{"id":7297,"date":"2012-01-01T18:48:24","date_gmt":"2012-01-01T18:48:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7297"},"modified":"2022-01-30T15:57:02","modified_gmt":"2022-01-30T15:57:02","slug":"o-tom-de-uma-nota-musical","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7297","title":{"rendered":"O tom de uma nota musical"},"content":{"rendered":"<p><ul id='GTTabs_ul_7297' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7297' class='GTTabs_curr'><a  id=\"7297_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7297' ><a  id=\"7297_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_7297'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O tom de uma nota musical \u00e9 determinado pela frequ\u00eancia da vibra\u00e7\u00e3o que a gerou.<\/p>\n<p>Usando os valores a tabela:<\/p>\n<table class=\" aligncenter\" style=\"width: 70%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"background-color: #e6e6fa; border: #00008b 1px solid;\">N.\u00ba de oitavas acima do D\u00f3 m\u00e9dio ($n$)<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">0<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">1<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">2<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">3<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #e6e6fa; border: #00008b 1px solid;\">Frequ\u00eancia em Hertz ($f$)<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">263<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">526<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">1052<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">2104<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">4208<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Mostre que a sequ\u00eancia das frequ\u00eancias das oitavas acima do D\u00f3 m\u00e9dio do piano s\u00e3o valores tais que o quociente de dois consecutivos \u00e9 constante.<\/li>\n<li>Escreva a express\u00e3o que define $f$ em fun\u00e7\u00e3o de $n$.<\/li>\n<li>Calcule a frequ\u00eancia de duas oitavas abaixo do D\u00f3 m\u00e9dio.<\/li>\n<li>O ouvido humano percebe quatro oitavas abaixo e sete acima do D\u00f3 m\u00e9dio como aud\u00edveis.<br \/>\nDetermine qual o intervalo de frequ\u00eancias aud\u00edveis.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7297' onClick='GTTabs_show(1,7297)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7297'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\" aligncenter\" style=\"width: 70%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"background-color: #e6e6fa; border: #00008b 1px solid;\">N.\u00ba de oitavas acima do D\u00f3 m\u00e9dio ($n$)<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">0<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">1<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">2<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">3<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #e6e6fa; border: #00008b 1px solid;\">Frequ\u00eancia em Hertz ($f$)<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">263<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">526<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">1052<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">2104<\/td>\n<td style=\"text-align: center; background-color: #e6e6fa; border: #00008b 1px solid;\">4208<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00ad<\/p>\n<ol>\n<li>A sequ\u00eancia das frequ\u00eancias das oitavas acima do D\u00f3 m\u00e9dio do piano s\u00e3o valores tais que o quociente de dois consecutivos \u00e9 constante: $$\\frac{526}{263}=\\frac{1052}{526}=\\frac{2104}{1052}=\\frac{4208}{2104}=2$$<\/li>\n<li>Uma express\u00e3o que define $f$ em fun\u00e7\u00e3o de $n$ \u00e9: $$f(n)=263\\times {{2}^{n}}$$<\/li>\n<li>A frequ\u00eancia de duas oitavas abaixo do D\u00f3 m\u00e9dio \u00e9 $f(-2)=263\\times {{2}^{-2}}=\\frac{263}{4}=65,75$ Hz.<br \/>\n\u00ad<\/li>\n<li>Como\u00a0$$f(-4)=263\\times {{2}^{-4}}=\\frac{263}{16}=16,4375$$ e $$f(7)=263\\times {{2}^{7}}=263\\times 128=33664$$ o intervalo pedido \u00e9\u00a0$\\left[ 16,4375;\\,\\,33664 \\right]$ (em Hz).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7297' onClick='GTTabs_show(0,7297)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O tom de uma nota musical \u00e9 determinado pela frequ\u00eancia da vibra\u00e7\u00e3o que a gerou. Usando os valores a tabela: N.\u00ba de oitavas acima do D\u00f3 m\u00e9dio ($n$) 0 1 2&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21117,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,267],"tags":[427,268],"series":[],"class_list":["post-7297","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-exponencial"],"views":2416,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/12V2Pag202-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7297","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=7297"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7297\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21117"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7297"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}