{"id":586,"date":"2016-11-17T09:41:03","date_gmt":"2016-11-17T16:41:03","guid":{"rendered":"https:\/\/sites.evergreen.edu\/psam1617\/?page_id=586"},"modified":"2016-11-17T10:12:09","modified_gmt":"2016-11-17T17:12:09","slug":"differential-equations-wave-equation-visualization-and-close-reading","status":"publish","type":"page","link":"https:\/\/sites.evergreen.edu\/psam1617\/differential-equations-wave-equation-visualization-and-close-reading\/","title":{"rendered":"Differential Equations: Wave Equation Visualization and Close Reading"},"content":{"rendered":"

Visualization<\/p>\n

    \n
  1. Go to https:\/\/www.desmos.com\/calculator\/gwha6ksu9m<\/a><\/strong><\/li>\n
  2. Examine the expression in line 2, and compare it to Eq. (19) and (20) in section 10.7 of your DiffEq book. In the Desmos calculator expression, note that L<\/em> and a<\/em> are chosen to be equal to 1. For the expression in the Desmos calculator, n<\/em> = 1. When looking at Eq. (20), note that the coefficient c<\/em>1<\/sub> is set to 1. In what remains, all the cn<\/sub><\/em>‘s will be set to 1 (but that is just for convenience and is rarely the actual case).<\/li>\n
  3. Note the axes on the graph. This is a snapshot of the wave at time t<\/em> = 0. To see what the wave looks like at different times, use the slider in line 1 to pick different values of t<\/em>.<\/li>\n
  4. Now, hit the play button to animate the graphs. After examining for a while, pause the animation.<\/li>\n
  5. In the line below the expression for\u00a0u<\/em>1<\/sub>, type in an expression for u<\/em>2<\/sub>. Compare these two graphs to Figure 10.7.3.<\/li>\n
  6. Play the animation again. Does u<\/em>2<\/sub> oscillate twice as fast as u<\/em>1<\/sub> as expected?<\/li>\n
  7. While watching the animation, see if you can imagine what the superposition of the two wave functions would look like. Discuss with your neighbors.<\/li>\n
  8. Pause the animation.<\/li>\n
  9. In the next line, type in u<\/em>1<\/sub> + u<\/em>2<\/sub>. Play the animation.<\/li>\n
  10. Pause the animation, and hide u<\/em>1<\/sub> + u<\/em>2<\/sub> by clicking on the colored circle all the way to the left of the line holding the expression.<\/li>\n
  11. Type in an expression for u<\/em>3<\/sub>. Compare the three graphs to Figure 10.7.3.<\/li>\n
  12. Play the animation again (which should just show the individual graphs). Again, imagine what the superposition of the three wave functions would look like.<\/li>\n
  13. Modify your u<\/em>1<\/sub> + u<\/em>2<\/sub> to add in u<\/em>3<\/sub>, show the graph, and animate it.<\/li>\n<\/ol>\n

    Close Reading<\/p>\n

      \n
    1. Go to this editable Google Doc<\/a><\/strong> (you don’t need to log into a google account unless you want to).<\/li>\n
    2. Read the instructions on the first page, and then proceed.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      Visualization Go to https:\/\/www.desmos.com\/calculator\/gwha6ksu9m Examine the expression in line 2, and compare it to Eq. (19) and (20) in section 10.7 of your DiffEq book. In the Desmos calculator expression, note that L and a are chosen to be equal … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":219,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_mi_skip_tracking":false},"_links":{"self":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/pages\/586"}],"collection":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/users\/219"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/comments?post=586"}],"version-history":[{"count":0,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/pages\/586\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/media?parent=586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}