. OK, I'll try to find the solutions and see if I manage to plot them in Matlab.

Erwin