Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.

Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.

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

Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

Question

Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae^-(bx-ct)^{^2} satisfies the wave equation: (?²?(?,?))/(?x²) = (1/v²) * (?²?(x,t))/(?t²) if the wave is given by the v = (c/b) and a, b, and c are constants.

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