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
5) Wave on transmission lines
(a) Derive wave equations for voltage and currents over the
transmission lines.
(b) Solve for general solutions
(c) Indicate the definition of characteristic impedance