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1. Graph the following function on the board: f(x) = - 0 1+x 1-x 0 -∞

1. Graph the following function on the board: f(x) = - 0 1+x 1-x 0 -∞

Advanced Engineering Mathematics
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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1. Graph the following function on the board: f(x)= 0 1+x 6. 1- x 0 −∞ <x<-1 -1<x<0 0≤x<+1 +1<x<+∞ 2. On another graph directly beneath this one, graph the same function with (x - 1) replacing x. 3. Repeat this process for a third graph replacing x in the original function with (x − 2). 4. If we replace the x in the function with (x − n), where we keep making n larger by 1 unit every second, then what will we see? 5. If we want to generalize this to the triangle moving to the right (the +x direction) at a speed v, then what should we replace n with? Is this behavior special to this function? 7. How do we change the function f(x) if we want the function to move to the left (the -x direction) at a speed v? II. Physical Interpretation of f(x – vt) 1. What are the units of the vertical axis for our graph? 2. What are some examples of physical waves, and what does the function value frepresent in these cases? 3. Could temperature be a quantity that f measures? 4. Do all waves have f's that represent the displacement of some stuff perpendicular to motion? 5. Draw a representation of a compression pulse with vertical line segments. Make it so that the density of line segments varies in the same way that f(x) does, and draw it directly below the original f(x) graph for comparison. 6. Do all physical waves have some kind of "stuff" that displaces?
Transcribed Image Text:1. Graph the following function on the board: f(x)= 0 1+x 6. 1- x 0 −∞ <x<-1 -1<x<0 0≤x<+1 +1<x<+∞ 2. On another graph directly beneath this one, graph the same function with (x - 1) replacing x. 3. Repeat this process for a third graph replacing x in the original function with (x − 2). 4. If we replace the x in the function with (x − n), where we keep making n larger by 1 unit every second, then what will we see? 5. If we want to generalize this to the triangle moving to the right (the +x direction) at a speed v, then what should we replace n with? Is this behavior special to this function? 7. How do we change the function f(x) if we want the function to move to the left (the -x direction) at a speed v? II. Physical Interpretation of f(x – vt) 1. What are the units of the vertical axis for our graph? 2. What are some examples of physical waves, and what does the function value frepresent in these cases? 3. Could temperature be a quantity that f measures? 4. Do all waves have f's that represent the displacement of some stuff perpendicular to motion? 5. Draw a representation of a compression pulse with vertical line segments. Make it so that the density of line segments varies in the same way that f(x) does, and draw it directly below the original f(x) graph for comparison. 6. Do all physical waves have some kind of "stuff" that displaces?
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