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https://texercises.raemilab.ch/exercise/sawtooth-wave/
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Exercise:
The shape of a wave is given by the piecewise definition fx left arraycr x & textfor xaO leq x leq xbO AO-x/ & textfor xbO leq x leq xcO & texteverywhere else array The wave travels with a velocity of vO. abcliste abc Draw the displacement vs position diagram for the fixed time t_txO. abc Draw the displacement vs time diagram for the fixed position x_xxO for t between tiO and tfO. abcliste

Solution:
The function fx describes a linear increase in the first part and a linear decrease in the second part. You can easily verify that it is continuous at xxbO. The shape see figure below resembles a em sawtooth hence the name of this exercise. abcliste abc The distance the wave has travelled after taO is given by: Delta x v t vtimestx dxP center includegraphicswidthcm#image_path:sawtooth-wavyx# center abc The wave front initally at xcO arrives at xxxO at t fracDelta xv fracxx-xcvtfrontP The right part less steep arrives first hence the shape of yt corresponds to the shape of yx mirrored about the y-axis. center includegraphicswidthcm#image_path:sawtooth-wavyt# center abcliste
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Exercise:
The shape of a wave is given by the piecewise definition fx left arraycr x & textfor xaO leq x leq xbO AO-x/ & textfor xbO leq x leq xcO & texteverywhere else array The wave travels with a velocity of vO. abcliste abc Draw the displacement vs position diagram for the fixed time t_txO. abc Draw the displacement vs time diagram for the fixed position x_xxO for t between tiO and tfO. abcliste

Solution:
The function fx describes a linear increase in the first part and a linear decrease in the second part. You can easily verify that it is continuous at xxbO. The shape see figure below resembles a em sawtooth hence the name of this exercise. abcliste abc The distance the wave has travelled after taO is given by: Delta x v t vtimestx dxP center includegraphicswidthcm#image_path:sawtooth-wavyx# center abc The wave front initally at xcO arrives at xxxO at t fracDelta xv fracxx-xcvtfrontP The right part less steep arrives first hence the shape of yt corresponds to the shape of yx mirrored about the y-axis. center includegraphicswidthcm#image_path:sawtooth-wavyt# center abcliste
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Attributes & Decorations
Branches
Mechanical Waves
Tags
propagation, wave
Content image
Difficulty
(1, default)
Points
0 (default)
Language
ENG (English)
Type
Descriptive / Quality
Creator by
Decoration