{"id":445,"date":"2023-06-17T19:35:41","date_gmt":"2023-06-17T19:35:41","guid":{"rendered":"https:\/\/physigeek.com\/tr\/duragan-dalga\/"},"modified":"2023-06-17T19:35:41","modified_gmt":"2023-06-17T19:35:41","slug":"duragan-dalga","status":"publish","type":"post","link":"https:\/\/physigeek.com\/tr\/duragan-dalga\/","title":{"rendered":"Dura\u011fan dalga"},"content":{"rendered":"<p>Bu makale fizikte duran dalgalar\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece duran dalgalar\u0131n denklemini, duran dalgalar\u0131n \u00f6zelliklerinin neler oldu\u011funu ve dahas\u0131, duran dalgalar\u0131n farkl\u0131 t\u00fcrlerinin neler oldu\u011funu bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-una-onda-estacionaria\"><\/span> Duran dalga nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Duran dalga,<\/strong> zirveleri dikey olarak sal\u0131nan ancak uzunlamas\u0131na ilerlemeyen sal\u0131n\u0131ml\u0131 bir rahats\u0131zl\u0131kt\u0131r. Duran dalgalar, ayn\u0131 \u00f6zelliklere sahip ancak z\u0131t y\u00f6nlerde hareket eden dalgalar\u0131n \u00fcst \u00fcste gelmesinden olu\u015fan iki veya daha fazla dalga aras\u0131ndaki giri\u015fimin sonucudur.<\/p>\n<p> \u00c7o\u011fu durumda, duran dalgalara fiziksel rezonans olgusu neden olur; \u00f6yle ki, bir dalga ile onun bir rezonat\u00f6r ortam\u0131nda yans\u0131yan dalgas\u0131 aras\u0131nda dalgadan dalgaya giri\u015fim meydana gelir.<\/p>\n<p> \u00d6rne\u011fin elastik bir ipi bir ucundan duvara ba\u011flad\u0131\u011f\u0131m\u0131zda ve ipi titre\u015ftirdi\u011fimizde duran bir dalga olu\u015fur. \u0130p sal\u0131n\u0131r ve titre\u015fimler ipin sabit ucuna yans\u0131t\u0131l\u0131r, b\u00f6ylece iki dalga \u00fcst \u00fcste gelir ve duran bir dalga olu\u015fur. <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"620\" height=\"265\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-par-ondes-stationnaires.gif\" alt=\"dura\u011fan dalga\" class=\"wp-image-8880\"><\/figure>\n<p> Yukar\u0131daki grafik, duran dalgay\u0131 (k\u0131rm\u0131z\u0131 dalga) ve duran dalgay\u0131 (ye\u015fil ve mavi dalgalar) olu\u015fturmak i\u00e7in \u00fcst \u00fcste gelen dalgalarla birlikte g\u00f6stermektedir. G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi ye\u015fil dalga sa\u011fa do\u011fru hareket ediyor, mavi dalga sola do\u011fru hareket ediyor ve tam tersine duran dalga yatay olarak hareket etmiyor, yaln\u0131zca dikey olarak titre\u015fiyor.<\/p>\n<p> Duran dalgalar ilk kez 1831&#8217;de \u0130ngiliz fizik\u00e7i Michael Faraday taraf\u0131ndan tan\u0131mland\u0131. Ancak &#8220;duran dalga&#8221; ad\u0131 1860 y\u0131l\u0131nda Alman fizik\u00e7i Franz Melde taraf\u0131ndan icat edildi. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-de-una-onda-estacionaria\"><\/span> Duran dalga denklemi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sabit bir denklem, orijinal dalgalar\u0131n genli\u011finin iki kat\u0131 \u00e7arp\u0131 dalga say\u0131s\u0131n\u0131n sin\u00fcs\u00fc \u00e7arp\u0131 uzama ve a\u00e7\u0131sal frekans\u0131n kosin\u00fcs\u00fc \u00e7arp\u0131 zaman \u00e7arp\u0131m\u0131ndan olu\u015fur. Dolay\u0131s\u0131yla <strong>duran dalgan\u0131n denklemi y=2\u00b7A\u00b7sin(k\u00b7x)\u00b7cos(\u03c9\u00b7t) olur<\/strong> .<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-530840c920e5032693233cc82579121c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2\\cdot A\\cdot \\text{sin}(k\\cdot x)\\cdot \\text{cos}(\\omega\\cdot t)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"229\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> duran dalgan\u0131n incelenen noktas\u0131n\u0131n uzamas\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> orijinal dalgalar\u0131n genli\u011fidir. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga say\u0131s\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> duran dalgan\u0131n \u00e7al\u0131\u015f\u0131lan noktas\u0131n\u0131n konumudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fbffdce91996e0a17795d82e8e6996d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> a\u00e7\u0131sal veya titre\u015fim frekans\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> zaman\u0131n an\u0131d\u0131r.<\/span><\/li>\n<\/ul>\n<p> <strong>Not:<\/strong> Duran dalga denklemini ifade etmenin birka\u00e7 yolu vard\u0131r; dolay\u0131s\u0131yla kitaba ba\u011fl\u0131 olarak biraz farkl\u0131 bir denklem bulabilirsiniz. Ancak fizikte en \u00e7ok kullan\u0131lan duran dalga denklemi bu makalede sunulan denklemdir.<\/p>\n<p> Duran bir dalgan\u0131n dalga say\u0131s\u0131 ve a\u00e7\u0131sal frekans\u0131n\u0131n a\u015fa\u011f\u0131daki form\u00fcller kullan\u0131larak hesapland\u0131\u011f\u0131n\u0131 unutmay\u0131n:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bd9a9c86ac7bfe615da6e49025b8b40f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}k=\\cfrac{2\\pi}{\\lambda}\\\\[4ex]\\omega=\\cfrac{2\\pi}{T}=2\\pi f\\end{ tableau}\" title=\"Rendered by QuickLaTeX.com\" height=\"104\" width=\"110\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga say\u0131s\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8c37d2f1acb1d49f3e5e655797880475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga boyudur, yani duran dalgan\u0131n iki e\u015fde\u011fer noktas\u0131 aras\u0131ndaki mesafedir. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fbffdce91996e0a17795d82e8e6996d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> a\u00e7\u0131sal veya titre\u015fim frekans\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalgan\u0131n bir noktadan ge\u00e7mesi ile tekrar e\u015fde\u011fer bir noktadan ge\u00e7mesi aras\u0131nda ge\u00e7en s\u00fcre olarak tan\u0131mlanan s\u00fcredir. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> dalgan\u0131n birim zamandaki sal\u0131n\u0131m say\u0131s\u0131 olan frekanst\u0131r. <\/span><\/li>\n<\/ul>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Duran dalga denkleminin g\u00f6sterimine bak\u0131n<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> A\u015fa\u011f\u0131daki denklemlerle tan\u0131mlanan iki yay\u0131lma dalgas\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-da9c518dd5d8c55b8ec331431c3b4198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}y_1=A\\cdot \\text{sin}(k\\cdot x-\\omega\\cdot t)\\\\[3ex]y_2=A\\cdot \\text{sin}(k \\cdot x+\\omega\\cdot t)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Duran dalga, iki sal\u0131n\u0131ml\u0131 dalgan\u0131n toplam\u0131 oldu\u011fundan, duran dalga denklemi \u00f6nceki iki denklemin toplam\u0131 olacakt\u0131r:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a035d8a9e422ca3984acb2bd87f96f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}y=y_1+y_2\\\\[3ex]y=A\\cdot \\text{sin}(k\\cdot x-\\omega\\cdot t)+A\\cdot \\text{ sin}(k\\cdot x+\\omega\\cdot t)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"353\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Daha sonra a\u015fa\u011f\u0131daki trigonometrik form\u00fclleri uygulayaca\u011f\u0131z: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-709f860df485f9933890e923dc1318a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sin}(A)+\\text{sin}(B)=2\\cdot \\text{sin}\\left(\\frac{A+B}{2}\\right)\\cdot\\ texte{cos}\\left(\\frac{AB}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"410\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ea98f48622d6f62856d337dc490738f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{cos}(-A)=\\text{cos}(A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> B\u00f6ylece \u00f6nceki trigonometrik form\u00fclleri uygulayarak duran dalga denklemine ula\u015f\u0131yoruz: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8137cf4db2e711b343e2ee3226bcdfe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle y=A\\cdot \\text{sin}(k\\cdot x-\\omega\\cdot t)+A\\cdot \\text{sin}(k\\cdot x+\\ omega\\cdot t)\\\\[4ex]\\displaystyle y=2\\cdot A\\cdot \\text{sin}\\left(\\frac{(k\\cdot x-\\omega\\cdot t)+(k\\cdot x + \\omega\\cdot t)}{2}\\right)\\cdot \\text{cos}\\left(\\frac{(k\\cdot x-\\omega\\cdot t)-(k\\cdot x+\\omega\\cdot t) }{2}\\right)\\\\[4ex]\\displaystyle y=2\\cdot A\\cdot \\text{sin}(k\\cdot x)\\cdot \\text{cos}(-\\omega\\cdot t)\\\\ [4ex]\\displaystyle y=2\\cdot A\\cdot \\text{sin}(k\\cdot x)\\cdot \\text{cos}(\\omega\\cdot t)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"187\" width=\"641\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Nodos-y-vientres-de-una-onda-estacionaria\"><\/span> Duran dalgan\u0131n d\u00fc\u011f\u00fcmleri ve antinotlar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Herhangi bir duran dalga, a\u015fa\u011f\u0131daki \u015fekilde tan\u0131mlanan d\u00fc\u011f\u00fcmlerden ve antinotlardan olu\u015fur:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>D\u00fc\u011f\u00fcmler<\/strong> : Duran dalgan\u0131n uzamas\u0131 minimum (y=0) olan noktalar\u0131d\u0131r. Bu noktalar ne yatay ne de dikey olarak hareket etmedi\u011finden tamamen sabittir.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>G\u00f6bekler (veya g\u00f6bekler)<\/strong> : Bunlar duran dalgan\u0131n uzamas\u0131 maksimum olan noktalar\u0131d\u0131r (y = 2A veya y = -2A). Bu noktalar y=2A uzamas\u0131ndan y=-2A&#8217;ya kadar dikey olarak sal\u0131n\u0131r.<\/span> <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/noeuds-et-ventres-dondes-stationnaires.png\" alt=\"Duran dalgan\u0131n d\u00fc\u011f\u00fcmleri ve antinotlar\u0131\" class=\"wp-image-8887\" width=\"601\" height=\"282\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/noeuds-et-ventres-dondes-stationnaires-300x141.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/noeuds-et-ventres-dondes-stationnaires-768x362.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/noeuds-et-ventres-dondes-stationnaires.png 927w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ondas-estacionarias-con-ambos-extremos-fijos\"><\/span> Her iki ucu sabit olan duran dalgalar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Duran dalgalar her iki ucu da sabit olarak \u00fcretildi\u011finde,<\/strong> bu, dalgan\u0131n u\u00e7lar\u0131n\u0131n d\u00fc\u011f\u00fcm oldu\u011fu anlam\u0131na gelir. Bu tip duran dalgalar, her iki taraf\u0131 kapal\u0131 t\u00fcplerde veya u\u00e7lar\u0131na ba\u011flanan titre\u015fen halatlarla ger\u00e7ekle\u015ftirilir.<\/p>\n<p> \u00d6rne\u011fin bir gitar\u0131n tellerini titre\u015ftirdi\u011fimizde iki ucu sabit olan duran dalgalar \u00fcretiriz.<\/p>\n<p> Bu durumda duran dalgan\u0131n dalga boyu ve frekans\u0131 a\u015fa\u011f\u0131daki form\u00fcllerle tan\u0131mlan\u0131r:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a602b1c2e671ce2b9f7ec1702c3e91df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\lambda_n=\\cfrac{2\\cdot L}{n}\\\\[4ex]f_n=\\cfrac{v}{\\lambda_n}=\\cfrac{n\\cdot v} {2\\cdot L}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"123\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8c37d2f1acb1d49f3e5e655797880475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga boyudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-48d71fca322532f0abc2c4ad2cf98154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"L\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> dizenin uzunlu\u011fudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> harmonik say\u0131d\u0131r (n=1, 2, 3, 4\u2026). <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> do\u011fal veya harmonik frekanst\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-796872219106704832bd95ce08640b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"v\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga yay\u0131lma h\u0131z\u0131d\u0131r. <\/span><\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/ondes-stationnaires-harmoniques-aux-deux-extremites-fixes.png\" alt=\"her iki ucu sabit olan duran dalgalar\u0131n harmonikleri.png\" class=\"wp-image-8893\" width=\"435\" height=\"507\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/ondes-stationnaires-harmoniques-aux-deux-extremites-fixes-257x300.png 257w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/ondes-stationnaires-harmoniques-aux-deux-extremites-fixes-768x896.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/ondes-stationnaires-harmoniques-aux-deux-extremites-fixes.png 864w\" sizes=\"auto, (max-width: 257px) 100vw, 257px\"><\/figure>\n<p> Yukar\u0131daki g\u00f6rselde g\u00f6rebilece\u011finiz gibi antinod say\u0131s\u0131 ve d\u00fc\u011f\u00fcm say\u0131s\u0131 harmonik say\u0131s\u0131na ba\u011fl\u0131d\u0131r. Her iki ucu sabit olan bir duran dalgan\u0131n antinot say\u0131s\u0131 harmonik say\u0131ya e\u015fde\u011ferdir, d\u00fc\u011f\u00fcm say\u0131s\u0131 ise harmonik say\u0131 art\u0131 birdir. <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5d6e18676743f2316cac6a5a7ad60f92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'nombre de n\u0153uds}=n+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"215\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a556d7447cad80f85f25ecb2806c1271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'nombre de ventres}=n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ondas-estacionarias-con-ambos-extremos-libres\"><\/span> Her iki ucu serbest olan duran dalgalar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, <strong>duran dalgalar\u0131n her iki ucu da serbest olabilir<\/strong> , b\u00f6ylece duran dalgan\u0131n her iki ucu da antinod olur.<\/p>\n<p> Bu t\u00fcr dura\u011fan dalgalar bir\u00e7ok nefesli \u00e7alg\u0131da her iki ucu da a\u00e7\u0131k oldu\u011fundan \u00fcretilir.<\/p>\n<p> Her iki ucu a\u00e7\u0131k olan bir duran dalgan\u0131n dalga boyu ve frekans\u0131 a\u015fa\u011f\u0131daki form\u00fcller kullan\u0131larak hesaplan\u0131r:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-cacd0cbaa519db536382349834eb0142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\lambda_{n}=\\cfrac{2\\cdot L}{n}\\\\[4ex]f_{n}=\\cfrac{v}{\\lambda_{n}} =\\cfrac{n\\cdot v}{2\\cdot L}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"123\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8c37d2f1acb1d49f3e5e655797880475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga boyudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-48d71fca322532f0abc2c4ad2cf98154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"L\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> dizenin uzunlu\u011fudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> harmonik say\u0131d\u0131r (n=1, 2, 3, 4\u2026). <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> do\u011fal veya harmonik frekanst\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-796872219106704832bd95ce08640b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"v\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalgan\u0131n yay\u0131lma h\u0131z\u0131d\u0131r. <\/span><\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/harmoniques-ondes-stationnaires-deux-extremes-libres.png\" alt=\"her iki ucu serbest olan duran dalgalar\" class=\"wp-image-9037\" width=\"435\" height=\"540\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/harmoniques-ondes-stationnaires-deux-extremes-libres-242x300.png 242w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/harmoniques-ondes-stationnaires-deux-extremes-libres-825x1024.png 825w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/harmoniques-ondes-stationnaires-deux-extremes-libres-768x953.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/harmoniques-ondes-stationnaires-deux-extremes-libres.png 868w\" sizes=\"auto, (max-width: 242px) 100vw, 242px\"><\/figure>\n<p> Yukar\u0131daki g\u00f6rsele bakt\u0131\u011f\u0131n\u0131zda bu t\u00fcr duran dalgalar\u0131n harmonik say\u0131s\u0131 kadar d\u00fc\u011f\u00fcm noktas\u0131 oldu\u011funu g\u00f6r\u00fcrs\u00fcn\u00fcz. Buna kar\u015f\u0131l\u0131k, bu dura\u011fan dalga s\u0131n\u0131f\u0131n\u0131n antinotlar\u0131n\u0131n say\u0131s\u0131 harmonik say\u0131 art\u0131 birdir. <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d7477820f4cd9c20e842ca77b0bcfd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'nombre de n\u0153uds}=n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"185\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a4431d38c9c7f59a49b69b29d3536f93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'nombre de ventres}=n+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"219\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ondas-estacionarias-con-un-extremo-fijo-y-un-extremo-libre\"><\/span>Bir sabit ucu ve bir serbest ucu olan duran dalgalar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Dalgan\u0131n bir ucunun sabit, di\u011fer ucunun serbest oldu\u011fu bir ortamda yay\u0131lmas\u0131<\/strong> , dalgan\u0131n bir ucunun d\u00fc\u011f\u00fcm, di\u011fer ucunun ise antinod olaca\u011f\u0131 anlam\u0131na gelir.<\/p>\n<p> Bu t\u00fcr dura\u011fan dalgalar bir\u00e7ok m\u00fczik enstr\u00fcman\u0131nda meydana gelir; \u00f6rne\u011fin, bir trompet, fl\u00fct veya klarnette \u00fcretilen dalgalar\u0131n, m\u00fczisyenin i\u00e7inden \u00fcfledi\u011fi bir sabit ucu ve m\u00fczisyenin i\u00e7inden \u00fcfledi\u011fi ba\u015fka bir serbest ucu vard\u0131r. Enstr\u00fcman.<\/p>\n<p> Bu durumda duran dalgan\u0131n uzunlu\u011fu ve frekans\u0131 a\u015fa\u011f\u0131daki form\u00fcllerle hesaplanabilir:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-79cd7218a7a133578e1c7cdf3b6b21f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\lambda_{2n-1}=\\cfrac{4\\cdot L}{2n-1}\\\\[4ex]f_{2n-1}=\\cfrac{v}{ \\lambda_{2n-1}}=\\cfrac{v}{4\\cdot L}\\cdot (2n-1)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"247\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8c37d2f1acb1d49f3e5e655797880475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalga boyudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-48d71fca322532f0abc2c4ad2cf98154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"L\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> dizenin uzunlu\u011fudur. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> harmonik say\u0131s\u0131n\u0131 (n=1, 2, 3, 4\u2026) belirleyen parametredir. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> do\u011fal veya harmonik frekanst\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-796872219106704832bd95ce08640b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"v\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> dalgan\u0131n yay\u0131lma h\u0131z\u0131d\u0131r.<\/span><\/li>\n<\/ul>\n<p> <strong>Not:<\/strong> Bu durumda yaln\u0131zca tek harmoniklerin mevcut oldu\u011funu unutmay\u0131n (1, 3, 5, 7\u2026), \u00e7\u00fcnk\u00fc bu t\u00fcr duran dalgalarda temel frekans\u0131n yaln\u0131zca tek katlar\u0131n\u0131 olu\u015fturmak m\u00fcmk\u00fcnd\u00fcr. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/onde-stationnaire-extremite-fixe-et-extremite-libre.png\" alt=\"sabit bir ucu ve serbest ucu olan duran dalgalar\" class=\"wp-image-9031\" width=\"434\" height=\"516\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/onde-stationnaire-extremite-fixe-et-extremite-libre-252x300.png 252w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/onde-stationnaire-extremite-fixe-et-extremite-libre-861x1024.png 861w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/onde-stationnaire-extremite-fixe-et-extremite-libre-768x913.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/onde-stationnaire-extremite-fixe-et-extremite-libre.png 869w\" sizes=\"auto, (max-width: 252px) 100vw, 252px\"><\/figure>\n<p> Bu durumda duran dalga, antinodlarla ayn\u0131 say\u0131da d\u00fc\u011f\u00fcme sahiptir. Somut olarak, duran dalgan\u0131n harmoni\u011fin n parametresinin de\u011feri kadar d\u00fc\u011f\u00fcm\u00fc ve antinodu vard\u0131r: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d7477820f4cd9c20e842ca77b0bcfd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'nombre de n\u0153uds}=n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"185\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a556d7447cad80f85f25ecb2806c1271_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{N\\'nombre de ventres}=n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"190\" style=\"vertical-align: 0px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale fizikte duran dalgalar\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece duran dalgalar\u0131n denklemini, duran dalgalar\u0131n \u00f6zelliklerinin neler oldu\u011funu ve dahas\u0131, duran dalgalar\u0131n farkl\u0131 t\u00fcrlerinin neler oldu\u011funu bulacaks\u0131n\u0131z. Duran dalga nedir? Duran dalga, zirveleri dikey olarak sal\u0131nan ancak uzunlamas\u0131na ilerlemeyen sal\u0131n\u0131ml\u0131 bir rahats\u0131zl\u0131kt\u0131r. Duran dalgalar, ayn\u0131 \u00f6zelliklere sahip ancak z\u0131t y\u00f6nlerde hareket eden dalgalar\u0131n \u00fcst \u00fcste gelmesinden &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/tr\/duragan-dalga\/\"> <span class=\"screen-reader-text\">Dura\u011fan dalga<\/span> Devam\u0131 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-445","post","type-post","status-publish","format-standard","hentry","category-sinematik"],"yoast_head":"<!-- This site is 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