Show explicitly that the wave function, y(x, t) = A cos(kx - wt) satisfies the wave equation, 0229(x, t) = √2012(x, t) v² Write the explicit value of v as a function of the parameters of the wave function, w, k and A. Note: Attached in the other image the answer, can you please explain it.

Show explicitly that the wave function, y(x, t) = A cos(kx - wt) satisfies the wave equation, 0229(x, t) = √2012(x, t) v² Write the explicit value of v as a function of the parameters of the wave function, w, k and A. Note: Attached in the other image the answer, can you please explain it.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Show explicitly that the wave function,
y(x, t) = A cos (kx – wt)
satisfies the wave equation,
8²
dx2 y(x, t):
=
1 0²
v² atzy (x, t)
Write the explicit value of v as a function of the parameters of
the wave function, w, k and A.
Note: Attached in the other image the answer, can you please
explain it.

F = 1
1/² ; W= 2πF; K= 2πTI ; v= XF
t
A
W = UK
y (x, t) = A 6₁ (Kx-wt)
d²y (x, t) = -w² Alor (kx - wt) = -w'y (x, t)
dt²
d²y (x, t) -K²A6₁ (Kx-wt) = -K²y(x, t)
ox²
v² = w ² y (x, t)
K² y(x, t)
d²y (x, t)
o/x²
=
1
-V²
-
d'y (x, t)
dt2
dzy (x, t)
olx²
d³y (x, t)
dt²
v² = -w² A6₁ (Kx-wt)
-K²A61 (Kx-wt)
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