Radiation pattern of point source on a plane

Dumbass · 31st January 2006, 04:14 PM

What is the theoretical radiation pattern of a point source on an infinite plane/baffle?

Is it simply one-half of spherical, or is it more like one-half of a dipole?

gfinlayson · 31st January 2006, 04:30 PM

It should be hemi-spherical.

Dumbass · 31st January 2006, 04:40 PM

Quote:

Originally posted by gfinlayson
It should be hemi-spherical.

That's my initial conjecture but now I'm not so sure.

Consider the unit circle, x^2 + y^2 = 1. If you restrict to upper half, can be represented as a function, y = sqrt (1 - x^2) for x between -1 and 1.

Now double the function, y = 2 x sqrt (1-x^2). Is no longer a semicircle, it is higher in the middle.

I don't know enough about sound and stuff to tell if this is a reasonable way of looking at it.

john k... · 31st January 2006, 04:51 PM

(JPK) If it's a true point source then it is a hemisphere as gfinlayson stated.

SY · 31st January 2006, 04:59 PM

Work backward and you'll see that you've changed the equation into an ellipse. "Doubling" the equation must happen on both sides to be valid.

gfinlayson · 31st January 2006, 05:03 PM

SY is right, you haven't doubled the function. If y = sqrt (1 - x^2), then y cannot also be equal to 2 x sqrt (1-x^2). 2 y can, however, so you still end up with a hemisphere.

Anyway, if you forget the mathematics and use common sense, a true point source radiates in a spherical pattern. So if you stick it onto an infinite plane it can only radiate in a hemi-spherical pattern.

Dumbass · 31st January 2006, 05:13 PM

I have convinced myself that it is still spherical, but not for any of the reasons you have stated.

Dumbass · 31st January 2006, 06:52 PM

My mistake was taken a representation in polar coordinates and wrongly thinking of it in terms of rectangular coordinates.

Thanks for the help.

31st January 2006, 04:14 PM	#1
Dumbass diyAudio Member Join Date: Mar 2003 Location: British Antarctic Territory	Radiation pattern of point source on a plane What is the theoretical radiation pattern of a point source on an infinite plane/baffle? Is it simply one-half of spherical, or is it more like one-half of a dipole?

31st January 2006, 04:51 PM	#4
john k... diyAudio Member Join Date: Aug 2004 Location: US	(JPK) If it's a true point source then it is a hemisphere as gfinlayson stated. __________________ John k.... Music and Design NaO Dipole Loudspeakers. "We have no right to assume that any physical laws exist, or if they have existed up to now, that will continue to exist in a similar manner in the future." Max Planck

31st January 2006, 04:59 PM	#5
SY diyAudio Moderator Join Date: Oct 2002 Location: Austin, TX Blog Entries: 1	Work backward and you'll see that you've changed the equation into an ellipse. "Doubling" the equation must happen on both sides to be valid. __________________ “Listening to records is like ****ing a picture of Brigitte Bardot.” - Sergiu Celibidache

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31st January 2006, 04:30 PM	#2
gfinlayson diyAudio Member Join Date: Jan 2006 Location: Aylesford, Kent, England	It should be hemi-spherical.

31st January 2006, 05:03 PM	#6
gfinlayson diyAudio Member Join Date: Jan 2006 Location: Aylesford, Kent, England	SY is right, you haven't doubled the function. If y = sqrt (1 - x^2), then y cannot also be equal to 2 x sqrt (1-x^2). 2 y can, however, so you still end up with a hemisphere. Anyway, if you forget the mathematics and use common sense, a true point source radiates in a spherical pattern. So if you stick it onto an infinite plane it can only radiate in a hemi-spherical pattern.

31st January 2006, 05:13 PM	#7
Dumbass diyAudio Member Join Date: Mar 2003 Location: British Antarctic Territory	I have convinced myself that it is still spherical, but not for any of the reasons you have stated.

31st January 2006, 06:52 PM	#8
Dumbass diyAudio Member Join Date: Mar 2003 Location: British Antarctic Territory	My mistake was taken a representation in polar coordinates and wrongly thinking of it in terms of rectangular coordinates. Thanks for the help.

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