# Loudspeaker Directivity Pattern for Beamforming

Can anyone explain me the equations regarding the Directivity Pattern of a Loudspeaker so that I can work on it's beamforming.Thank You.

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Bobbywhy
Gold Member
prusaga, Welcome to Physics Forums! No one will spoon-feed anyone else here, you have to read up/study some first, then ask your specific questions. Here are some websites you can visit to get ideas about what others are doing in this area.

www.isca-speech.org/archive_open/archive.../odys_101_p.pdf [Broken]
http://users.cecs.anu.edu.au/~williams/papers/P166.pdf
www.aes.org/.../loudspeakerarraysforfocusinganddiffusingsound.pdf [Broken]

I especially liked the last one. As soon as you have some doubts or specific questions, come right back here and members will help guide you on your way to knowledge!
Cheers,
Bobbywhy

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Welcome to physics forums ........ None of those links worked for me...... You will definitely not be 'spoon fed' anything here!
Do you know anything about diffraction?

Thank You.........Yea i'm definitly going to work on this topic.........Yes i have the idea about the phenomenon of Diffraction in waves.....The thing i am not understanding is how is the Directivity pattern of Loudspeaker system be expressed.Thank You

sophiecentaur
Gold Member
Have you Googled "Loudspeaker directivity pattern", for a start? Except at high audio frequencies, loudspeakers tend not to very directive (they are small compared with most audible wavelengths).
The same principle applies to beam forming with loudspeakers as with radio antennae and the general principle is probably more widely described in the context of antennae - if you want to read round the general idea. There are many designs of antennae, from medium frequency up to microwaves, which use beam forming. There is one serious problem in achieving this with sound and that is the fact that audible sound covers many octaves of frequency whereas there are only a few RF examples where an antenna needs to operate over as much as one octave, even.
Yes i have the idea about the phenomenon of Diffraction in waves
You need some specific knowledge rather than "an idea" because the whole thing is pretty mathematical - particularly if you want to do your own experimenting.

BTW, are you having a problem with the way directivity patterns are displayed? The display can be either cartesian or polar, with the sound level expressed in dB, relative to maximum plotted against angle. Sometimes, phase may also be plotted - but one thing at a time, I think. If you can't find many pictures of this then look at "antenna directivity patterns" for loads of example images. Why dB? Because they need to cover such a wide range of values and a log scale does this very well.

Yes I have understood the frequency response to the directivity of a loudspeaker and its dimensions......but my doubt is if we have a system or array of loudspeakers(knowing the Q value) can we predict a reasonable directivity pattern and precisely by the equations.In the first case ignoring and in the 2nd case considering the room effects and hw to take them into account...Thank You

sophiecentaur
Gold Member
Could you tell me where "Q" comes into this? There need be no resonance, whatsoever, in a directive array of loudspeakers or antennae.

Q (Directivity index) would help analysing from the point of view of each speaker of the array.

Can anyone help to see how a resonance condition is possible in the sound produced from a loudspeaker array and would it depend on the acoustics of the room.Thank You

sophiecentaur
Gold Member
Thanks for that. In my experience, "Q" stands for the quality factor of a resonator - (related to fractional bandwidth). You live and learn.
To find the directivity of an array would need more than a single figure to describe the directivity pattern of the individual loudspeaker elements - particularly if they are not all parallel. Also, the presence of reflective walls in a room makes the problem even worse. I should think that the only approach that could be used in that case would have to be by simulation.
I was assuming that your array could be modelled analytically as a linear array of radiators with known polar pattern and the contributions from each radiator could then be added vectorially at any point in space to give a resultant sound vector (just an extension of the Youngs Slits interference calculation). Far field could be simpler but near field would not be too hard. Introducing the effect of reflecting surfaces would mean a much more complicated treatment if you wanted a reliable result.

sophiecentaur
Gold Member
Can anyone help to see how a resonance condition is possible in the sound produced from a loudspeaker array and would it depend on the acoustics of the room.Thank You
The room dimensions could easily have a profound effect on resonances and that could, in turn, have a huge effect on the apparent directivity of an array at different points in the room. By that, I mean that, rather than producing a simple polar directivity pattern, you would get a response in the room that would be a three dimensional standing wave pattern, which varies with frequency. This 'colouration' is guaranteed to upset any directional information that a listener could get from an array.
Perhaps it would be a good time to explain what you want in more detail and where directionality comes into the system.

Hi all, i am new here. Actually I am readings something about the loudspeaker array applications. Now I am totally confused about the different terms for loudspeaker array applications. Can anyone tell me the difference?

loudspeaker array directivity vs loudspeaker array directivity pattern vs loudspeaker array beamforming vs loudspeaker array beamshaping

Bobbywhy
Gold Member
ezlink, Welcome here to Physics Forums! Will you please read post #2 above? The correct acoustic engineering terminology is absolutely necessary to communicate about this exciting field. You can't get it all in just a few posts here; it's a step-by step process that you need to go through.

Specifically, learn to use Google to search for your terms. Google is your friend. Here are a few examples found in a few minutes:

http://www.mcsquared.com/speakers1.htm
http://en.wikipedia.org/wiki/Directional_sound
http://en.wikipedia.org/wiki/Beamforming

Note about studying Wiki pages: once you read through the whole page and decide that you have grasped all the ideas, concepts, and processes then have a look at the sections near the bottom called “See Also”. For example, on the Beamforming page there is a list of twelve separate beamforming solutions, all hyperlinked. Then there is a list of twelve additional “Related Issues” for a more thorough explanation. Then notice the list of “References”. These give you the chance to explore the source material for the Wiki page itself.

Now, after you have studied the basic terminology on your own, when you have some specific question or doubt, then do come right back here and post it. Members here are always willing to assist others on their way towards more scientific knowledge.

Cheers,
Bobbywhy

Can anyone explain me the equations regarding the Directivity Pattern of a Loudspeaker so that I can work on it's beamforming.Thank You.
p(r,θ,t)=j/2 ρ_0 c U_0 a/r ka[(2J_1 ka sinθ)/(ka sinθ)] e^j(ωt-kr)

This will give you pressure at a point (r,θ,t) from the source if you calculate this for the 180 degrees in one plane of a loudspeaker you will be able to get the polar directivity pattern. The e.q. is from kinsler and frey 'fundamentals of acoustics' chapter 7 might be available on google books, if so that's what you want and will give more detail on how to use the above equation (beyond the scope of a PF post to be honest). You can use it to model arrays then use phase differences in each piston of the array to create a beam, the direction of which can be varied by adjusting the relative phase of the speakers.

Ben.

If its a big problem get in touch and I can probably send you some matlab code that will model piston directivity etc from an old assignment I did at university.

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sophiecentaur