Answered: Verify by direct substitution that the…

Verify by direct substitution that the wave function for a standing wave given by: y= (2A cos kx) cos wt is a solution of the general linear wave equation: azy_ 1 a?y ax2 2 at?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter14: Superposition And Standing Waves

Section: Chapter Questions

Problem 16P

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Concept explainers

Stretched string

A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.

Question

Verify by direct substitution that the wave function for a standing wave given by:
y= (2A cos kx) cos wt
is a solution of the general linear wave equation:
1 a?y
ax?

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