. Traveling Wave A traveling wave is graphed at the instant t = 0. If it is moving to theright with velocity 6, find an equation of the form y(x, t) = A sin(kx – kut) for this wave.y2.7-4.69.213.8-2.7+

Velocity: To find: An equation of the form

Answered: . Traveling Wave A traveling wave is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

. Traveling Wave A traveling wave is graphed at the instant t = 0. If it is moving to the
right with velocity 6, find an equation of the form y(x, t) = A sin(kx – kut) for this wave.
y
2.7-
4.6
9.2
13.8
-2.7+

Expert Solution

Step 1: Given:

Velocity: $v equals 6 space$

To find: An equation of the form $y left parenthesis x comma t right parenthesis equals A sin left parenthesis k x minus k v t right parenthesis$

Step 2: Finding the equation.

In $y left parenthesis x comma t right parenthesis equals A sin left parenthesis k x minus k v t right parenthesis$ , $A space equals space Amplitude$ and $k equals fraction numerator 2 pi over denominator Period end fraction$

From the graph, $A equals space 2.7$ and $Period space equals space 9.2$ .

Thus,

$table attributes columnalign right center left columnspacing 0px end attributes row k equals cell fraction numerator 2 pi over denominator 9.2 end fraction end cell row blank equals cell 0.7662 end cell end table$

Substituting values of $v comma space A$ and k in the function.

$table attributes columnalign right center left columnspacing 0px end attributes row cell y left parenthesis x comma t right parenthesis end cell equals cell 2.7 sin left parenthesis 0.7662 x minus open parentheses 0.7662 close parentheses open parentheses 6 close parentheses t right parenthesis end cell row blank equals cell 2.7 sin left parenthesis 0.7662 x minus 4.597 t right parenthesis end cell end table$