WAVE ON A CANAL A wave on the surface a long canal us described by the function
(a)
To find:
The function that models the positions of the point
Answer to Problem 1P
Solution:
The function that models the position of the point
Explanation of Solution
Given:
The equation of wave is
Approach:
Substituting
Here,
Calculation:
The equation of wave is as follows.
Substitute
Compare the above equation with standard equation
Here,
Therefore, the function that models the position of the point
(b)
To sketch:
Shape of the wave when
Answer to Problem 1P
Solution:
The graphs are shown below in figure
Explanation of Solution
Approach:
Substitute
Here,
Calculation:
Write the given equation.
Substitute
The graphs of
Figure
Above figure is shifting with respect to time, thus it is a travelling wave.
Therefore, the graphs are shown above and the given wave is a travelling wave.
(c)
To find:
The velocity of the wave.
Answer to Problem 1P
Solution:
The velocity
Explanation of Solution
Approach:
Compare the given equation with standard equation
Calculation:
Write the given equation
Take
Compare the given equation with standard equation.
Here,
Therefore, the velocity is
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