Why Does Group Velocity of Microwaves Increase with Frequency in Waveguides?

[flexifirm]

Do anyone know why the group velocity of microwaves inside a rectangular waveguide goes up when frequency goes up?

To me it seems like a higher frequency means a smaller wavelength, and thus a more ZIG ZAG patterns off the walls (to meet the boundary conditions).

If the wave is zig zagging more, then it must be propagating down the waveguide at a slower rate?

Yet group velocity goes up (every resource says this).

Can anyone help me on this?

 

[jdoane]

Angle Of The Wave Travel In A Wave Guide

The Sin Of The Angle Of Travel = Wave Length /Wave length guide.
As The Freq. Goes Up The Wave Length Goes Down.
As The Wave Length Goes Down The Sin Of The Angle Goes Down.
As The Sin Of The Angle The Angle Is Less Degrees - Straighter.
The Cosin Of This Angle Goes Up.

Group Or Guide Velosity = Cosin Of The Angle * V (True Wave Velosity)

See RF Cafe Web Site For Some Of This Information.

Remember Wave Guides Have A Cutoff Freq.(Lowest Freq. That Will Travel Down The Guide)
As The Freq. Goes Down The Angle Of Travel Heads Towards 90 Degrees (Just Goes Up And Down - No Forward Travel At The Cutoff Freq.)