Starting with Maxwell's equations show that the magnetic field
satisfies the same wave equation as the electric field. in
particular, that is, too, propagates with the same speed.
Separate the wave equation in two-dimensional rectangular
coordinates x, y. Consider a rectangular membrane, rigidly attache
to supports along its sides, such that a ≤ x ≤ 0 and b ≤ y ≤ 0.
Find the solution, including the specification of the
characteristic frequencies of the membrane oscillations. In the
case of a = b, show that two or more modes of vibration correspond
to a single frequency
Derive wave equation for H (eq. 9.7 in the textbook) from
Maxwell’s equations for
source-free region filled with linear, homogeneous, and lossless
material of permittivity ε and
permeability μ.
Consider the following one-dimensional partial differentiation
wave equation. Produce the solution u(x, t) of this equation. 4Uxx
= Utt 0 < x 0 Boundary Conditions: u (0, t) = u (2π, t) = 0,
Initial Conditions a shown below: consider g(x)= 0 in both
cases.
(a) u (x, 0) = f(x) = 3sin 2x +3 sin7x , 0 < x <2π
(b) u (x, 0) = x +2, 0 < x <2π