{"id":161088,"date":"2024-11-03T22:48:20","date_gmt":"2024-11-03T22:48:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=161088"},"modified":"2024-11-03T22:48:23","modified_gmt":"2024-11-03T22:48:23","slug":"calculate-the-lowest-frequency-that-could-possibly-resonate-with-your-pipe-using-the-formulas-below-including-speed-of-soundfrequencyxwavelength","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/03\/calculate-the-lowest-frequency-that-could-possibly-resonate-with-your-pipe-using-the-formulas-below-including-speed-of-soundfrequencyxwavelength\/","title":{"rendered":"Calculate the lowest frequency that could possibly resonate with your pipe using the formulas below, including speed of sound=frequency\u00d7wavelength."},"content":{"rendered":"\n<p>Calculate the lowest frequency that could possibly resonate with your pipe using the formulas below, including speed of sound=frequency\u00d7wavelength.<\/p>\n\n\n\n<p>Given: &#8211; Ln =1.078m &#8211; Xo =1.30m Choose the correct frequency: A. 137.65 Hz B. 144.15 Hz C. 151.42 Hz D. 159.21 Hz<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the lowest frequency that could resonate with the pipe, we need to consider it as an open or closed pipe and use the formula:<\/p>\n\n\n\n<p>[<br>f = \\frac{v}{\\lambda}<br>]<\/p>\n\n\n\n<p>where ( f ) is the frequency, ( v ) is the speed of sound (approximately 343 m\/s at room temperature), and ( \\lambda ) is the wavelength. For a pipe with a length ( L ), the resonant frequencies depend on whether the pipe is open or closed at one or both ends.<\/p>\n\n\n\n<p>Let&#8217;s assume it\u2019s a closed pipe (one end closed), which produces odd harmonics (1st, 3rd, 5th, etc.) only. For the fundamental frequency (1st harmonic) of a closed pipe, the wavelength (\\lambda) is given by:<\/p>\n\n\n\n<p>[<br>\\lambda = 4L<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the Wavelength<\/h3>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Effective length (L_n = 1.078) m<\/li>\n\n\n\n<li>Using ( \\lambda = 4L_n ):<\/li>\n<\/ul>\n\n\n\n<p>[<br>\\lambda = 4 \\times 1.078 \\, \\text{m} = 4.312 \\, \\text{m}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the Frequency<\/h3>\n\n\n\n<p>Using the speed of sound (v = 343) m\/s,<\/p>\n\n\n\n<p>[<br>f = \\frac{v}{\\lambda} = \\frac{343}{4.312} \\approx 79.56 \\, \\text{Hz}<br>]<\/p>\n\n\n\n<p>However, the fundamental frequency given here is not among the answer choices, so it seems the options might be referring to higher harmonics or if we interpret ( Xo = 1.3 ) m as the adjusted effective length due to end corrections.<\/p>\n\n\n\n<p>If we consider the second harmonic (since higher frequencies are in the options):<\/p>\n\n\n\n<p>For the third harmonic (3rd multiple of fundamental):<br>[<br>f_3 = 3 \\times 79.56 = 238.68 \\, \\text{Hz}<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the lowest frequency that could possibly resonate with your pipe using the formulas below, including speed of sound=frequency\u00d7wavelength. Given: &#8211; Ln =1.078m &#8211; Xo =1.30m Choose the correct frequency: A. 137.65 Hz B. 144.15 Hz C. 151.42 Hz D. 159.21 Hz The Correct Answer and Explanation is: To calculate the lowest frequency that could [&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-161088","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161088","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=161088"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161088\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161088"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161088"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}