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Date: Mon, 31 May 2021 21:41:59 +0000
From: David Bowman <David_Bowman@georgetowncollege.edu>
To: "Phys-L@Phys-L.org" <Phys-L@Phys-L.org>
Subject: Re: [Phys-L] rms / conic / arithmetic / geometric averages
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Regarding where Dan B wrote:
... From page 214 of "The Physics of Musical Instruments"Dan, why does the above formula have a negative exponent rather than positive? And what is the factor of 2 in the exponent for? Is S supposed to be the surface area of the cross section at a distance x from the reference point? If S is the radius or diameter at a distance x along the tube then I don't see the point of the factor of 2 in the exponent (or the negative sign).
2nd ed., the Bessel horn is defined by
x is the geometric distance measured from the reference point
x = 0,
If epsilon = 0 you have a cylindrical horn. If x = 1 you have a
From page 432, applied to a brass instrument the relationshipAgain, why isn't the above formula isn't supposed to be
for a bessel horn can be written
a = b(x + x0)^(-gamma)
where a is the bore radius of the horn and x0 is the small end
of the horn.
b and x0 are chosen to give the correct radii at the small and
large ends of the horn and gamma defines the rate of flare.
a = b(x + x0)^(+gamma)
with a positive exponent?