{"id":196140,"date":"2025-03-03T05:03:13","date_gmt":"2025-03-03T05:03:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196140"},"modified":"2025-03-03T05:03:15","modified_gmt":"2025-03-03T05:03:15","slug":"the-decibel-level-of-a-jackhammer-is-130-db-relative-to-the-threshold-of-hearing","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/03\/the-decibel-level-of-a-jackhammer-is-130-db-relative-to-the-threshold-of-hearing\/","title":{"rendered":"The decibel level of a jackhammer is 130 dB relative to the threshold of hearing"},"content":{"rendered":"\n<p>The decibel level of a jackhammer is 130 dB relative to the threshold of hearing. Determine the sound intensity produced by the jack hammer <\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the sound intensity produced by the jackhammer, we can use the formula that relates sound intensity and decibel level:<\/p>\n\n\n\n<p>[<br>\\text{dB} = 10 \\times \\log \\left( \\frac{I}{I_0} \\right)<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\\text{dB}) is the decibel level (130 dB in this case),<\/li>\n\n\n\n<li>(I) is the sound intensity we need to find,<\/li>\n\n\n\n<li>(I_0) is the reference intensity, which is the threshold of hearing and equals (1 \\times 10^{-12} \\, \\text{W\/m}^2).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step calculation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Rearrange the formula<\/strong> to solve for the sound intensity (I):<\/li>\n<\/ol>\n\n\n\n<p>[<br>\\frac{I}{I_0} = 10^{\\frac{\\text{dB}}{10}}<br>]<\/p>\n\n\n\n<p>[<br>I = I_0 \\times 10^{\\frac{\\text{dB}}{10}}<br>]<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Substitute the known values<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\text{dB} = 130 \\, \\text{dB} )<\/li>\n\n\n\n<li>( I_0 = 1 \\times 10^{-12} \\, \\text{W\/m}^2 )<\/li>\n<\/ul>\n\n\n\n<p>[<br>I = 1 \\times 10^{-12} \\times 10^{\\frac{130}{10}}<br>]<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>Simplify the exponent<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>[<br>\\frac{130}{10} = 13<br>]<\/p>\n\n\n\n<p>[<br>I = 1 \\times 10^{-12} \\times 10^{13}<br>]<\/p>\n\n\n\n<p>[<br>I = 10^{1} = 10 \\, \\text{W\/m}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final answer:<\/h3>\n\n\n\n<p>The sound intensity produced by the jackhammer is (10 \\, \\text{W\/m}^2).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Sound intensity is a measure of the energy transported by sound waves through a medium (such as air). The decibel scale is logarithmic, meaning a small increase in decibels represents a large increase in sound intensity. A 130 dB level, as in the case of the jackhammer, indicates an extremely loud sound.<\/p>\n\n\n\n<p>In this case, a jackhammer produces a sound that is 130 dB relative to the threshold of hearing, which means its sound intensity is (10 \\, \\text{W\/m}^2). For context, this is a very high sound intensity. For example, normal conversation occurs at about 60 dB, which corresponds to a sound intensity of (10^{-12} \\, \\text{W\/m}^2), while a rock concert might reach 120 dB.<\/p>\n\n\n\n<p>Because the scale is logarithmic, every increase of 10 dB represents a tenfold increase in sound intensity. Thus, the jackhammer&#8217;s sound intensity is 10 times higher than a sound at 120 dB and 100 times higher than a sound at 110 dB.<\/p>\n\n\n\n<p>This makes jackhammers one of the loudest sources of sound in everyday life, often requiring ear protection to avoid hearing damage.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The decibel level of a jackhammer is 130 dB relative to the threshold of hearing. Determine the sound intensity produced by the jack hammer The Correct Answer and Explanation is : To determine the sound intensity produced by the jackhammer, we can use the formula that relates sound intensity and decibel level: [\\text{dB} = 10 [&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-196140","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196140","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=196140"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196140\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}