{"id":1842,"date":"2022-02-07T13:21:42","date_gmt":"2022-02-07T04:21:42","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=1842"},"modified":"2022-08-24T16:06:35","modified_gmt":"2022-08-24T07:06:35","slug":"%e9%9f%b3%e3%81%ae%e3%83%89%e3%83%83%e3%83%97%e3%83%a9%e3%83%bc%e5%8a%b9%e6%9e%9c","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/1842\/","title":{"rendered":"\u97f3\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c"},"content":{"rendered":"<p>\u9ad8\u6821\u306e\u7269\u7406\u3067\u7fd2\u3046\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u5f0f\u306e\u5c0e\u51fa\u304c\u7406\u89e3\u3067\u304d\u306a\u304b\u3063\u305f\u3002\u7406\u89e3\u3067\u304d\u306a\u3044\u307e\u307e\u9ad8\u6821\u3092\u5352\u696d\u3057\u3066\uff0c\u306a\u307e\u3058\u76f8\u5bfe\u8ad6\u306a\u3093\u304b\u304b\u3058\u3063\u305f\u3082\u306e\u3060\u304b\u3089\uff0c\u540c\u3058\u76f8\u5bfe\u901f\u5ea6\u306a\u306e\u306b\u3069\u3046\u3057\u3066\u89b3\u6e2c\u8005\u304c\u52d5\u304f\u304b\uff0c\u97f3\u6e90\u304c\u52d5\u304f\u304b\u3067\u7b54\u3048\u304c\u9055\u3046\u306e\u304b\u7406\u89e3\u3067\u304d\u306a\u304b\u3063\u305f\u3002\u76f8\u5bfe\u901f\u5ea6\u304c\u540c\u3058\u306a\u3089\u7269\u7406\u3082\u540c\u3058\u3060\u308d\u3046\uff0c\u305d\u308c\u304c\u76f8\u5bfe\u6027\u539f\u7406\u3060\u308d\u3046&#8230; \u306a\u3069\u3046\u305d\u3076\u3044\u3066\u8aa4\u3063\u305f\u8003\u3048\u3092\u6301\u3061\u305d\u3046\u306b\u306a\u3063\u305f\u306e\u3067\uff0c\u3042\u3089\u305f\u3081\u3066\uff08\u5b66\u751f\u306b\u805e\u304b\u308c\u3066\u3082\u3057\u3063\u304b\u308a\u7b54\u3048\u3089\u308c\u308b\u3088\u3046\u306b\uff09\u307e\u3068\u3081\u3066\u307f\u305f\u3002\u305f\u3060\u3057\uff0c\u6a19\u6e96\u7684\u306a\u6559\u79d1\u66f8\u306b\u8f09\u3063\u3066\u3044\u308b\u89e3\u8aac\u3068\u540c\u3058\u3067\u306f\u9762\u767d\u304f\u306a\u3044\u306e\u3067\uff0c\u3061\u3087\u3063\u3068\u72ec\u81ea\u8272\u3092\u51fa\u3057\u3066\u307f\u305f\u3002<\/p>\n<p><!--more--><\/p>\n<p>&nbsp;<\/p>\n<p>$$f&#8217; = f \\frac{V &#8211; v_o}{V &#8211; v_s}$$<\/p>\n<ul>\n<li><a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%89%E3%83%83%E3%83%97%E3%83%A9%E3%83%BC%E5%8A%B9%E6%9E%9C\">\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>\u6ce2\u3092\u8868\u3059\u8af8\u91cf\u306e\u304a\u3055\u3089\u3044<\/h3>\n<ul>\n<li><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u6ce2\u9577<\/strong><\/span>\uff1a$\\lambda$<br \/>\n\u6ce21\u3064\u5206\u306e\u9577\u3055<\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u632f\u52d5\u6570<\/strong><\/span>\uff1a$f$<br \/>\n1\u79d2\u9593\u306b\u4f55\u56de\uff0c\u6ce2\u304c\u30d7\u30eb\u30d7\u30eb\u3068\u632f\u52d5\u3059\u308b\u304b\u3092\u8868\u3059\u3002<\/li>\n<li><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5468\u671f<\/strong><\/span>\uff1a$T$<br \/>\n\u6ce2\u304c1\u56de\u30d7\u30eb\u30c3\u3068\u632f\u52d5\u3059\u308b\u306e\u306b\u304b\u304b\u308b\u6642\u9593 $\\displaystyle T = \\frac{1}{f}$<\/li>\n<li>\u6ce2\u306e\u4f1d\u308f\u308b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u901f\u3055<\/strong><\/span>\uff08\u97f3\u306e\u5834\u5408\u306f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u97f3\u901f<\/strong><\/span>\uff09\uff1a$V$<br \/>\n\u6ce21\u3064\u5206\u306e\u9577\u3055 $\\lambda$ \u3092\u9032\u3080\u306e\u306b\u6642\u9593 $T$ \u304b\u304b\u308b\u306e\u3060\u304b\u3089 $\\displaystyle V = \\frac{\\lambda}{T} = \\lambda f$<\/li>\n<\/ul>\n<h3>\u305d\u3082\u305d\u3082\u4f55\u306b\u5bfe\u3059\u308b\u901f\u3055\u304b<\/h3>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u30ac\u30ea\u30ec\u30a4\u5909\u63db<\/strong><\/span>\u3068\u304b<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u901f\u5ea6\u306e\u5408\u6210\u5247<\/strong><\/span>\u3068\u304b\u3044\u3046\u8a00\u8449\u3092\u3054\u5b58\u77e5\u3067\u3042\u308c\u3070\uff0c\u6ce2\u306e\u4f1d\u308f\u308b\u901f\u3055\u306f $v$ \u3067\u3042\u308b\uff0c\u3068\u3044\u3063\u305f\u3068\u304d\uff0c\u300c\u305d\u308c\u306f\u4f55\u306b\u5bfe\u3059\u308b\u901f\u3055\u304b\u300d\u306b\u610f\u5473\u304c\u3042\u308b\u3053\u3068\u306f\u304a\u308f\u304b\u308a\u3060\u308d\u3046\u3002<\/p>\n<p>\u97f3\u901f\u3092 $V$ \u3068\u66f8\u304f\u3053\u3068\u306b\u3059\u308b\u304c\uff0c\u3053\u308c\u306f\u4f55\u306b\u5bfe\u3059\u308b\uff0c\u3042\u308b\u3044\u306f\u3069\u306e\u3088\u3046\u306a\u9759\u6b62\u7cfb\u306b\u5bfe\u3059\u308b\u901f\u3055\u304b\u3068\u3044\u3046\u3053\u3068\u3092\uff0c\u304f\u3069\u3044\u3088\u3046\u3060\u304c\uff0c\u306f\u3063\u304d\u308a\u3055\u305b\u3066\u304a\u304f\u3002<\/p>\n<p>\u304a\u304a\u3088\u305d\u6ce2\u3068\u3044\u3046\u3082\u306e\u306b\u306f\uff0c\u305d\u308c\u304c\u4f1d\u308f\u3063\u3066\u3044\u304f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u5a92\u8cea<\/strong><\/span>\u3068\u3044\u3046\u3082\u306e\u304c\u5fc5\u8981\u3067\u3042\u308b\u3002\u97f3\u3092\u4f1d\u3048\u308b\u5a92\u8cea\u306f\uff08\u6c34\u4e2d\u3068\u304b\uff0c\u500b\u4f53\u4e2d\u30fb\u91d1\u5c5e\u4e2d\u3068\u304b\u3067\u306a\u3051\u308c\u3070\uff0c\u901a\u5e38\u306f\uff09\u7a7a\u6c17\u3067\u3042\u308b\u3002<\/p>\n<p>\u5f93\u3063\u3066\uff0c\u97f3\u901f\u3068\u306f\uff0c\u5a92\u8cea\u3067\u3042\u308b\u7a7a\u6c17\u306e\u9759\u6b62\u7cfb\u306b\u5bfe\u3059\u308b\u901f\u3055\u3067\u3042\u308b\u3002\u5a92\u8cea\uff08\u7a7a\u6c17\uff09\u9759\u6b62\u7cfb\u306b\u5bfe\u3057\u3066\u9759\u6b62\u3057\u3066\u3044\u308b\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\uff0c\u6ce2\u3068\u3057\u3066\u306e\u97f3\u306e\u4f1d\u308f\u308b\u901f\u3055\u3067\u3042\u308b\u3002\uff08\u3053\u308c\u3092\u300c\u98a8\u304c\u306a\u3044\u3068\u304d\u300d\u306a\u3069\u3068\u98a8\u6d41\u306a\u8a00\u3044\u65b9\u3092\u3059\u308b\u5834\u5408\u3082\u3042\u308b\u3002\uff09<\/p>\n<h3>\u89b3\u6e2c\u8005\u304c\u5a92\u8cea\u9759\u6b62\u7cfb\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u5834\u5408<\/h3>\n<p>\u89b3\u6e2c\u8005\u304c\u5a92\u8cea\uff08\u7a7a\u6c17\uff09\u9759\u6b62\u7cfb\u306b\u9759\u6b62\u3057\u3066\u3044\u308b\u5834\u5408\uff0c\u89b3\u6e2c\u3059\u308b\u97f3\u901f $V$ \u3068\u6ce2\u9577 $\\lambda$\uff0c\u632f\u52d5\u6570 $f$ \u306e\u95a2\u4fc2\u306f\uff0c\u5b9a\u7fa9\u306b\u3088\u308a<br \/>\n$$V =\\lambda f, \\quad \\therefore\\ \\ f = \\frac{V}{\\lambda}$$<\/p>\n<p>\u3053\u308c\u304b\u3089\u304a\u3055\u3089\u3044\u3059\u308b\u3088\u3046\u306b\uff0c\u89b3\u6e2c\u8005\u3084\u97f3\u6e90\u306e\u904b\u52d5\u306b\u3088\u3063\u3066\uff0c\u89b3\u6e2c\u3059\u308b\u632f\u52d5\u6570\u304c\u5909\u5316\u3059\u308b\u306e\u304c\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u3067\u3042\u308b\u3002\u4e0a\u8a18\u306e\u5f0f\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\u632f\u52d5\u6570 $f$ \u3092\u5909\u5316\u3055\u305b\u308b\u8981\u56e0\u306f\u4ee5\u4e0b\u306e2\u3064\u3002<\/p>\n<ul>\n<li>\u8981\u56e01\uff1a\u97f3\u901f\u304c\u304b\u308f\u308b\u3002\uff08\u901f\u5ea6\u306e\u5408\u6210\u5247\u306b\u3088\u308a\uff0c\u89b3\u6e2c\u3059\u308b\u97f3\u901f\u304c\u5909\u308f\u308b\u306e\u306f\u3042\u308a\u3046\u308b\u3002\uff09<\/li>\n<li>\u8981\u56e02\uff1a\u6ce2\u9577\u304c\u304b\u308f\u308b\u3002\uff08\u30ed\u30fc\u30ec\u30f3\u30c4\u53ce\u7e2e\u3067\u3082\u3057\u306a\u3044\u9650\u308a\u9577\u3055\u304c\u5909\u308f\u308b\u306a\u3069\u3068\u3044\u3046\u3053\u3068\u306f\u8003\u3048\u306a\u304f\u3066\u3082\u3088\u3044\u3060\u308d\u3046\u3002\uff09<\/li>\n<\/ul>\n<p>\u8981\u56e01\u304c\u97f3\u306e\u30c9\u30c3\u30d7\u30e9\u30fc\u52b9\u679c\u306e\u30ad\u30e2\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\u307e\u305a\uff0c\u89b3\u6e2c\u8005\u304c\u904b\u52d5\u3057\u3066\u3044\u308b\u5834\u5408\u306e\uff0c\u632f\u52d5\u6570\u3092\u5909\u5316\u3055\u305b\u308b\u8981\u56e0\u306b\u3064\u3044\u3066\u304a\u3055\u3089\u3044\u3059\u308b\u3002<\/p>\n<h3>\u89b3\u6e2c\u8005\u304c\u5a92\u8cea\u9759\u6b62\u7cfb\u306b\u5bfe\u3057\u3066\u904b\u52d5\u3057\u3066\u3044\u308b\u5834\u5408<\/h3>\n<p>\u97f3\u6e90\u304c\u5a92\u8cea\u9759\u6b62\u7cfb\u306e\u539f\u70b9\u306b\u9759\u6b62\u3057\uff0c\u89b3\u6e2c\u8005 (<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>o<\/strong><\/span>bserver \u306e $o$) \u304c\u901f\u5ea6 $v_o$ \u3067\u97f3\u6e90\u304b\u3089$x$ \u306e\u6b63\u65b9\u5411\u3078\u9060\u3056\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3002<\/p>\n<p>\u904b\u52d5\u3059\u308b\u89b3\u6e2c\u8005\u306b\u3068\u3063\u3066\u306f\uff0c\u901f\u5ea6\u306e\u5408\u6210\u5247\u306b\u3088\u308a\uff0c\u97f3\u901f\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u3002<br \/>\n$$V&#8217; = V &#8211; v_o$$<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\uff0c\u3053\u306e\u89b3\u6e2c\u8005\u304c\u89b3\u6e2c\u3059\u308b\u632f\u52d5\u6570\u306f<br \/>\n$$f&#8217; = \\frac{V&#8217;}{\\lambda} = \\frac{f}{V} V&#8217; = f \\frac{V &#8211; v_o}{V}$$<\/p>\n<h3>\u97f3\u6e90\u304c\u5a92\u8cea\u9759\u6b62\u7cfb\u306b\u5bfe\u3057\u3066\u904b\u52d5\u3057\u3066\u3044\u308b\u5834\u5408<\/h3>\n<p>\u89b3\u6e2c\u8005\u304c\u5a92\u8cea\u9759\u6b62\u7cfb\u306b\u5bfe\u3057\u3066\u9759\u6b62\u3057\uff0c\u97f3\u6e90 (<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>s<\/strong><\/span>ource \u306e $s$) \u304c\u901f\u5ea6 $v_s$ \u3067\u89b3\u6e2c\u8005\u304b\u3089$x$ \u306e\u6b63\u65b9\u5411\u3078\u9060\u3056\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3002<\/p>\n<p>\u5a92\u8cea\u9759\u6b62\u7cfb\u306b\u5bfe\u3057\u3066\uff0c\u901f\u5ea6 $v_s$ \u3067 $x$ \u306e\u6b63\u65b9\u5411\u3078\u904b\u52d5\u3059\u308b\u5225\u306e\u6163\u6027\u7cfb $S&#8217;$ \u3067\u8003\u3048\u308b\u3068\uff0c\u3053\u308c\u306f\u97f3\u6e90\u304c\u9759\u6b62\u3057\uff0c\u89b3\u6e2c\u8005\u304c $v_s$ \u3067\u9060\u3056\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3068\u540c\u7b49\u3067\u3042\u308b\u304b\u3089\uff0c\u4e0a\u3067\u6c42\u3081\u305f\u5f0f\u304c\u305d\u306e\u307e\u307e\u4f7f\u3048\u308b\u306f\u305a\u3067\u3042\u308b\u3002<\/p>\n<p>\u305f\u3060\u3057\uff0c\u3053\u306e\u5834\u5408\uff0c$S&#8217;$ \u7cfb\u3067\u306f\u901f\u5ea6\u5408\u6210\u5247\u306b\u3088\u308a\uff0c\u97f3\u901f\u304c $V \\rightarrow V^{&#8221;} = V + v_s$ \u306b\u306a\u308b\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066<\/p>\n<p>$$f&#8217; = f \\frac{V^{&#8221;} &#8211; v_s}{V^{&#8221;}} = f \\frac{(V + v_s) &#8211; v_s}{V + v_s}\u00a0 = f \\frac{V }{V + v_s} $$<\/p>\n<h3>\u89b3\u6e2c\u8005\u30fb\u97f3\u6e90\u3068\u3082\u306b\u904b\u52d5\u3057\u3066\u3044\u308b\u5834\u5408<\/h3>\n<p>\u5408\u308f\u305b\u6280\u3067<\/p>\n<p>$$f&#8217; = f \\frac{V &#8211; v_o }{V + v_s}$$<\/p>\n<p>&#8230; \u3068\u3044\u3046\u7406\u89e3\u306f\u3069\u3046\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u5168\u3066\u306e\u901f\u5ea6\u306f\u5a92\u8cea\uff08\u7a7a\u6c17\uff09\u9759\u6b62\u7cfb\u306b\u5bfe\u3059\u308b\u901f\u5ea6\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3092\u3042\u304b\u3089\u3055\u307e\u306b\u3057\uff0c<span style=\"font-family: helvetica, arial, 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