{"id":473,"date":"2023-06-16T05:57:52","date_gmt":"2023-06-16T05:57:52","guid":{"rendered":"https:\/\/physigeek.com\/de\/dreidimensionale-welle\/"},"modified":"2023-06-16T05:57:52","modified_gmt":"2023-06-16T05:57:52","slug":"dreidimensionale-welle","status":"publish","type":"post","link":"https:\/\/physigeek.com\/de\/dreidimensionale-welle\/","title":{"rendered":"Dreidimensionale welle"},"content":{"rendered":"<p>Dieser Artikel erkl\u00e4rt, was dreidimensionale Wellen in der Physik sind. So finden Sie die Definition einer dreidimensionalen Welle, ihre Eigenschaften und die Gleichung einer dreidimensionalen Welle. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-una-onda-tridimensional\"><\/span> Was ist eine dreidimensionale Welle?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Eine <strong>dreidimensionale Welle<\/strong> , auch <strong>Kugelwelle<\/strong> genannt, ist eine Welle, die sich in drei Dimensionen ausbreitet. Mit anderen Worten: Dreidimensionale Wellen breiten sich im Raum in alle Richtungen aus.<\/p>\n<p> Beispielsweise ist eine Schallwelle eine dreidimensionale Welle, weil sie sich in allen drei Raumdimensionen ausbreitet. Auch Lichtwellen sind Beispiele f\u00fcr dreidimensionale Wellen.<\/p>\n<p> Daher sind die Wellenfronten dreidimensionaler Wellen konzentrische Kugeln, die sich durch den Raum ausbreiten, weshalb sie auch Kugelwellen genannt werden. Das Zentrum dieser konzentrischen Kugeln ist der Fokus oder Ursprung der dreidimensionalen Welle. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Caracteristicas-de-las-ondas-tridimensionales\"><\/span> Eigenschaften dreidimensionaler Wellen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dreidimensionale Wellen haben folgende Eigenschaften:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Amplitude (A)<\/strong> : ist der Abstand zwischen dem h\u00f6chsten Punkt der Wellenschwingungen und ihrem Durchschnittswert.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Periode (T)<\/strong> : ist die Zeit, die die Welle ben\u00f6tigt, um eine vollst\u00e4ndige Schwingung auszuf\u00fchren.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Frequenz (f)<\/strong> : ist die Anzahl der Schwingungen oder Vibrationen, die die Welle pro Zeiteinheit erzeugt.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Winkelfrequenz oder Pulsation (\u03c9)<\/strong> : Dies ist die Geschwindigkeit, mit der die Welle schwingt.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ausbreitungsgeschwindigkeit (v)<\/strong> : Dies ist die Geschwindigkeit, mit der sich die Welle ausbreitet.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-de-una-onda-tridimensional\"><\/span> Gleichung einer dreidimensionalen Welle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Wenn wir angesichts der sph\u00e4rischen Symmetrie dreidimensionaler Wellen davon ausgehen, dass sich die dreidimensionale Welle durch ein isotropes Medium wie Luft oder Wasser ausbreitet, kann die Gleichung, die ihre Bewegung beschreibt, wie folgt in sph\u00e4rischen Koordinaten geschrieben werden:<\/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-26b4b369cc2fa9266d113d8857650944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{r^2} \\frac{\\partial}{\\partial r}\\left( r^2\\frac{\\partial \\Psi}{\\partial r} \\right)-\\ frac{1}{c^2}\\frac{\\partial^2 \\Psi}{\\partial t^2} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"270\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Indem wir die vorherige Differentialgleichung durch Integration l\u00f6sen, gelangen wir zu der Formel f\u00fcr die <strong>Gleichung einer dreidimensionalen Welle<\/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-a0a3b7234b7cd9d7a416a1002d15f926_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Psi(r,t) = A\\cdot\\text{sin}( \\omega\\cdot t - k\\cdot r+ \\phi_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"256\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Gold: <\/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-96d558896734bc27372c9e3216e687db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Psi\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> ist die Ausdehnung der dreidimensionalen Welle. <\/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-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> ist der Abstand zwischen dem Ursprung der Welle und dem Untersuchungspunkt. <\/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> ist die Amplitude der dreidimensionalen Welle. <\/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> ist die Wellenzahl. <\/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> ist die Kreisfrequenz oder Pulsation der Welle. <\/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> ist der Moment der Zeit. <\/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-c8618f3820889d0002a7eefeeb2aaf41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\phi_0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> ist die Anfangsphase der Welle. <\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Otros-tipos-de-ondas\"><\/span> Andere Arten von Wellen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Abh\u00e4ngig von den Dimensionen, in denen sie sich ausbreiten, werden Wellen in longitudinale, zweidimensionale oder dreidimensionale Wellen eingeteilt. Neben dreidimensionalen Wellen gibt es also auch die folgenden zwei Arten von Wellen:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Eindimensionale Welle<\/strong> : Wellentyp, der sich in einer einzigen Dimension, also in einer einzigen Richtung, ausbreitet.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Zweidimensionale Welle<\/strong> : Wellentyp, der sich in zwei Dimensionen, also entlang einer Oberfl\u00e4che, ausbreitet.<\/span> <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Siehe:<\/strong> <a href=\"https:\/\/physigeek.com\/de\/eindimensionale-welle\/\">Eindimensionale Welle<\/a><br \/> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Siehe:<\/strong> <a href=\"https:\/\/physigeek.com\/de\/zweidimensionale-welle\/\">Zweidimensionale Welle<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Dieser Artikel erkl\u00e4rt, was dreidimensionale Wellen in der Physik sind. So finden Sie die Definition einer dreidimensionalen Welle, ihre Eigenschaften und die Gleichung einer dreidimensionalen Welle. Was ist eine dreidimensionale Welle? Eine dreidimensionale Welle , auch Kugelwelle genannt, ist eine Welle, die sich in drei Dimensionen ausbreitet. Mit anderen Worten: Dreidimensionale Wellen breiten sich im &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/de\/dreidimensionale-welle\/\"> <span class=\"screen-reader-text\">Dreidimensionale welle<\/span> Mehr lesen &quot;<\/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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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