{"id":209158,"date":"2024-03-21T14:06:19","date_gmt":"2024-03-21T14:06:19","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/%e6%b3%a2%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f-%e8%a7%a3%e8%aa%ac%e3%80%81%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95%e3%80%81%e5%bf%9c%e7%94%a8%e4%be%8b\/"},"modified":"2024-05-17T15:08:12","modified_gmt":"2024-05-17T15:08:12","slug":"%e6%b3%a2%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f-%e8%a7%a3%e8%aa%ac%e3%80%81%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95%e3%80%81%e5%bf%9c%e7%94%a8%e4%be%8b","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/ja\/%e6%b3%a2%e5%8b%95%e6%96%b9%e7%a8%8b%e5%bc%8f-%e8%a7%a3%e8%aa%ac%e3%80%81%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95%e3%80%81%e5%bf%9c%e7%94%a8%e4%be%8b\/","title":{"rendered":"\u6ce2\u52d5\u65b9\u7a0b\u5f0f | \u89e3\u8aac\u3001\u8a08\u7b97\u65b9\u6cd5\u3001\u5fdc\u7528\u4f8b"},"content":{"rendered":"

\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066\u3001\u57fa\u672c\u306e\u89e3\u8aac\u3068\u8a08\u7b97\u65b9\u6cd5\u3001\u5149\u3084\u96fb\u78c1\u6ce2\u3001\u97f3\u6ce2\u3001\u5730\u9707\u6ce2\u306a\u3069\u306e\u5177\u4f53\u7684\u306a\u5fdc\u7528\u4f8b\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n

\u6ce2\u52d5\u65b9\u7a0b\u5f0f | \u89e3\u8aac\u3001\u8a08\u7b97\u65b9\u6cd5\u3001\u5fdc\u7528\u4f8b<\/h2>\n

\u7269\u7406\u5b66\u306b\u306f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u3084\u60c5\u5831\u304c\u3069\u306e\u3088\u3046\u306b\u7a7a\u9593\u3092\u901a\u3058\u3066\u4f1d\u64ad\u3059\u308b\u304b\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306e\u6570\u591a\u304f\u306e\u65b9\u7a0b\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u4e2d\u3067\u3082\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306f\u3001\u975e\u5e38\u306b\u57fa\u672c\u3067\u3042\u308a\u306a\u304c\u3089\u5f37\u529b\u306a\u9053\u5177\u3067\u3059\u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u5149\u3084\u96fb\u78c1\u6ce2\u3001\u97f3\u6ce2\u3001\u6c34\u9762\u6ce2\u306a\u3069\u3001\u69d8\u3005\u306a\u73fe\u8c61\u3092\u89e3\u6790\u3059\u308b\u624b\u52a9\u3051\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3\u8aac<\/h3>\n

\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306f\u3001\u4e3b\u306b\u6ce2\u306e\u6642\u9593\u3068\u7a7a\u9593\u306b\u304a\u3051\u308b\u5909\u52d5\u3092\u8a18\u8ff0\u3059\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3059\u3002\u305d\u306e\u57fa\u672c\u5f62\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n

\\[
\n\\frac{\\partial^2 u}{\\partial t^2} = c^2 \\nabla^2 u
\n\\]<\/p>\n

\u3053\u3053\u3067\u3001
\n– \\( u \\) \u306f\u6ce2\u306e\u5909\u4f4d\uff08\u4f8b\u3048\u3070\u3001\u97f3\u6ce2\u306a\u3089\u7a7a\u6c17\u306e\u5727\u529b\u5909\u52d5\u3001\u5149\u6ce2\u306a\u3089\u96fb\u5834\uff09\u3001
\n– \\( t \\) \u306f\u6642\u9593\u3001
\n– \\( c \\) \u306f\u6ce2\u306e\u901f\u5ea6\u3001
\n– \\( \\nabla^2 \\) \u306f\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\uff08\u7a7a\u9593\u306e\u4e8c\u968e\u5fae\u5206\u6f14\u7b97\u5b50\uff09\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n

\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u3001\u4e00\u3064\u306e\u6b21\u5143\u306b\u5236\u7d04\u3057\u305f\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u7c21\u7565\u5316\u3055\u308c\u307e\u3059\uff1a<\/p>\n

\\[
\n\\frac{\\partial^2 u}{\\partial t^2} = c^2 \\frac{\\partial^2 u}{\\partial x^2}
\n\\]<\/p>\n

\u4f8b\u984c\u3068\u8a08\u7b97\u65b9\u6cd5<\/h3>\n

\u5177\u4f53\u4f8b\u3068\u3057\u3066\u3001\u4e00\u65b9\u5411\u306b\u4f1d\u308f\u308b\u6ce2\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u521d\u671f\u6761\u4ef6\u3068\u3057\u3066\u4ee5\u4e0b\u3092\u8003\u3048\u307e\u3059\uff1a
\n– \u6642\u9593 \\( t = 0 \\) \u306e\u6642\u3001\u6ce2\u306e\u5f62\u306f \\( f(x) \\) \u3067\u3042\u308b\u3002
\n– \u6642\u9593 \\( t = 0 \\) \u306e\u6642\u3001\u6ce2\u306e\u901f\u5ea6\u306f\u30bc\u30ed\u3001\u3064\u307e\u308a \\( \\frac{\\partial u}{\\partial t} = 0 \\)\u3002<\/p>\n

\u3053\u308c\u3092\u4f7f\u3063\u3066\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\u3001\u4e00\u822c\u7684\u306a\u89e3\u306f\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n

\\[
\nu(x, t) = f(x – ct) + g(x + ct)
\n\\]<\/p>\n

\u3053\u3053\u3067\u3001\\( f \\) \u3068 \\( g \\) \u306f\u521d\u671f\u6761\u4ef6\u306b\u5f93\u3063\u305f\u95a2\u6570\u3067\u3059\u3002\u6ce2\u304c\u5de6\u65b9\u5411\u3068\u53f3\u65b9\u5411\u306b\u9032\u3080\u4e8c\u3064\u306e\u6210\u5206\u306b\u5206\u304b\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n

\u5177\u4f53\u4f8b\u3068\u3057\u3066\u3001\u521d\u671f\u6761\u4ef6 \\( f(x) = \\sin(kx) \\) \u3068 \\( g(x) = 0 \\) \u306e\u5834\u5408\u3001\u89e3\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n

\\[
\nu(x, t) = \\sin(k(x – ct))
\n\\]<\/p>\n

\u3053\u308c\u306f\u6ce2\u304c \\( x \\) \u65b9\u5411\u306b\u901f\u5ea6 \\( c \\) \u3067\u9032\u3080\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n

\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306e\u5fdc\u7528<\/h3>\n

\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306f\u591a\u304f\u306e\u5206\u91ce\u3067\u5fdc\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3044\u304f\u3064\u304b\u306e\u5177\u4f53\u4f8b\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n

\u96fb\u78c1\u6ce2<\/h4>\n

\u30de\u30c3\u30af\u30b9\u30a6\u30a7\u30eb\u306e\u65b9\u7a0b\u5f0f\u304b\u3089\u5c0e\u304b\u308c\u308b\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306f\u3001\u96fb\u78c1\u6ce2\u306e\u4f1d\u64ad\u3092\u8a18\u8ff0\u3057\u307e\u3059\u3002\u5149\u3084\u96fb\u6ce2\u306f\u3053\u306e\u65b9\u7a0b\u5f0f\u306b\u5f93\u3044\u3001\u7a7a\u9593\u3092\u4f1d\u308f\u308a\u307e\u3059\u3002\u5149\u901a\u4fe1\u6280\u8853\u3084\u7121\u7dda\u901a\u4fe1\u6280\u8853\u306e\u57fa\u790e\u306b\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u304c\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n

\u97f3\u6ce2<\/h4>\n

\u97f3\u6ce2\u306f\u7a7a\u6c17\u4e2d\u3092\u4f1d\u308f\u308b\u5727\u529b\u5909\u52d5\u3068\u3057\u3066\u8a18\u8ff0\u3055\u308c\u3001\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u97f3\u97ff\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\u3067\u306f\u97f3\u6ce2\u304c\u3069\u306e\u3088\u3046\u306b\u4f1d\u64ad\u3057\u3001\u53cd\u5c04\u3057\u3001\u5e72\u6e09\u3059\u308b\u304b\u3092\u4e88\u6e2c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u30b9\u30d4\u30fc\u30ab\u30fc\u8a2d\u8a08\u3084\u5efa\u7bc9\u97f3\u97ff\u306b\u304a\u3044\u3066\u91cd\u8981\u3067\u3059\u3002<\/p>\n

\u5730\u9707\u6ce2<\/h4>\n

\u5730\u9707\u6ce2\u3082\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u3067\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002\u5730\u9707\u767a\u751f\u6642\u306b\u751f\u3058\u308b\u6ce2\uff08P\u6ce2\u3001S\u6ce2\uff09\u306f\u5730\u7403\u5185\u90e8\u3092\u4f1d\u308f\u308a\u3001\u5730\u8868\u3067\u89b3\u6e2c\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5730\u9707\u306e\u30e2\u30cb\u30bf\u30ea\u30f3\u30b0\u3084\u5730\u7403\u5185\u90e8\u69cb\u9020\u306e\u7814\u7a76\u304c\u884c\u308f\u308c\u307e\u3059\u3002<\/p>\n

\u6c34\u9762\u6ce2<\/h4>\n

\u6c34\u9762\u6ce2\u306f\u6d41\u4f53\u529b\u5b66\u306e\u4e00\u90e8\u3067\u3042\u308a\u3001\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u6d25\u6ce2\u306e\u4e88\u6e2c\u3084\u6d77\u6d0b\u5de5\u5b66\u306b\u304a\u3051\u308b\u6ce2\u6d6a\u8a2d\u8a08\u304c\u884c\u308f\u308c\u307e\u3059\u3002<\/p>\n

\u307e\u3068\u3081<\/h3>\n

\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u306f\u3001\u591a\u304f\u306e\u7269\u7406\u73fe\u8c61\u3092\u89e3\u6790\u3059\u308b\u305f\u3081\u306e\u91cd\u8981\u306a\u30c4\u30fc\u30eb\u3067\u3059\u3002\u305d\u306e\u57fa\u672c\u5f62\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u3067\u3001\u6570\u591a\u304f\u306e\u5fdc\u7528\u5206\u91ce\u306b\u304a\u3044\u3066\u5f79\u7acb\u3064\u77e5\u8b58\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6ce2\u52d5\u65b9\u7a0b\u5f0f\u3092\u901a\u3058\u3066\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u3084\u60c5\u5831\u306e\u4f1d\u64ad\u306b\u3064\u3044\u3066\u6df1\u304f\u7406\u89e3\u3057\u3001\u3055\u3089\u306a\u308b\u5b66\u3073\u3092\u9032\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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