Answered: Show that p(t, x) = A sin (ωt − kx + φ)…

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Show that p(t, x) = A sin (ωt − kx + φ) satisfies the wave equation.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter16: Electromagnetic Waves

Section: Chapter Questions

Problem 92AP: Show that the wave equation in one dimension 2fx2=1v22ft2 Is satisfied by any doubly differentiable...

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Concept explainers

Electromagnetic Waves

Electromagnetic waves are waves that consist of magnetic field and electric field components perpendicular to each other. These field components are also perpendicular to the direction of propagation of the wave.

Question

Show that p(t, x) = A sin (ωt − kx + φ) satisfies the wave equation.

Expert Solution

Step 1

To show that the given equation satisfies the wave equation.

Given:
The equation:
$p (x, t) = A \sin (ω t - k x + φ) . . . (i)$

To show:
The equation satisfies the wave equation.

The wave equation is a second order linear partial differential equation that describes the behavior of waves as perceived in classical physics.
The wave equation is given as:
$\frac{\partial^{2} p}{\partial t^{2}} = c^{2} \frac{\partial^{2} p}{\partial x^{2}}$
where $c$ is a positive real constant.

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