Mathcad Professional 14.0 <description/> <author>John C. Bean</author> <company/> <keywords/> <revisedBy>John C. Bean</revisedBy> </userData> <identityInfo> <revision>31</revision> <documentID>6537AB06-4714-44EE-82D4-634757E7E620</documentID> <versionID>A46BA0F3-BF0D-47D9-96D3-05A356D94574</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="14" font-weight="bold" font-style="normal" 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font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Trebuchet MS" font-charset="0" font-size="11" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Trebuchet MS" font-charset="0" font-size="11" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Trebuchet MS" font-charset="0" font-size="11" font-weight="bold" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="landscape" print-single-page-width="false" page-width="792" page-height="612"> <margins left="50.328" right="50.328" top="50.328" bottom="50.328"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="false" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="791" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="241" left="6" top="6.75" width="226.5" height="14.25" align-x="6" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12"> <b> <c val="#f00">"Mathcad_waves_lecture_2.mcd"</c> </b> </f> </p> </text> </region> <region region-id="264" left="246" top="7.5" width="43.5" height="15" align-x="260.25" align-y="18" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="266" left="384" top="7.5" width="54" height="15" align-x="398.25" align-y="18" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ω</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="248" left="12" top="68.25" width="105" height="12" align-x="24" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Make a circular wave:</b> </p> </text> </region> <region region-id="258" left="138" top="57.75" width="193.5" height="29.25" align-x="214.5" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">R</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve" subscript="o">x</ml:id> <ml:id xml:space="preserve" subscript="o">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve" subscript="o">x</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve" subscript="o">y</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="259" left="378" top="48" width="265.5" height="71.25" align-x="485.25" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Wave</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve" subscript="o">x</ml:id> <ml:id xml:space="preserve" subscript="o">y</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">λ</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">R</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve" subscript="o">x</ml:id> <ml:id xml:space="preserve" subscript="o">y</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">t</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">R</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve" subscript="o">x</ml:id> <ml:id xml:space="preserve" subscript="o">y</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> <ml:real>10</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="270" left="12" top="116.25" width="201.75" height="12" align-x="24" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Show it behaves properly along X, Y axes:</b> </p> </text> </region> <region region-id="207" left="6" top="138" width="337.5" height="96" align-x="6" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="6"/> <rendering item-idref="7"/> </region> <region region-id="263" left="366" top="138" width="313.5" height="96" align-x="366" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="8"/> <rendering item-idref="9"/> </region> <region region-id="402" left="258" top="266.25" width="96" height="12" align-x="258" align-y="276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Animating this with</b> </p> </text> </region> <region region-id="400" left="360" top="265.5" width="111.75" height="15" align-x="389.25" align-y="276" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">time</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="383" left="102" top="288" width="399.75" height="138.75" align-x="102" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="11"/> <rendering item-idref="12"/> </region> <region region-id="607" left="48" top="518.25" width="177" height="12" align-x="48" align-y="528" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>3D version of single point source:</b>:</p> </text> </region> <region region-id="674" left="42" top="542.25" width="187.5" height="12" align-x="42" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Animating this with FRAME = 0 to 100</b> </p> </text> </region> <region region-id="677" left="72" top="565.5" width="111.75" height="15" align-x="101.25" align-y="576" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">time</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="678" left="36" top="589.5" width="184.5" height="19.5" align-x="102.75" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="1">Wave</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id xml:space="preserve">Wave</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve">time</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="672" left="18" top="606" width="203.25" height="213" align-x="118.5" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="15" disable-calc="false"> <inputs> <ml:id xml:space="preserve" subscript="1" xmlns:ml="http://schemas.mathsoft.com/math30">Wave</ml:id> </inputs> <outputs/> </component> <rendering item-idref="16"/> </region> <region region-id="429" left="294" top="1034.25" width="139.5" height="12" align-x="318" align-y="1044" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Three point sources in a row:</b> </p> </text> </region> <region region-id="666" left="276" top="1058.25" width="187.5" height="12" align-x="276" align-y="1068" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Animating this with FRAME = 0 to 100</b> </p> </text> </region> <region region-id="665" left="312" top="1075.5" width="111.75" height="15" align-x="341.25" align-y="1086" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">time</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>0.1</ml:real> <ml:id xml:space="preserve">FRAME</ml:id> </ml:apply> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="664" left="138" top="1099.5" width="477" height="19.5" align-x="204.75" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="3">Wave</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve">Wave</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:mult/> <ml:real>-50</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> <ml:id xml:space="preserve">time</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Wave</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> <ml:real>0</ml:real> <ml:id xml:space="preserve">time</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Wave</ml:id> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:real>0</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:id xml:space="preserve">cm</ml:id> </ml:apply> <ml:id xml:space="preserve">time</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="439" left="258" top="1128" width="210.75" height="233.25" align-x="362.25" align-y="1128" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="19" disable-calc="false"> <inputs> <ml:id xml:space="preserve" subscript="3" xmlns:ml="http://schemas.mathsoft.com/math30">Wave</ml:id> </inputs> <outputs/> </component> <rendering item-idref="20"/> </region> <region region-id="652" left="102" top="1544.25" width="121.5" height="12" align-x="111.75" align-y="1554" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b>11 point sources in a row</b> </f> <b>:</b> </p> </text> </region> <region region-id="487" left="462" top="1550.25" width="161.25" height="12" align-x="471.75" align-y="1560" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b>41 point sources in a row</b> </f> <b>:</b> </p> </text> </region> <region region-id="655" left="78" top="1568.25" width="187.5" height="12" align-x="78" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Animating this with FRAME = 0 to 100</b> </p> </text> </region> <region region-id="659" left="450" top="1574.25" width="187.5" height="12" align-x="450" align-y="1584" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <b>Animating this with FRAME = 0 to 100</b> </p> </text> 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b>81 point sources in a row</b> </f> <b>:</b> </p> </text> </region> <region region-id="660" left="408" top="2054.25" width="221.25" height="12" align-x="417.75" align-y="2064" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b>81 point sources, zoomed, with shrinking row</b> </f> <b>:</b> </p> </text> </region> <region region-id="647" left="78" top="2078.25" width="186.75" height="12" align-x="78" 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tag=""> <component hide-arguments="false" clsid-buddy="013500E0-1122-11DB-9380-000D56C6051A" item-idref="36" disable-calc="false"> <inputs> <ml:id xml:space="preserve" subscript="81_shrinking" xmlns:ml="http://schemas.mathsoft.com/math30">Wave</ml:id> </inputs> <outputs/> </component> <rendering item-idref="37"/> </region> <region region-id="767" left="216" top="2576.25" width="221.25" height="12" align-x="225.75" align-y="2586" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b>Shrinking gap, 51 sources on each side</b> </f> <b>:</b> </p> </text> </region> <region region-id="768" left="246" top="2606.25" width="187.5" height="12" align-x="246" align-y="2616" show-border="false" 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