# Bessel functions, acoustics circular room

• erwinscat
In summary, the conversation revolves around the topic of multiple reflections of acoustic waves in a circular room and the use of Bessel functions to find the modes of this system. The person is seeking advice and resources for solving the problem and plotting the functions in Matlab.
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

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).

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

## 1. What are Bessel functions?

Bessel functions are a type of special mathematical functions that are used to solve linear differential equations. They are named after the mathematician Friedrich Bessel and are commonly used in physics, engineering, and other scientific fields.

## 2. How are Bessel functions used in acoustics?

Bessel functions are used in acoustics to describe the behavior of sound waves in a circular room. They are used to calculate the sound pressure level and the distribution of sound energy in the room.

## 3. What is the relationship between Bessel functions and circular room acoustics?

Bessel functions play a crucial role in circular room acoustics because they represent the standing waves that are formed when sound waves bounce off the walls of a circular room. These standing waves determine the overall sound quality in the room.

## 4. How do Bessel functions affect the acoustics of a circular room?

The values of the Bessel functions affect the amplitude and phase of the sound waves in a circular room, which in turn affect the sound pressure level and distribution of sound energy. Different values of the Bessel functions can result in different acoustic characteristics in the room.

## 5. What are some applications of Bessel functions in circular room acoustics?

Bessel functions are commonly used in the design and analysis of circular concert halls, theaters, and other performance spaces to ensure optimal acoustics. They are also used in noise control and sound engineering to improve the sound quality in circular rooms.

• MATLAB, Maple, Mathematica, LaTeX
Replies
5
Views
1K
• Differential Equations
Replies
3
Views
2K
• Calculus
Replies
3
Views
2K
• Electromagnetism
Replies
8
Views
3K
Replies
13
Views
2K
• Classical Physics
Replies
3
Views
588
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Other Physics Topics
Replies
1
Views
2K