As we€™ve seen, Eq. (7.33) describes the beat pattern. Let€™s now derive a different version of that expression assuming that the two overlapping equal-amplitude cosine waves have angular spatial frequencies of k_c+ Δk and k_c- Δk, and angular temporal frequencies of ω_c+ Δω and ω_c- Δω, respectively. Here k_cand ω_ccorrespond to the central frequencies. Show that the resultant wave is then

Explain how each term relates back to
Prove that the speed of the envelope, which is the wavelength of the envelope divided by the period of the envelope, equals the group velocity, namely, Δω/Δk.

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E = 2E01 cos (Akx – Awt) cos (kx – w.t) Figure P.7.19 (a) E Eo --Eo (b) х