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I'm interested in performing a speaker simulation to extract an approximate polar pattern for two custom speaker designs.

First design: A half wave pipe (transmission line) subwoofer 24 hz to 56 hz in range utilizing a 12 foot pipe (48 hz resonant frequency at half wave) with one end open and the other end sealed with a woofer (on the outside) aiming toward the open end.

Second design: A more complex version of this device that is available in a few commercial locations. See photo: screencast.com/t/No8YTbMq

Our theory is in the far field this would be a cardioid polar pattern but in the near field the two radiating areas (open pipe end / woofer end) function separately. There is a noticeable delay which is likely 12 ms from 12 ft of distance that could very likely complicate the simulation process.

I am partial to using python libraries for the simulation.

Thank you!

Zhenya Warshavsky
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If you only have one end open and the woofer is in the pipe, there is only one radiation area which is very small compared to the wave length. There is no point in modelling this: it will be omni directional.

EDIT Given the size of the wavelength you can simply model this as two volume velocity point sources that are spatially separated by 12'. The one at the end of the tube has the same absolute volume velocity but it's out of phase and delayed by 12 ms.

Hilmar
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  • The woofer is on the outside of the pipe and the pipe functions as a monopole. There is clearly directionality to this and it is is not omnidirection. Half wave pipes are by their very nature not omnidirectional at resonance. The wave length is half the length of the pipe (12 feet). I am also wanting to model a more complex version of this device that is available in a few commercial locations. See photo: https://screencast.com/t/No8YTbMq – Zhenya Warshavsky Aug 13 '19 at 20:14
  • So you are venting one side of the woofer directly outside and the other side into the pipe? What's your pipe dimensions? Length and diameter? – Hilmar Aug 13 '19 at 20:42
  • Correct. For reference: [link] (https://screencast.com/t/tloy5ttpl). Please also see the description of the second design in the body of main question. Pipe is 12 ft L x 12" diameter. – Zhenya Warshavsky Aug 13 '19 at 20:51
  • Thank you! I've been looking into boundary method simulations. Can you point me to an app or python library for a simple implementation? – Zhenya Warshavsky Aug 14 '19 at 21:27
  • Hi, Hilmar. Any additional info from my previous question would be greatly appreciated. – Zhenya Warshavsky Aug 16 '19 at 14:39