Speaker directivity

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Provided that the model for a circular piston-type radiator is an adequate
tool for measuring the directivity of normal home or monitor speakers, how
does one calculate an approximation of how the different frequencies are
spread from the speaker cone?
Is there any easy way of doing that, since I consider myself as a
mathematically semi-challenged person? <g>

I know the directivity is a by-product of the speaker cone's radius,
however, some people say that "the radius of the cone must be at least 1/4th
of the frequency's wavelenght in order for it to not radiate it
spherically", while others say that the truth is closer to a situation where
a normal speaker cone's radius has to be almost as large as the wavelenght
itself in order for it to prevent radiating the frequency in all directions.

Thanks for all the answers.

Archived from groups: rec.audio.pro,rec.audio.tech (More info?)

On Mon, 19 Apr 2004 01:44:07 +0300, "Tommi" <tommiwide@suomi24.fi>
wrote:

>Provided that the model for a circular piston-type radiator is an adequate
>tool for measuring the directivity of normal home or monitor speakers, how
>does one calculate an approximation of how the different frequencies are
>spread from the speaker cone?
>Is there any easy way of doing that, since I consider myself as a
>mathematically semi-challenged person? <g>
>
>I know the directivity is a by-product of the speaker cone's radius,
>however, some people say that "the radius of the cone must be at least 1/4th
>of the frequency's wavelenght in order for it to not radiate it
>spherically", while others say that the truth is closer to a situation where
>a normal speaker cone's radius has to be almost as large as the wavelenght
>itself in order for it to prevent radiating the frequency in all directions.

Try to find a copy of Martin Colloms' High Performance Loudspeakers,
which contains all the information most people will ever need about
loudspeakers.
--

Stewart Pinkerton | Music is Art - Audio is Engineering

Archived from groups: rec.audio.pro,rec.audio.tech (More info?)

"Chris Berry" <christoforos@Notmail.com> wrote in message
news:c60hi1$6gv$05$1@news.t-online.com...
> It depends on a few assumptions....
> What you mean by non-directional and what is satisfactorily
> non-directional.... are you refering to 45 degrees off axis? more? less?

I guess my practical purpose is to find an equation for determining a
"directional" frequency for a given speaker, in its widest sense; that being
something like much over 100 degrees off axis.
Say I have a cone with a 6" radius back against a wall. How do I calculate,
roughly at which frequency it starts to radiate sound to the back?

Archived from groups: rec.audio.pro,rec.audio.tech (More info?)

"Tommi" <tommiwide@suomi24.fi> wrote in message news:<KoDgc.2394$YN7.314@reader1.news.jippii.net>...
> Provided that the model for a circular piston-type radiator is an adequate
> tool for measuring the directivity of normal home or monitor speakers, how
> does one calculate an approximation of how the different frequencies are
> spread from the speaker cone?
> Is there any easy way of doing that, since I consider myself as a
> mathematically semi-challenged person? <g>
>
> I know the directivity is a by-product of the speaker cone's radius,
> however, some people say that "the radius of the cone must be at least 1/4th
> of the frequency's wavelenght in order for it to not radiate it
> spherically", while others say that the truth is closer to a situation where
> a normal speaker cone's radius has to be almost as large as the wavelenght
> itself in order for it to prevent radiating the frequency in all directions.
>
> Thanks for all the answers.

You might want to try to simulate it numerically. Spread out a number
of point sources over the piston surface and take the different
source-listener distances into consideration for the different
listening positions. Complex math is the key to doing the addition of
sources manageable.

In the real world, the cone does not behave like a piston, but it
seems as if you have already realised this. In principle, the point
sources could be given different amplitudes and phases to model this
behaviour, but finding out the appropriate phase and amplitude values
will definitely be tricky.

Archived from groups: rec.audio.pro,rec.audio.tech (More info?)

In article <c6190n$3su$00$1@news.t-online.com>,
Chris Berry <christoforos@Notmail.com> wrote:
>> Say I have a cone with a 6" radius back against a wall. How do I
>calculate,
>> roughly at which frequency it starts to radiate sound to the back?
>
>It's only the cabinet resonance that gets radiated to the back so it's a
>pretty moot point.
>The only other way you'll get sound radiated behind the speaker is using
>open back cabs or have something reflect the sound back at the speaker -
>Only the open back cab will do this effectively and then you're stumped for
>high frequencies...

With a monopole speaker the rear output will essentially match the front once
your wavelengths are 3X baffle width, and there's some effect with wavelengths
as short as 1/3 width.

In free-space you get a 6dB drop in on-axis SPL when this happens.

This is why speakers need baffle step compensation.

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Life is a terminal sexually transmitted disease.