波动方程Asin(kx-ωt)中kx和ωt分别表示波的什么？ 物理学科分类
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Physics
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\u25cf 1900~1926\u5e74 \u5efa\u7acb\u4e86\u91cf\u5b50\u529b\u5b66\u3002
\u25cf 1926\u5e74 \u5efa\u7acb\u4e86\u8d39\u7c73\u72c4\u62c9\u514b\u7edf\u8ba1\u3002
\u25cf 1927\u5e74 \u5efa\u7acb\u4e86\u5e03\u6d1b\u8d6b\u6ce2\u7684\u7406\u8bba\u3002
\u25cf 1928\u5e74 \u7d22\u672b\u83f2\u63d0\u51fa\u80fd\u5e26\u7684\u731c\u60f3\u3002
\u25cf 1929\u5e74 \u6d3e\u5c14\u65af\u63d0\u51fa\u7981\u5e26\u3001\u7a7a\u7a74\u7684\u6982\u5ff5\uff0c\u540c\u5e74\u8d1d\u7279\u63d0\u51fa\u4e86\u8d39\u7c73\u9762\u7684\u6982\u5ff5\u3002
\u25cf 1947\u5e74\u8d1d\u5c14\u5b9e\u9a8c\u5ba4\u7684\u5df4\u4e01\u3001\u5e03\u62c9\u987f\u548c\u8096\u514b\u83b1\u53d1\u660e\u4e86\u6676\u4f53\u7ba1\uff0c\u6807\u5fd7\u7740\u4fe1\u606f\u65f6\u4ee3\u7684\u5f00\u59cb\u3002
\u25cf 1957\u5e74 \u76ae\u5e15\u5f97\u6d4b\u91cf\u4e86\u7b2c\u4e00\u4e2a\u8d39\u7c73\u9762\u8d85\u6676\u683c\u6750\u6599\u7eb3\u7c73\u6750\u6599\u5149\u5b50\u3002
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\u5b66\u79d1\u6027\u8d28
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k=2*π/λ，代表波数
w=2πf，角频率，振动频率
绛旓細浜庢槸锛(*) 鍙敼鍐欎负锛歽(z,t) = A cos [kiri + 蠁]鐜板湪寮曞叆鈥滃鎸箙鈥濈殑姒傚康锛屼篃姝ｅ鐢电鍦虹悊璁轰腑鐨勬蹇典竴鏍枫備簬鏄細y(z,t) = ℜ(A ej蠁 exp (jkiri))浠わ細唯 = A exp (jkiri)鍙互 璇佹槑 唯 婊¤冻娉㈠姩鏂圭▼锛∂2唯/∂ri∂ri= 鈻∥...
绛旓細涓嶆槸涓涓剰鎬!娉㈠姩鏂圭▼,鎸姩鏂圭▼鏄姩鍔涘鏂圭▼,鏁板褰㈠紡涓婂畠涓鑸槸涓涓井鍒嗘柟绋嬧斺旀煇涓嚱鏁板強璇ュ嚱鏁扮殑鍚勯樁瀵兼暟鐨勫悇绉嶇粍鍚堟墍婊¤冻鐨勪竴涓瓑寮,姣斿鏈绠鍗曠殑鎸姩鏂圭▼褰㈠x''+wwx=0,鍏朵腑w鏄釜甯告暟,x鏄椂闂寸殑鍑芥暟,x''=d(dx/dt)/dt,鏄痻鍏充簬t鐨勪簩闃跺鏁.婊¤冻x''+wwx=0鐨勮Вx=Asin(wt+b)灏辨槸...
绛旓細涓夈佸彉閲忎笉鍚岋細鎸姩鏂圭▼鐨勫彉閲忔槸t锛娉㈠姩鏂圭▼鐨勫彉閲忔槸x锛宼銆傜畝浠嬶細鏂圭▼锛坋quation锛夛紝鏄寚鍚湁鏈煡鏁扮殑绛夊紡銆傛槸琛ㄧず涓や釜鏁板寮忥紙濡備袱涓暟銆佸嚱鏁般侀噺銆佽繍绠楋級涔嬮棿鐩哥瓑鍏崇郴鐨勪竴绉嶇瓑寮忥紝浣跨瓑寮忔垚绔嬬殑鏈煡鏁扮殑鍊肩О涓衡滆В鈥濇垨鈥滄牴鈥濄傛眰鏂圭▼鐨勮В鐨勮繃绋嬬О涓衡滆В鏂圭▼鈥濄傞氳繃鏂圭▼姹傝В鍙互鍏嶅幓閫嗗悜鎬濊冪殑涓嶆槗...
绛旓細棣栧厛浣犲緱鐭ラ亾娉紶鎾殑閫熷害锛屽洜涓烘尟鍔ㄩ熷害鍜屾尝浼犳挱鐨勯熷害鏄笉涓鏍风殑锛屼簩鑰呬箣闂存病鏈変换浣曞叧绯汇傜煡閬撲簡娉㈢殑浼犳挱閫熷害涔嬪悗锛岀‘瀹氬師鐐癸紝纭畾鍒濈浉浣嶈涓簑0銆傛尝閫*鎸姩鍛ㄦ湡=娉㈤暱璁颁负x锛屾尟鍔ㄦ柟绋嬬殑鏈澶т綅绉绘槸娉㈢殑H鎸箙璁颁负A鍒欐尝鐨勬柟绋嬪彲浠ュ啓鎴Asin(nx+w0)娉㈠姩鏂圭▼鐨勬湰璐ㄦ槸鎸姩鏂圭▼锛屽舰寮忎笂鑷劧涓鏍凤紝浠栦滑鐨勫尯鍒...
绛旓細娉㈠姩鏂圭▼y=Asin锛埾塼-2蟺x/位+蠁锛堿=0.4m 位=12m 灏嗗浘鍍忎腑t=0锛寈=1锛寉=0.2甯﹀叆涓婂紡鍙緱蠁=蟺/3 灏唗=5锛寈=1锛寉=0甯﹀叆寰椣/6 鎵浠ユ尝鍔ㄦ柟绋媦=0.4sin锛埾t/6-蟺x/6+蟺/3锛
绛旓細鍒欓┗娉㈢殑娉㈠姩鏂圭▼涓猴細u锛坸,t锛=2Asin锛x锛塻in锛蠅t锛=A锛坸锛塻in锛埾塼锛夎拷闂細鏈夋帹瀵艰繃绋嬪悧锛熻拷绛旓細浠绘剰姝ｅ鸡娉㈢殑鏂圭▼鏄細唯锛坺,t锛=Asin(蠅t-kz+蠁)棰戠巼鍜屾尟骞呭潎鐩稿悓瀹存帢銆佹尟鍔ㄦ柟鍚戜竴鑷淬佷紶鎾柟鍚戠浉鍙嶇殑涓ゅ垪娉㈢殑鏂圭▼涓粎鏈墇杩欎竴椤规槸涓嶅悓鐨勶紝绗﹀彿鐩稿弽锛屼綘鎶婁袱涓紡瀛愬睍寮璁＄畻涓嬪氨鍑烘潵浜嗐俒...
绛旓細e^i胃=cos胃+isin胃 Acos(k∙r-蠅t)鏄疉e^(i(k∙r-蠅t))鍙栧疄閮 蔚=Acos(k∙r-蠅t)鏄彧鍚疄鏁扮殑娉㈠姩鏂圭▼ 蔚=Ae^(i(k∙r-蠅t))鏄冭檻铏氶儴鐨勬尝鍔ㄦ柟绋 铏界劧铏氶儴鏄棤娉曟祴閲忕殑锛屼絾铏氶儴鏄湁鎰忎箟鐨
绛旓細鍙互鐢ㄦ尟鍔ㄦ柟绋嬪紡鏉ヨ〃杈撅細鎸姩鏂圭▼琛ㄨ揪寮忥細x=Acos(蠅t+蠁)锛屾尟鍔ㄦ柟绋嬩篃绉颁箣涓烘槸娉㈠姩鏂圭▼绠鍗曟潵璇寸殑璇濇槸涓绉嶉噸瑕佺殑鍋忓井鍒嗘柟绋嬬殑鍐呭锛屼富瑕佹槸鐢ㄦ潵鎻忚堪鑷劧鐣屼腑鎴栬呮垜浠兘澶熺悊瑙ｇ殑涓浜涘悇绉嶆尝鍔ㄧ殑鐜拌薄锛岃繖涓浜涚幇璞′腑鍖呭惈鐨勬槸妯尝銆佺旱娉紝鎵浠ユ尝鍔ㄦ柟绋嬩富瑕佹槸鏉ヨ嚜浜庡０瀛︺佹祦浣撳姏瀛︿互鍙婄數纾佸绛夊涓鍩熴傛í娉㈢旱娉...
绛旓細璁娉㈠姩鏂圭▼涓簓=Asin锛埾塼-2蟺x/位+蠁锛夛紝棰樼洰缁欏嚭A=10cm锛屛=200cm锛寁=100cm/s锛屽洜涓烘尝閫焩=位/T锛屽懆鏈烼=2蟺/蠅锛屾墍浠ヨ閫熷害蠅=2蟺v/位=蟺 rad/s 鎵浠ユ尝鍔ㄦ柟绋嬩负y=10sin锛埾t-0.01蟺x+蠁锛夋牴鎹垵濮嬫潯浠秚=0鏃跺師鐐瑰璐ㄧ偣鍦ㄥ钩琛′綅缃悜姝ｄ綅绉绘柟鍚戣繍鍔紝寰楀垵鐩镐綅蠁=0 鎵浠ユ尝鍔ㄦ柟绋嬩负...
绛旓細璁娉㈠姩鏂圭▼涓簓=Asin锛埾塼-2蟺x/位+蠁锛夛紝棰樼洰缁欏嚭A=10cm锛屛=200cm锛寁=100cm/s锛屽洜涓烘尝閫焩=位/T锛屽懆鏈烼=2蟺/蠅锛屾墍浠ヨ閫熷害蠅=2蟺v/位=蟺 rad/s 鎵浠ユ尝鍔ㄦ柟绋嬩负y=10sin锛埾t-0.01蟺x+蠁锛夋牴鎹垵濮嬫潯浠秚=0鏃跺師鐐瑰璐ㄧ偣鍦ㄥ钩琛′綅缃悜姝ｄ綅绉绘柟鍚戣繍鍔紝寰楀垵鐩镐綅蠁=0 鎵浠ユ尝鍔ㄦ柟绋嬩负...
