{"id":24746,"date":"2011-04-21T16:14:05","date_gmt":"2011-04-21T08:14:05","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=24746"},"modified":"2021-10-06T16:27:38","modified_gmt":"2021-10-06T08:27:38","slug":"%e6%b0%b4%e6%b3%a2%e7%9a%84%e6%b3%a2%e9%80%9f%e3%80%88speed-of-water%e3%80%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e6%b0%b4%e6%b3%a2%e7%9a%84%e6%b3%a2%e9%80%9f%e3%80%88speed-of-water%e3%80%89\/","title":{"rendered":"\u6c34\u6ce2\u7684\u6ce2\u901f"},"content":{"rendered":"

\u6c34\u6ce2\u7684\u6ce2\u901f (Speed of Water)<\/span><\/strong>
\n\u570b\u7acb\u5609\u7fa9\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1 \u674e\u6587\u5802\u8001\u5e2b \/ \u570b\u7acb\u5f70\u5316\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb \u6d2a\u9023\u8f1d\u6559\u6388 \u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u9ad8\u4e2d\u7269\u7406\u8ab2\u7a0b\u4e2d\uff0c\u6c34\u6ce2\u662f\u975e\u5e38\u91cd\u8981\u7684\u4e00\u500b\u55ae\u5143\uff0c\u65e5\u5e38\u751f\u6d3b\u4e2d\u4e5f\u5e38\u770b\u5230\u6c34\u6ce2\uff0c\u6c34\u6ce2\u69fd\u5be6\u9a57\u66f4\u662f\u5fc5\u505a\u7684\u5206\u7d44\u5be6\u9a57\uff1b\u8b93\u5b78\u751f\u6df1\u611f\u7591\u60d1\u7684\u662f\uff1a\u8ab2\u672c\u901a\u5e38\u770b\u4e0d\u5230\u6709\u95dc\u6c34\u6ce2\u7684\u6ce2\u901f\u7684\u516c\u5f0f\u3002\u5728\u672c\u5e73\u53f0\u4e0a\u767b\u6709\u300c\u5178\u578b\u7684\u6d77\u6d6a\u300d\u4ecb\u7d39\u6df1\u6c34\u7684\u8868\u9762\u6ce2\u7684\u516c\u5f0f\uff0c\u672c\u6587\u91dd\u5c0d\u4e00\u4e9b\u6ce2\u9577\u8f03\u77ed\u7684\u6ce2\u4f5c\u4ecb\u7d39\u3002<\/p>\n

\u6c34\u9762\u6ce2\u7684\u6ce2\u901f $$v$$<\/span><\/strong><\/p>\n

$$\\displaystyle v^2=\\left(\\frac{g\\lambda}{2\\pi}+\\frac{2\\pi T}{\\rho\\lambda}\\right)\\tanh\\frac{2\\pi H}{\\lambda}~~~~~~~~~(1)$$<\/p>\n

$$\\displaystyle \\tanh x=\\frac{e^{2x}-1}{e^{2x}+1}$$ \u662f\u96d9\u66f2\u6b63\u5207\u51fd\u6578\uff0c$$e$$ \u662f\u81ea\u7136\u5c0d\u6578\u7684\u5e95 $$e\\approx 2.718$$\uff1b\u6240\u4ee5\u6c34\u6ce2\u7684\u6ce2\u901f\u96a8\u8457 (1) \u91cd\u529b\u52a0\u901f\u5ea6 $$g$$ (2) \u6c34\u7684\u8868\u9762\u5f35\u529b $$T$$ (3) \u6c34\u7684\u5bc6\u5ea6 $$\\rho$$ (4) \u6c34\u7684\u6df1\u5ea6 $$H$$ (5) \u6ce2\u9577 $$\\lambda$$<\/span><\/strong>\u00a0\u6539\u8b8a\u3002\u8981\u5f97\u77e5\u6c34\u6ce2\u7684\u6ce2\u901f\uff0c\u5fc5\u9808\u5c07\u4e0a\u8ff0\u7684\u4e94\u500b\u5df2\u77e5\u689d\u4ef6\u5e36\u5165\u516c\u5f0f\uff0c\u624d\u80fd\u6c42\u5f97\u3002<\/p>\n

\u4ee5\u4e0b\u4ecb\u7d39\u5e7e\u7a2e\u7279\u4f8b\uff0c\u53ef\u4ee5\u7528\u8f03\u7c21\u55ae\u7684\u516c\u5f0f\u6c42\u51fa\u6c34\u6ce2\u7684\u6ce2\u901f\u3002<\/p>\n

$$1.$$ \u6c60\u5858\u7684\u6c34\u5982\u679c\u6df1\u5ea6\u8d85\u904e $$5~cm$$\uff0c\u6ce2\u9577\u4e0d\u8d85\u904e $$5~cm$$\uff0c$$x=\\frac{2\\pi H}{\\lambda}\\ge 6.28$$\uff0c$$x$$ \u5df2\u7d93\u904e\u5927\u5230 $$\\tanh x\\approx x$$\uff0c\u6240\u4ee5\u6ce2\u901f\u53ef\u7c21\u5316\u6210\u4e0b\u5217\u5f0f\u5b50:<\/p>\n

$$\\displaystyle v=\\sqrt{\\frac{g\\lambda}{2\\pi}+\\frac{2\\pi T}{\\rho\\lambda}}~~~~~~~~~~~~(2)$$<\/p>\n

\u7531\u300c\u7b97\u8853\u5e73\u5747\u6578\u5927\u65bc\u6216\u7b49\u65bc\u5e7e\u4f55\u5e73\u5747\u6578\u300d\u53ef\u77e5\u4e0b\u5217\u5f0f\u5b50:<\/p>\n

$$\\displaystyle \\frac{g\\lambda}{2\\pi}+\\frac{2\\pi T}{\\rho\\lambda}\\ge 2\\sqrt{\\frac{g\\lambda}{2\\pi}\\times\\frac{2\\pi T}{\\rho\\lambda}}=2\\sqrt{\\frac{gT}{\\rho}}$$<\/p>\n

\u7576\uff1a$$\\frac{g\\lambda}{2\\pi}=\\frac{2\\pi T}{\\rho\\lambda}$$\u00a0\u6642\uff0c\u6c34\u6ce2\u7684\u6ce2\u901f\u6709\u6975\u5c0f\u503c\uff0c\u7b49\u65bc $$2\\sqrt{\\frac{gT}{\\rho}}$$<\/p>\n

\u5c07\u6c34\u7684\u8868\u9762\u5f35\u529b $$T\\approx 72~dy\/cm$$\uff0c\u5bc6\u5ea6 $$\\rho\\approx 1~g\/cm^3$$\uff0c$$g=980~cm\/s^2$$\u00a0\u4ee3\u5165\u4e0a\u4e8c\u5f0f\uff0c\u5f97\u5230\u6ce2\u9577 $$1.7~cm$$ \u7684\u6c34\u6ce2\u6ce2\u901f\u6700\u6162 $$=23~cm\/s$$\uff0c\u6ce2\u9577\u5927\u65bc\u6216\u5c0f\u65bc $$1.7~cm$$\uff0c\u6c34\u6ce2\u7684\u6ce2\u901f\u5747\u5927\u65bc $$23~cm\/s$$\u3002<\/p>\n

\u6ce2\u9577\u5c0f\u65bc $$1.7~cm$$ \u8005\uff0c\u662f\u4ee5\u8868\u9762\u5f35\u529b\u70ba\u6062\u5fa9\u529b\u7684\u8868\u9762\u5f35\u529b\u6ce2 (Capillary wave)\uff0c\u4f8b\u5982\u5c0f\u87f2\u5728\u6c34\u9762\u884c\u8d70\u9020\u6210\u7684\u6c34\u6ce2\uff0c\u5fae\u98a8\u5439\u52d5\u6c34\u9762\u6642\uff0c\u6c34\u4e2d\u67af\u679d\u65c1\u7684\u6c34\u6ce2\uff0c\u91e3\u9b5a\u7dda\u65c1\u7684\u6c34\u6ce2\uff0c\u90fd\u5c6c\u65bc\u9019\u7a2e\u8868\u9762\u5f35\u529b\u6ce2\u3002<\/p>\n

$$2.$$ \u6d17\u624b\u524d\u6c34\u5f9e\u6c34\u9f8d\u982d\u843d\u4e0b\uff0c\u649e\u64ca\u5230\u6c34\u5e73\u677f\uff0c\u6703\u5f62\u6210\u5713\u5f62\u6c34\u8e8d(\u8a73\u898b\u672c\u5e73\u53f0\u53e6\u6587)\uff0c\u6c34\u5e73\u677f\u4e0a\u7684\u6c34\u6df1\u4e0d\u5230 $$1~mm$$\uff0c\u6ce2\u9577\u8d85\u904e $$2~cm$$\uff0c$$x=\\frac{2\\pi H}{\\lambda}$$\u00a0\u4f7f\u5f97 $$\\tanh(\\frac{2\\pi H}{\\lambda})\\approx(\\frac{2\\pi H}{\\lambda})$$\uff0c\u5982\u679c\u8868\u9762\u5f35\u529b\u5ffd\u7565\u4e0d\u8a08\uff0c\u4ee3\u5165\u516c\u5f0f $$(1)$$ \u4e2d\u5f97\u5230\uff1a$$v=\\sqrt{gH}$$\u00a0\u7684\u91cd\u529b\u6ce2\u3002<\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a
\n<\/strong>1.\u00a0\u694a\u5b5f\u6b23\uff1a\u5178\u578b\u7684\u6d77\u6d6a\uff0c\u672c\u5e73\u53f0\uff0c\u7269\u7406\u7de8\u865f03062008\u3002
\n2.\u00a0Vance A. \u201cWaves and water beetles\u201d, The Phys. Teach. 10-19 (1971)
\n3.\u00a0Richard M. \u201cMeasuring g and\u00a0 \u00a0with water waves\u201d, The Phys. Teach. 302-304 (1997)<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u6c34\u6ce2\u7684\u6ce2\u901f (Speed of Water) \u570b\u7acb\u5609\u7fa9\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1 \u674e\u6587\u5802\u8001\u5e2b \/ \u570b\u7acb\u5f70\u5316\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb …<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19,20,107],"tags":[1988,1131,1726],"class_list":["post-24746","post","type-post","status-publish","format-standard","hentry","category-physics04","category-physics04-01","category-physics00","tag-1988","tag-1131","tag-1726","loop-entry","cat-19","cat-20","cat-107","no-thumbnail"],"views":19574,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/24746","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=24746"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/24746\/revisions"}],"predecessor-version":[{"id":88623,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/24746\/revisions\/88623"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=24746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=24746"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=24746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}