AES Journal Forum

Hi Jeff Candy.

Thank you for writing an AES article related to loudspeakers. I received the JAES for June 2013 today and immediately read your article and I find your article very interesting, including the approach to handling diffraction as well as the multitude of valuable information gained (including off-axis response + the radiation impedance on the transducer itself).

At low frequencies it is well known that the SPL doesn't drop as much as the commonly mentioned 6 dB. Furthermore it is well known that room gain isn't as much as you would think either. Although I haven't tested your method yet, it seems that the information gained at low frequencies provide good insight into room gain aspects as well (I'm well aware that the situation in a specific room is dominated by a specific vibration mode) and could be helpful for loudspeaker system designers.

P.S. Only a few software packages exist that I know of, which is commercially available and which will simulate radiation behind the speaker and also document the influence from rear edges of the box onto the on-axis response. One such software is LEAP EnclosureShop V5. The manual can be found on the internet (at www.linearx.com). The exact method in EnclosureShop is not publicly available. I appreciate that you describe clearly with a recipe how to complete the calculations and thereby provide a publicly available method for such simulations.

Hello Claus,

Thanks for the clarifications and comments.  Yes, nearby reflecting surfaces can be treated with MFS.  A trivial example is woofer floor-bounce, which can be solved using the method of images (i.e., place a mirror-image of the loudspeaker under the floor).   I have tried this and it appears to work correctly.   A more challenging and general approach is also possible, in priciple, whereby sources can be placed not only inside the loudspeaker but also just outside the walls of the room to enforce the boundary conditions (zero normal velocity) on all reflecting surfaces.  I have not tried this, and my guess is that it would have more severe high-frequency limitations (due to matrix condition number problems) than the case of an isolated loudspeaker.  But yes, in principle, the effect of walls, cone geometry, bizzare enclosure shapes, are treatable.  Before I would embark on these more advanced applications, however, I would improved the algorithm for source placement so as to reduce the matrix condition problems.  Source placement is critical to the success of the method.  Another alternative would be to use quad precision arithmetic. 

Regarding LEAP, I am sorry if I mischaracterized the most up-to-date algorithm.  I did not know the BTM method had been implemented.  This is certainly not a high-frequency asymptotic method like ray tracing.  My limited understanding of BTM is that solutions are exact only for certain geometries, but I am afraid I cannot comment further.  The litmus test of course is to carry out a benchmark, and for that I suggest Chris S. might simulate the case shown in Fig. 2 of the paper with LEAP.  Here the gain is much less than 6dB.  

Finally, thanks very to Peter for his clarifications.  I would be happy to spend some time on a benchmark of MFS versus the integral formulation of BTM you describe.  I have the feeling that a hybrid method might be optimal: MFS at low frequency where the method is well-conditioned and BTM at higher frequency where it must be far more efficient than MFS.

Shall we continue this discussion via email?  I would prefer that.

Hello, 

Very good paper!. Congratulations! 

For an example of application to horns you can see 

L. Godinho, J. Ramis, W. Cardenas, J. Carbajo, P. Amado Mendes - A numerical MFS

model for computational analysis of acoustic horns. Acta Acustica united with Acustica 98,

916-927, 2012.

PS: I can send the paper by e-mail. I am a co-author