Dynamic Demonstration of Wave Superposition
2020-05-13 05:05
This GeoGebra applet dynamically demonstrates wave superposition. By constructing circles, vectors, segments, and trigonometric functions, it visually illustrates interference when multiple waves meet. Users can adjust parameters to observe crest and trough interactions and resultant amplitude changes, providing deep insights into wave mechanics for physics and math education.
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<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<expression label="s" exp="s(x) = If[x(A1) ≤ x < 20, y(A0) + (abs(v) * sin((a * x) + γ - (a * x(A1)))) + (abs(w) * sin((aa * x) + δ - (aa * x(A1))))]" />
<element type="function" label="s">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<element type="boolean" label="o">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="112" y="150"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="θ=If( o, 180°, 0° )"/>
<caption val="反相"/>
</element>
<command name="If">
<input a0="o" a1="180°" a2="0°"/>
<output a0="θ"/>
</command>
<element type="angle" label="θ">
<angleStyle val="3"/>
<value val="3.141592653589793"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<expression label="f" exp="f(x) = If[e ≤ x ≤ g ∧ h ≠ i, (2 * sin(x - a2)) + (2 * sin(x + a2 - θ)), If[(-2 * π) + a2 < x < (-π) + a2, (2 * sin(x - a2)), If[(4 * π) - a2 < x < (5 * π) - a2, (2 * sin(x + a2 - θ)), 0]]]" />
<element type="function" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="127" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
</element>
</construction>
</geogebra>