{"id":216272,"date":"2025-05-19T03:47:16","date_gmt":"2025-05-19T03:47:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=216272"},"modified":"2025-05-19T03:47:18","modified_gmt":"2025-05-19T03:47:18","slug":"a-company-with-loud-machinery-needs-to-cut-its-sound-intensity-to-44-of-its-original-level","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/19\/a-company-with-loud-machinery-needs-to-cut-its-sound-intensity-to-44-of-its-original-level\/","title":{"rendered":"A company with loud machinery needs to cut its sound intensity to 44% of its original level."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A company with loud machinery needs to cut its sound intensity to 44% of its original level. By how many decibels would the loudness be reduced? Use the formula L=101logI\/Io. Round to the nearest hundredth. (1 point)3.57 decibels<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the reduction in decibels when a company&#8217;s sound intensity is cut to 44% of its original level, we use the <strong>decibel formula<\/strong>: L=10log\u2061(II0)L = 10 \\log \\left(\\frac{I}{I_0}\\right)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>LL is the <strong>sound level in decibels (dB)<\/strong>,<\/li>\n\n\n\n<li>II is the <strong>final sound intensity<\/strong>,<\/li>\n\n\n\n<li>I0I_0 is the <strong>original sound intensity<\/strong>,<\/li>\n\n\n\n<li>log\u2061\\log is the base-10 logarithm.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Understand the problem<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The problem says the <strong>new sound intensity is 44%<\/strong> of the original, so: II0=0.44\\frac{I}{I_0} = 0.44<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We want to know how many <strong>decibels the loudness is reduced<\/strong> by \u2014 in other words, how much less intense it is in decibels.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Use the formula to calculate decibel reduction<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We plug the ratio II0=0.44\\frac{I}{I_0} = 0.44 into the formula: L=10log\u2061(0.44)L = 10 \\log(0.44)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now compute the logarithm: log\u2061(0.44)\u2248\u22120.3565\\log(0.44) \\approx -0.3565<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiply by 10: L=10\u00d7(\u22120.3565)=\u22123.565L = 10 \\times (-0.3565) = -3.565<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Rounding to the nearest hundredth: L\u2248\u22123.57&nbsp;decibelsL \\approx -3.57 \\text{ decibels}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The negative sign indicates a <strong>reduction<\/strong> in loudness.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Interpret the result<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The sound has <strong>decreased by approximately 3.57 decibels<\/strong>. This means that if the original sound level was at a certain dB, reducing its intensity to 44% of the original will <strong>reduce the perceived loudness by 3.57 dB<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remember, <strong>decibels are a logarithmic scale<\/strong>, so even a few decibels&#8217; change represents a <strong>significant difference<\/strong> in intensity. A decrease of 3.57 dB is quite noticeable in an environment, especially in places where noise control is important for health and safety.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer: 3.57 decibels<\/strong><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>A company with loud machinery needs to cut its sound intensity to 44% of its original level. By how many decibels would the loudness be reduced? Use the formula L=101logI\/Io. Round to the nearest hundredth. (1 point)3.57 decibels The Correct Answer and Explanation is: To determine the reduction in decibels when a company&#8217;s sound intensity [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-216272","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216272","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=216272"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/216272\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=216272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=216272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=216272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}