Re: Bogus proof?

To: tesla-at-pupman-dot-com
Subject: Re: Bogus proof?
From: richard hull <rhull-at-richmond.infi-dot-net>
Date: Thu, 13 Feb 1997 00:17:49 -0500 (EST)
Subscriber: rhull-at-richmond.infi-dot-net Wed Feb 12 23:13:10 1997
At 11:26 PM 2/11/97 -0700, you wrote:
>Subscriber: jd231825-at-engr.colostate.edu Tue Feb 11 23:07:41 1997
>Date: Tue, 11 Feb 1997 16:11:13 -0700
>From: Jeff Detweiler <jd231825-at-engr.colostate.edu>
>To: tesla-at-pupman-dot-com
>Subject: Bogus proof?
>
>Hi all,
>
>I was doing some reading up on transmission line theory and I don't
>understand what the 1/4 wavelength principle of the secondary has to do
>with resonance. Consider this proof:
>
>Velocity of a wave travelling down a transmission line is:
>
>v = l/sqrt(LC)         l = length of transmission line
>                       C = capacitance of the length "l" transmission line
>                       L = inductance " " " "
>
>And we know the resonant frequency of a secondary coil is:
>
>f = 1/(2*pi*sqrt(LC))        eq. 2
>
>also, since
>
>v = f*lamda    lambda = wavelength
>               f = frequency
>
>then:
>
>l/sqrt(LC) = f*lamda         eq. 3
>
>substituting resonant eq. 2 into eq. 3 for "f":
>
>l/sqrt(LC) = lambda/(2*pi*sqrt(LC))
>
>cancelling terms and solving for "l" the length of the transmission line:
>
>l = lambda/(2*pi)
>
>Thus at resonance, the actual physical length of the wire should be 1/2pi
>of the wavelength, and not 1/4. So where is this proof bogus? What exactly
>does the 1/4 wavelength frequency have to do with resonance? I thought
>resonance is only a function of the L and C of the coil. I hope Fr. McGahee
>will include this in the Guide.
>
>Thanks,
>Jeff Detweiler
>
>
>
Jeff,

Common theoretical mistake.  Good mathin'.  You mathed it to death and came
up with a swell, (read swollen), identity.

1.  Problem is the wavelength equation is for a straight piece of wire in
interstellar space!  (not a real world coil on earth)  By cancelling out the
L and C from the equation, you lost the reality of what would be wound. We
have isotrpoic capacity in the real world too, in addition to self
inductance and self capacitances in a helical resonator. 

2. The lambda equation is for a full wavelength.  We gain voltage in the
Tesla resonator system by making something with an "odd" quarter wavelength.
Thus we ground the base of our coil and get max voltages, as on any
transmission line, at the 1/4, 3/4, 5/4, etc, wavelength points.

Good luck in future math efforts.

Richard Hull, TCBOR