Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
-----Original Message-----
From: Phys-l <phys-l-bounces@mail.phys-l.org<mailto:phys-l-bounces@mail.phys-l.org> > On Behalf Of Dan Beeker via
Phys-l
Sent: Tuesday, June 1, 2021 9:20 PM
To: phys-l@mail.phys-l.org <mailto:phys-l@mail.phys-l.org>
Cc: Dan Beeker <debeeker@comcast.net <mailto:debeeker@comcast.net> >
Subject: Re: [Phys-L] Phys-l Digest, Vol 198, Issue 1
David,
I should have been more explicit.
1. You are correct. S is the cross sectional area. In terms of radius
(a) the formula would be
a = b(x^-epsilon) = b/(x^epsilon)
The factor of 2 in th formula for S comes because the area is (pi)r^2.
Sub a into the area formula.
area S = (pi)r^2 = (pi)a^2 = pi[b/x^epsilon]^2 = pi[b^2/x^2epsilon]
pi*B^2 morphs into the constant b.
2. As far as whether the exponent epsilon is positive or negative, I'llhave to
ponder this. I think epsilon should be positive so the function getssmaller as one
moves away from the large end of the bell.
3. And I see a typo in
If epsilon = 0 you have a cylindrical horn. If x = 1 you have a conicalhorn.
Should read:
If epsilon = 0 you have a cylindrical horn. If epsilon = 1 you have aconical horn.
4. And I believe I made another typo which may explain the confusion.
where a is the bore radius of the horn and x0 is the small end of thehorn.
Should read
where a is the bore radius of the horn and x0 is the large end of thehorn.
So embarrassing.
Dan