Question

Using Fourier integral theorem, obtain the expression for the velocity of a wave packet in a medium for which the dispersion relation is given as 

20 Feb 2025
Answer :
Word Count : 481

In classical electrodynamics, wave propagation is often described by wave packets, which are superpositions of sinusoidal waves with different frequencies. The Fourier integral theorem plays a crucial role in analyzing wave packets, especially in determining the velocity of a wave packet in a medium. To derive the expression for the velocity of a wave packet using the Fourier integral theorem, we first need to understand the dispersion relation of the medium.

Consider a medium with a dispersion relation given by ω(k)\omega(k), where ω\omega is the angular frequency and kk is the wave vector. A wave packet is typically represented as a superposition of plane waves with different frequencies and wave numbers. The general form of a wave packet in terms ____ _________ __________ _______ ________ ____ ________ ___ __________.
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