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13434-ph-ng-tr-nh-s-ng-la-gi [2018/11/07 17:13] (current)
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 +<​HTML><​br><​div id="​mw-content-text"​ lang="​vi"​ dir="​ltr"><​div class="​mw-parser-output"><​dl><​dd><​i>​Phân biệt với hàm sóng - nghiệm của phương trình sóng, nhưng thường dùng để chỉ nghiệm phương trình Schrodinger</​i></​dd></​dl><​div class="​thumb tright"><​div class="​thumbinner"​ style="​width:​276px;"><​img alt=""​ src="​http://​upload.wikimedia.org/​wikipedia/​commons/​1/​1f/​Wave_equation_1D_fixed_endpoints.gif"​ width="​274"​ height="​121"​ class="​thumbimage"​ data-file-width="​274"​ data-file-height="​121"/> ​ <div class="​thumbcaption">​Một sóng trên một sợi dây</​div></​div></​div>​
 +<​p><​b>​Phương trình sóng</​b>​ là phương trình vi phân riêng phần tuyến tính bậc hai mô tả các sóng trong vật lý<sup id="​cite_ref-1"​ class="​reference">​[1]</​sup>​. Cũng có phương trình vi phân riêng phần mô tả sóng trong vật lý không tuyến tính bậc hai, như phương trình Schrodinger mô tả sóng vật chất.
 +</​p><​p>​Ở dạng đơn giản nhất, trong phương trình sóng có biến số thời gian <​i>​t</​i>,​ một hoặc một vài biến số không gian <​i>​x</​i><​sub>​1</​sub>,​ <​i>​x</​i><​sub>​2</​sub>,​ …, <​i>​x</​i><​sub><​i>​n</​i></​sub>,​ và một hàm vô hướng, gọi là hàm sóng cần thỏa mãn phương trình này <​i>​u</​i>​ = <​i>​u</​i>​(<​i>​x</​i><​sub>​1</​sub>,​ <​i>​x</​i><​sub>​2</​sub>,​ …, <​i>​x</​i><​sub><​i>​n</​i></​sub>;​ <​i>​t</​i>​). Giá trị của hàm sóng có thể thể hiện ly độ của sóng. Phương trình sóng khi đó có thể biểu diễn là:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {partial ^{2}u over partial t^{2}}=c^{2}nabla ^{2}u}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mrow><​msup><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​u</​mi></​mrow><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​msup><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mo>​=</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​msup><​mi mathvariant="​normal">​∇<​!-- &nabla; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​u</​mi></​mstyle></​mrow>​{displaystyle {partial ^{2}u over partial t^{2}}=c^{2}nabla ^{2}u}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​75a9ffe02fba001388931079b7bab7c9e4dea451"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.171ex; width:​14.043ex;​ height:​6.009ex;"​ alt="​{displaystyle {partial ^{2}u over partial t^{2}}=c^{2}nabla ^{2}u}"/></​span></​dd></​dl><​p>​với <span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle scriptstyle nabla ^{2}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mstyle displaystyle="​false"​ scriptlevel="​1"><​msup><​mi mathvariant="​normal">​∇<​!-- &nabla; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mstyle></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle scriptstyle nabla ^{2}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​5d08709d6f47f1a00a38b6e641c8a693c3078923"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.338ex; width:​2.2ex;​ height:​2.009ex;"​ alt="​{displaystyle scriptstyle nabla ^{2}}"/></​span>​ là <a href="​http://​vi.wikipedia.org/​wiki/​To%C3%A1n_t%E1%BB%AD_Laplace"​ title="​Toán tử Laplace">​toán tử Laplace và <​i>​c</​i>​ là một hệ số, thường đặc trưng cho tốc độ lan truyền của sóng.
 +</​p><​p>​Để xác định các hàm sóng cụ thể là nghiệm của phương trình sóng, thường phải cần biết thêm các điều kiện ban đầu và các điều kiện biên.
 +</​p><​p><​br/>​Với sóng chuyển động trên một chiều không gian <​i>​x</​i>,​ phương trình sóng có thể viết ở dạng đơn giản là:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {frac {partial ^{2}u}{partial t^{2}}}=c^{2}{frac {partial ^{2}u}{partial x^{2}}}.,​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mrow><​msup><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​u</​mi></​mrow><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​msup><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mo>​=</​mo><​msup><​mi>​c</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mrow><​msup><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mi>​u</​mi></​mrow><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​msup><​mi>​x</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mo>​.</​mo><​mspace width="​thinmathspace"/></​mstyle></​mrow>​{displaystyle {frac {partial ^{2}u}{partial t^{2}}}=c^{2}{frac {partial ^{2}u}{partial x^{2}}}.,​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​8cff9b541151578928c75a5fdc36883cda35d02d"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.171ex; width:​15.32ex;​ height:​6.009ex;"​ alt="​{displaystyle {frac {partial ^{2}u}{partial t^{2}}}=c^{2}{frac {partial ^{2}u}{partial x^{2}}}.,​}"/></​span></​dd></​dl><​p>​Nghiệm tổng quát có thể được tìm dựa theo <a href="​http://​vi.wikipedia.org/​w/​index.php?​title=Nguy%C3%AAn_l%C3%BD_Duhamel&​amp;​action=edit&​amp;​redlink=1"​ class="​new"​ title="​Nguyên lý Duhamel (trang chưa được viết)">​nguyên lý Duhamel.<​sup id="​cite_ref-Struwe_2-0"​ class="​reference">​[2]</​sup>,​ nó là các hàm sóng:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle u(x, t)=F(x-c t)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​u</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>,</​mo><​mtext>​ </​mtext><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mi>​F</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​c</​mi><​mtext>​ </​mtext><​mi>​t</​mi><​mo stretchy="​false">​)</​mo></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle u(x, t)=F(x-c t)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​7333c10390499b2f2cff20f786db1ad8386dc7cd"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​20.169ex;​ height:​2.843ex;"​ alt="​{displaystyle u(x, t)=F(x-c t)}"/></​span> ​ (chuyển động theo chiều dương trục <​i>​x</​i>​)</​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle u(x, t)=G(x+c t)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​u</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>,</​mo><​mtext>​ </​mtext><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mi>​G</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>​+</​mo><​mi>​c</​mi><​mtext>​ </​mtext><​mi>​t</​mi><​mo stretchy="​false">​)</​mo></​mstyle></​mrow>​{displaystyle u(x, t)=G(x+c t)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​7f3bb48adefb3302725ba74e1a5796d606c5ea45"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​20.255ex;​ height:​2.843ex;"​ alt="​{displaystyle u(x, t)=G(x+c t)}"/></​span> ​ (chuyển động theo chiều âm trục <​i>​x</​i>​)</​dd></​dl><​p>​hay tổng quát hơn, theo <a href="​http://​vi.wikipedia.org/​w/​index.php?​title=C%C3%B4ng_th%E1%BB%A9c_d%27Alembert&​amp;​action=edit&​amp;​redlink=1"​ class="​new"​ title="​Công thức d'​Alembert (trang chưa được viết)">​công thức d'​Alembert:<​sup id="​cite_ref-Graaf_3-0"​ class="​reference">​[3]</​sup></​p>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle u(x,​t)=F(x-ct)+G(x+ct).,​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​u</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>,</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mi>​F</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​c</​mi><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​+</​mo><​mi>​G</​mi><​mo stretchy="​false">​(</​mo><​mi>​x</​mi><​mo>​+</​mo><​mi>​c</​mi><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​.</​mo><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle u(x,​t)=F(x-ct)+G(x+ct).,​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​0eea6d3723150d01db9610a588cc270cf41f12be"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​32.534ex;​ height:​2.843ex;"​ alt="​{displaystyle u(x,​t)=F(x-ct)+G(x+ct).,​}"/></​span></​dd></​dl>​
  
 +<​h2><​span id="​Ph.C6.B0.C6.A1ng_Tr.C3.ACnh_S.C3.B3ng_Dao_.C4.90.E1.BB.99ng_L.C3.B2_Xo"/><​span class="​mw-headline"​ id="​Phương_Trình_Sóng_Dao_Động_Lò_Xo">​Phương Trình Sóng Dao Động Lò Xo</​span><​span class="​mw-editsection"><​span class="​mw-editsection-bracket">​[</​span>​sửa<​span class="​mw-editsection-divider">​ | </​span>​sửa mã nguồn<​span class="​mw-editsection-bracket">​]</​span></​span></​h2>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle m{frac {d^{2}}{dt^{2}}}f(t)+kf(t)=0}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​m</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​msup><​mi>​d</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mrow><​mi>​d</​mi><​msup><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​+</​mo><​mi>​k</​mi><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mn>​0</​mn></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle m{frac {d^{2}}{dt^{2}}}f(t)+kf(t)=0}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​7e426cffe5c69a927045c0f70d165bfe72a950dd"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.171ex; width:​22.154ex;​ height:​6.009ex;"​ alt="​{displaystyle m{frac {d^{2}}{dt^{2}}}f(t)+kf(t)=0}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)=-omega f(t)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​msup><​mi>​d</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mrow><​mi>​d</​mi><​msup><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mo>​−<​!-- &minus; --></​mo><​mi>​ω<​!-- &omega; --></​mi><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)=-omega f(t)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​dcec9927120fcc3ecf37972d3c631223c6a051d9"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.171ex; width:​18.153ex;​ height:​6.009ex;"​ alt="​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)=-omega f(t)}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle omega ={sqrt {frac {k}{m}}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​ω<​!-- &omega; --></​mi><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​msqrt><​mfrac><​mi>​k</​mi><​mi>​m</​mi></​mfrac></​msqrt></​mrow></​mstyle></​mrow>​{displaystyle omega ={sqrt {frac {k}{m}}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​e901183c61a98d7f3f967c78f7ec02c0f0507be5"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.338ex; width:​9.745ex;​ height:​6.176ex;"​ alt="​{displaystyle omega ={sqrt {frac {k}{m}}}}"/></​span></​dd></​dl><​h2><​span id="​Ph.C6.B0.C6.A1ng_Tr.C3.ACnh_S.C3.B3ng_Dao_.C4.90.E1.BB.99ng_.C4.90i.E1.BB.87n"/><​span class="​mw-headline"​ id="​Phương_Trình_Sóng_Dao_Động_Điện">​Phương Trình Sóng Dao Động Điện</​span><​span class="​mw-editsection"><​span class="​mw-editsection-bracket">​[</​span><​a href="​http://​vi.wikipedia.org/​w/​index.php?​title=Ph%C6%B0%C6%A1ng_tr%C3%ACnh_s%C3%B3ng&​amp;​veaction=edit&​amp;​section=2"​ class="​mw-editsection-visualeditor"​ title="​Sửa đổi phần “Phương Trình Sóng Dao Động Điện”">​sửa<​span class="​mw-editsection-divider">​ | </​span>​sửa mã nguồn<​span class="​mw-editsection-bracket">​]</​span></​span></​h2>​
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)+{frac {1}{T}}=0}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​msup><​mi>​d</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mrow><​mi>​d</​mi><​msup><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​+</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mn>​1</​mn><​mi>​T</​mi></​mfrac></​mrow><​mo>​=</​mo><​mn>​0</​mn></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)+{frac {1}{T}}=0}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​ac0a2232e638b7b186274290acec6ce7f4605648"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.171ex; width:​17.447ex;​ height:​6.009ex;"​ alt="​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)+{frac {1}{T}}=0}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)=-omega f(t)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​msup><​mi>​d</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mrow><​mi>​d</​mi><​msup><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mrow></​mfrac></​mrow><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mo>​−<​!-- &minus; --></​mo><​mi>​ω<​!-- &omega; --></​mi><​mi>​f</​mi><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)=-omega f(t)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​dcec9927120fcc3ecf37972d3c631223c6a051d9"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.171ex; width:​18.153ex;​ height:​6.009ex;"​ alt="​{displaystyle {frac {d^{2}}{dt^{2}}}f(t)=-omega f(t)}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle omega ={sqrt {frac {1}{T}}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​ω<​!-- &omega; --></​mi><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​msqrt><​mfrac><​mn>​1</​mn><​mi>​T</​mi></​mfrac></​msqrt></​mrow></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle omega ={sqrt {frac {1}{T}}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​d66886a84745260a6d8a032199f0ef84ef3008a0"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.338ex; width:​9.34ex;​ height:​6.176ex;"​ alt="​{displaystyle omega ={sqrt {frac {1}{T}}}}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle T=LC}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​T</​mi><​mo>​=</​mo><​mi>​L</​mi><​mi>​C</​mi></​mstyle></​mrow>​{displaystyle T=LC}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​e877f3836c9f9841867b838545cc528a307e5dc8"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.338ex; width:​8.084ex;​ height:​2.176ex;"​ alt="​{displaystyle T=LC}"/></​span></​dd></​dl><​h2><​span id="​Ph.C6.B0.C6.A1ng_Tr.C3.ACnh_S.C3.B3ng_Dao_.C4.90.E1.BB.99ng_.C4.90i.E1.BB.87n_T.E1.BB.AB"/><​span class="​mw-headline"​ id="​Phương_Trình_Sóng_Dao_Động_Điện_Từ">​Phương Trình Sóng Dao Động Điện Từ</​span><​span class="​mw-editsection"><​span class="​mw-editsection-bracket">​[</​span><​a href="​http://​vi.wikipedia.org/​w/​index.php?​title=Ph%C6%B0%C6%A1ng_tr%C3%ACnh_s%C3%B3ng&​amp;​veaction=edit&​amp;​section=3"​ class="​mw-editsection-visualeditor"​ title="​Sửa đổi phần “Phương Trình Sóng Dao Động Điện Từ”">​sửa<​span class="​mw-editsection-divider">​ | </​span>​sửa mã nguồn<​span class="​mw-editsection-bracket">​]</​span></​span></​h2>​
 +<​p>​Phương trình Maxwell mô tả Sóng Dao Động Điện Từ trong Không Khí
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle nabla cdot mathbf {E} =0}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi mathvariant="​normal">​∇<​!-- &nabla; --></​mi><​mo>​⋅<​!-- &sdot; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​bold">​E</​mi></​mrow><​mo>​=</​mo><​mn>​0</​mn></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle nabla cdot mathbf {E} =0}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​bcbd9a4bd688b1331c2fd3c7fd1d50f0bf87fc28"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.338ex; width:​9.633ex;​ height:​2.176ex;"​ alt="​{displaystyle nabla cdot mathbf {E} =0}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle nabla cdot mathbf {B} =0}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi mathvariant="​normal">​∇<​!-- &nabla; --></​mi><​mo>​⋅<​!-- &sdot; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​bold">​B</​mi></​mrow><​mo>​=</​mo><​mn>​0</​mn></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle nabla cdot mathbf {B} =0}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​16ee950683349dacdd9e9c262ff6133812747edd"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.338ex; width:​9.777ex;​ height:​2.176ex;"​ alt="​{displaystyle nabla cdot mathbf {B} =0}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle nabla times mathbf {E} =-{frac {1}{c}}{frac {partial mathbf {B} }{partial t}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi mathvariant="​normal">​∇<​!-- &nabla; --></​mi><​mo>​×<​!-- &times; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​bold">​E</​mi></​mrow><​mo>​=</​mo><​mo>​−<​!-- &minus; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mn>​1</​mn><​mi>​c</​mi></​mfrac></​mrow><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​bold">​B</​mi></​mrow></​mrow><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mi>​t</​mi></​mrow></​mfrac></​mrow></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle nabla times mathbf {E} =-{frac {1}{c}}{frac {partial mathbf {B} }{partial t}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​d547090a502047c2fa10d924871a2ea71e1bcc6a"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.005ex; width:​17.494ex;​ height:​5.509ex;"​ alt="​{displaystyle nabla times mathbf {E} =-{frac {1}{c}}{frac {partial mathbf {B} }{partial t}}}"/></​span></​dd>​
 +<​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle nabla times mathbf {B} ={frac {1}{c}}{frac {partial mathbf {E} }{partial t}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi mathvariant="​normal">​∇<​!-- &nabla; --></​mi><​mo>​×<​!-- &times; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​bold">​B</​mi></​mrow><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mn>​1</​mn><​mi>​c</​mi></​mfrac></​mrow><​mrow class="​MJX-TeXAtom-ORD"><​mfrac><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​bold">​E</​mi></​mrow></​mrow><​mrow><​mi mathvariant="​normal">​∂<​!-- &part; --></​mi><​mi>​t</​mi></​mrow></​mfrac></​mrow></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle nabla times mathbf {B} ={frac {1}{c}}{frac {partial mathbf {E} }{partial t}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​4be2d8749127d39bacf7cf623d485fd867fd7737"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -2.005ex; width:​15.686ex;​ height:​5.509ex;"​ alt="​{displaystyle nabla times mathbf {B} ={frac {1}{c}}{frac {partial mathbf {E} }{partial t}}}"/></​span></​dd></​dl>​
 +
 +<div class="​reflist"​ style="​list-style-type:​ decimal;">​
 +<ol class="​references"><​li id="​cite_note-1"><​b>​^</​b>​ <span class="​reference-text">​Halliday,​ Resnick, Walker, Principles of Physics, 9th edition, International student version, John Wiley &amp; Son, 2011, ISBN 978-0-470-56158-4,​ trang 424</​span>​
 +</li>
 +<li id="​cite_note-Struwe-2"><​b>​^</​b>​ <span class="​reference-text">​
 +<span class="​citation book">​Jalal M. Ihsan Shatah, Michael Struwe (2000). “The linear wave equation”. <​i>​Geometric wave equations</​i>​. American Mathematical Society Bookstore. tr. 37 <​i>​ff</​i>​. ISBN 0-8218-2749-9.</​span><​span title="​ctx_ver=Z39.88-2004&​amp;​rfr_id=info%3Asid%2Fvi.wikipedia.org%3APh%C6%B0%C6%A1ng+tr%C3%ACnh+s%C3%B3ng&​amp;​rft.atitle=The+linear+wave+equation&​amp;​rft.au=Jalal+M.+Ihsan+Shatah%2C+Michael+Struwe&​amp;​rft.aulast=Jalal+M.+Ihsan+Shatah%2C+Michael+Struwe&​amp;​rft.btitle=Geometric+wave+equations&​amp;​rft.date=2000&​amp;​rft.genre=bookitem&​amp;​rft.isbn=0-8218-2749-9&​amp;​rft.pages=37+%27%27ff%27%27&​amp;​rft.pub=American+Mathematical+Society+Bookstore&​amp;​rft_id=http%3A%2F%2Fbooks.google.com%2F%3Fid%3DzsasG2axbSoC%26pg%3DPA37&​amp;​rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook"​ class="​Z3988"><​span style="​display:​none;">​ </​span></​span></​span>​
 +</li>
 +<li id="​cite_note-Graaf-3"><​b>​^</​b>​ <span class="​reference-text">​
 +<span class="​citation book">​Karl F Graaf (1991). <​i>​Wave motion in elastic solids</​i>​ . Dover. tr. 13–14. ISBN 978-0-486-66745-4.</​span><​span title="​ctx_ver=Z39.88-2004&​amp;​rfr_id=info%3Asid%2Fvi.wikipedia.org%3APh%C6%B0%C6%A1ng+tr%C3%ACnh+s%C3%B3ng&​amp;​rft.au=Karl+F+Graaf&​amp;​rft.aulast=Karl+F+Graaf&​amp;​rft.btitle=Wave+motion+in+elastic+solids&​amp;​rft.date=1991&​amp;​rft.edition=Reprint+of+Oxford+1975&​amp;​rft.genre=book&​amp;​rft.isbn=978-0-486-66745-4&​amp;​rft.pages=13-14&​amp;​rft.pub=Dover&​amp;​rft_id=http%3A%2F%2Fbooks.google.com%2F%3Fid%3D5cZFRwLuhdQC%26printsec%3Dfrontcover&​amp;​rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook"​ class="​Z3988"><​span style="​display:​none;">​ </​span></​span></​span>​
 +</li>
 +</​ol></​div>​
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13434-ph-ng-tr-nh-s-ng-la-gi.txt · Last modified: 2018/11/07 17:13 (external edit)