Friday, February 28, 2014

Wavelength Formula

In 1917 Audel & Co. published Hawkins Electrical Guide. There the formula for wavelength is described as follows:
"That point where the electric wharp and the magnetic flux meet, or the distance through space traveled during one oscillation cycle is considered the wave length..."
I'd always understood it just as the distance between peaks. The Hawkins definition remained the same through at least 1922 including that archaic use of the word "wharp." Wikipedia defines it very differently today.
"It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns."

This formula back in 1917 was given as W = 3.1416 x 2 x 2V √LxC. Given:
  • W = Wavelength in meters
  • V =  The velocity of light (186,600 miles per second)
  • L = Inductance in Henries
  • C = Capacity in farads.

You would think a century after the metric system they'd be using different metrics. Clearly this was an American edition. In that form I barely understand the formula. I would re-write that first bit as as "2π x 2V" but who's quibbling?  They're calculating frequency then multiplying by 2π. Today remnants of that formula can be seen in resonance calculations for LC circuits. Such as 1 ÷ 2π x LC. which calculates the resonant angular frequency. More here.

Today that same wavelength calculation is given much more succinctly as:
 λ = V ÷F. Given:
  • V = Wave speed/velocity (in meters per second, m/s)
  • F = Frequency in Hertz
  • λ =Wavelegnth in meters
It's amazing even today what the metric system has done for our understanding of even the things we already understood.