c) State under what conditions the propagation velocity of the waves is almost independent of ω. Determine the velocity in this case.
Given constants:
When sine waves propagate in an infinite LC-grid (see the figure below) the phase of the acvoltage across two successive capacitors differs by Φ.
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Formulae:
cosα−cosβ=−2⋅sin(2α+β)⋅sin(2α−β)sinα−sinβ=2⋅cos(2α+β)⋅sin(2α−β)
Context question:
a) Determine how Φ depends on ω,L and C ( ω is the angular frequency of the sine wave).
Context answer:
φ=2⋅arcsin(2ω⋅L⋅C) with 0≤ω≤L⋅C2
Context question:
b) Determine the velocity of propagation of the waves if the length of each unit is ℓ.
Context answer:
2⋅arcsin(2ω⋅L⋅C)ω⋅ℓ