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 − kvt) for this wave.
To find: The equation of the travelling wave which is moving with velocity 6 from the graph.
Answer to Problem 3P
The equation of the wave is
Explanation of Solution
Given:
A graph showing a wave at
The equation of the wave has a form
Calculation:
From the figure observe that the maximum value reached by the wave along the y-axis is 2.7.
Therefore, the amplitude of the wave is A = 2.7.
The wave repeats itself after x = 9.2.
Therefore, period of the wave is 9.2.
Calculate the value of the k as follows.
Therefore,
It is given that velocity is
Using all the above values the equation of the wave is
Simplifying further the equation of the wave is
Chapter 7 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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