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6) In a dispetsive medium with a frequency-dependent dielectie function Elw, one may represent a wave group in terms of (real? fields East) and BC2,t)

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6) In a dispetsive medium with a frequency-dependent dielectie function Elw, one may represent a wave group in terms of (real? fields East) and BC2,t) having the Fourier expansions like &) SE,) eist dws DE, E = mSaew) Q)etat dw where El-w)=E(wi", cand the field BC2,+) (= ho,t) , with 4 set to 1 ) having on analogous expansion. We here wish to study the implication 00 - 3 4TC on the of the local energy equation ( SRT 3) = 7-9, (= x) speed of energy propagation as the wave group moves. ci) Show that what we have on the left hand side of the above local energy equation can be cast as - , with the local energy density Ux,t) given by Ut) = er dudo eta u5t [bew_wcws] ,6). ,00) ci Then, for a nearly monochromatic wave group with a central frequ-, ency , show that we have the approximate relation U6 1)

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