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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?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter16: Waves

Section: Chapter Questions

Problem 125AP: Given the wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kxt+) with 2 , show that y1(x,t)+y2(x,t)...

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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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