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2) Comment on the Phase velocity (Vp) of the waves for increased values of Awo and Δ.Κ.

2) Comment on the Phase velocity (Vp) of the waves for increased values of Awo and Δ.Κ.

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I'm studying topic of phase velocity and group velocity. For different values of (w) and (k), I'm obtaining same group velocity as 1 but different wave pattern. I need help for Q2) in inferences and bit theory behind it.

w- S.Thoushik 21MIS1058 Phase abd group velocity Qv Search in Document Home Insert Draw Design Layout References Mailings Review View Table Design Layout + Share Times New R... 14 A- A- Áa AaBbCcDdEe AaBb( AaBbCcDdEe AaBbCcDdE AaBbCcDc АаBbСcDdEe AgBbCcDdEe v abe X2 x² A Subtle Emph... Styles Pane Paste Normal No Spacing Heading 1 Heading 2 Title Subtitle Emphasis Phase and Group velocity of EM waves Tools required: http://demonstrations.wolfram.com/GroupAndPhaseVelocity/ Objective: To understand the nature of EM waves travelling in a medium with the help of Phase and Group velocities. Theory: Any real signal consists of travelling-waves of many different frequencies, which travel together as a group, at a speed that will always be less than or equal to the speed of light in vacuum. To gain some in Bold into what may happen when a real signal travels through a dispersive medium, we consider adding two waves of equal amplitude. When two travelling waves with unit amplitude fi(z.t) = cos(kz-mit) and f(z,t) = cos(k2z-@²t) are added, we get fi(z.t) + f,(z,t)= cos(k,z– 0,t) + cos(k,z – 0,t) Ak = 2 cos 2 Δω t cos(k · z 2 (1-0 – 2 Ak k, - k, k + k, k = W, + W2 Δω ωω 2 Where, 2 2 and The result is a fast oscillating wave that travels with a phase velocity k and the Δω YV ) Page 1 of 6 278 words English (India) Focus + 140% 18 || II
Transcribed Image Text:w- S.Thoushik 21MIS1058 Phase abd group velocity Qv Search in Document Home Insert Draw Design Layout References Mailings Review View Table Design Layout + Share Times New R... 14 A- A- Áa AaBbCcDdEe AaBb( AaBbCcDdEe AaBbCcDdE AaBbCcDc АаBbСcDdEe AgBbCcDdEe v abe X2 x² A Subtle Emph... Styles Pane Paste Normal No Spacing Heading 1 Heading 2 Title Subtitle Emphasis Phase and Group velocity of EM waves Tools required: http://demonstrations.wolfram.com/GroupAndPhaseVelocity/ Objective: To understand the nature of EM waves travelling in a medium with the help of Phase and Group velocities. Theory: Any real signal consists of travelling-waves of many different frequencies, which travel together as a group, at a speed that will always be less than or equal to the speed of light in vacuum. To gain some in Bold into what may happen when a real signal travels through a dispersive medium, we consider adding two waves of equal amplitude. When two travelling waves with unit amplitude fi(z.t) = cos(kz-mit) and f(z,t) = cos(k2z-@²t) are added, we get fi(z.t) + f,(z,t)= cos(k,z– 0,t) + cos(k,z – 0,t) Ak = 2 cos 2 Δω t cos(k · z 2 (1-0 – 2 Ak k, - k, k + k, k = W, + W2 Δω ωω 2 Where, 2 2 and The result is a fast oscillating wave that travels with a phase velocity k and the Δω YV ) Page 1 of 6 278 words English (India) Focus + 140% 18 || II
w- S.Thoushik 21MIS1058 Phase abd group velocity Qv Search in Document Home Insert Draw Design Layout References Mailings Review View Table Design Layout + Share Times New R... 14 A- A- AaBbCcDdE AaBbCcDc AaBbCcDdEe AaBb( AaBbCcDdEe АаBbСcDdEe AgBbCcDdEe v abe X2 x² A Subtle Emph... Styles Pane Paste Normal No Spacing Heading 1 Heading 2 Title Subtitle Emphasis 5 10 15 20 25 30 0.5 0.5 1 + 2 Ak + 0.5 + 0.5 Bold Vg = 1. 10 15 20 25 30 Inferences: 1) Are the wave patterns for various values of Ao and Ak same? If not, why? 2) Comment on the Phase velocity (Vp) of the waves for increased values of Ao and Ak. 3) When do we see Vn and Vg being the same. 4) Draw a typical dispersion relation curve (@-k curve) for V= Vg and Va + Vg cases. Page 5 of 6 278 words English (India) Focus + 140%
Transcribed Image Text:w- S.Thoushik 21MIS1058 Phase abd group velocity Qv Search in Document Home Insert Draw Design Layout References Mailings Review View Table Design Layout + Share Times New R... 14 A- A- AaBbCcDdE AaBbCcDc AaBbCcDdEe AaBb( AaBbCcDdEe АаBbСcDdEe AgBbCcDdEe v abe X2 x² A Subtle Emph... Styles Pane Paste Normal No Spacing Heading 1 Heading 2 Title Subtitle Emphasis 5 10 15 20 25 30 0.5 0.5 1 + 2 Ak + 0.5 + 0.5 Bold Vg = 1. 10 15 20 25 30 Inferences: 1) Are the wave patterns for various values of Ao and Ak same? If not, why? 2) Comment on the Phase velocity (Vp) of the waves for increased values of Ao and Ak. 3) When do we see Vn and Vg being the same. 4) Draw a typical dispersion relation curve (@-k curve) for V= Vg and Va + Vg cases. Page 5 of 6 278 words English (India) Focus + 140%
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