{"id":7342,"date":"2012-01-19T18:04:03","date_gmt":"2012-01-19T18:04:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7342"},"modified":"2022-01-30T16:09:45","modified_gmt":"2022-01-30T16:09:45","slug":"o-nivel-de-um-som","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7342","title":{"rendered":"O n\u00edvel de um som"},"content":{"rendered":"<p><ul id='GTTabs_ul_7342' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7342' class='GTTabs_curr'><a  id=\"7342_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7342' ><a  id=\"7342_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7342'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O n\u00edvel $S$ de um som, medido em decib\u00e9is, \u00e9 fun\u00e7\u00e3o da sua intensidade $I$, medida em Watt por metro quadrado, de acordo com a lei $$S=10\\log \\left( \\frac{I}{{{I}_{0}}} \\right)$$ sendo ${{I}_{0}}={{10}^{-12}}$ Watt por metro quadrado a menor intensidade de som que o ouvido humano pode detetar:<\/p>\n<ol>\n<li>\u00a0Calcule o n\u00edvel de som quando $I={{I}_{0}}$.<\/li>\n<li>Verifique que $S=120+10\\log I$.<\/li>\n<li>Admita que o n\u00edvel de ru\u00eddo de m\u00fasica rock amplificada, ouvido por algu\u00e9m que se encontra numa discoteca, \u00e9 de $110$ decib\u00e9is. Determine a intensidade desse som, em Watt por metro quadrado.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7342' onClick='GTTabs_show(1,7342)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7342'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote><p>O n\u00edvel $S$ de um som, medido em decib\u00e9is, \u00e9 fun\u00e7\u00e3o da sua intensidade $I$, medida em Watt por metro quadrado, de acordo com a lei $$S=10\\log \\left( \\frac{I}{{{I}_{0}}} \\right)$$ sendo ${{I}_{0}}={{10}^{-12}}$ Watt por metro quadrado a menor intensidade de som que o ouvido humano pode detetar<\/p><\/blockquote>\n<p>\u00ad<\/p>\n<ol>\n<li>Para $I={{I}_{0}}={{10}^{-12}}$, temos: $$\\begin{array}{*{35}{l}} \u00a0\u00a0 S({{I}_{0}}) &amp; = &amp; 10\\log \\left( \\frac{{{I}_{0}}}{{{I}_{0}}} \\right)\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; 10\\log 1\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; 10\\times 0\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; 0\u00a0 \\\\ \\end{array}$$ Quando $I={{I}_{0}}$, o n\u00edvel de som \u00e9 $0$ dB.<br \/>\n\u00ad<\/li>\n<li>Ora, $$\\begin{array}{*{35}{l}} \u00a0\u00a0 S &amp; = &amp; 10\\log \\left( \\frac{I}{{{10}^{-12}}} \\right)\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; 10\\left( \\log I-\\log {{10}^{-12}} \\right)\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; 10\\times \\log I-10\\times (-12)\u00a0 \\\\ \u00a0\u00a0 {} &amp; = &amp; 120+10\\log I\u00a0 \\\\ \\end{array}$$<br \/>\n\u00ad<\/li>\n<li>Pretende-se determinar o valor de $I$ para $S=110$ dB. Ora, $$\\begin{array}{*{35}{l}} \u00a0\u00a0 S=110 &amp; \\Leftrightarrow\u00a0 &amp; 120+10\\log I=110\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; 10\\log I=-10\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\log I=-1\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; I={{10}^{-1}}\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; I=0,1\u00a0 \\\\ \\end{array}$$ \u00c9 de $0,1$ Watt\/m<sup>2<\/sup> a intensidade desse som.<\/li>\n<\/ol>\n<p><span class=\"aligncenter\"><object data=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/soundintensity.swf\" type=\"application\/x-shockwave-flash\" width=\"400\" height=\"300\"><\/object><\/span><\/p>\n<p>Filme em Flash: <a href=\"http:\/\/www.yteach.co.uk\/\" target=\"_blank\" rel=\"noopener\">http:\/\/www.yteach.co.uk\/<\/a><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7342' onClick='GTTabs_show(0,7342)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O n\u00edvel $S$ de um som, medido em decib\u00e9is, \u00e9 fun\u00e7\u00e3o da sua intensidade $I$, medida em Watt por metro quadrado, de acordo com a lei $$S=10\\log \\left( \\frac{I}{{{I}_{0}}} \\right)$$ sendo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21122,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,267],"tags":[427,275,274],"series":[],"class_list":["post-7342","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-exponenciais-e-logaritmicas","tag-12-o-ano","tag-funcao-logaritmica","tag-regras-operatorias-de-logaritmos"],"views":2343,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/12V2Pag203-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7342","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7342"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7342\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21122"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7342"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}