{"id":259134,"date":"2025-07-18T18:13:50","date_gmt":"2025-07-18T18:13:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=259134"},"modified":"2025-07-18T18:13:57","modified_gmt":"2025-07-18T18:13:57","slug":"3a-suppose-one-has-a-wave-that-travels-at-a-speed-of-1125-feet-per-second-about-the-speed-of-a-sound-wave","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/18\/3a-suppose-one-has-a-wave-that-travels-at-a-speed-of-1125-feet-per-second-about-the-speed-of-a-sound-wave\/","title":{"rendered":".3a &#8211; Suppose one has a wave that travels at a speed of 1125 feet per second (about the speed of a sound wave)."},"content":{"rendered":"\n<p>.<br>3a &#8211; Suppose one has a wave that travels at a speed of 1125 feet per second (about the speed of a sound wave). Suppose we can produce waves with the following different Wavelengths: i- Wavelength of 1 foot; ii- Wavelength of 10 feet, iii- Wavelength of 0.1 foot; iv- Wavelength of 4.25 feet. Calculate the Frequency for each of the Wavelengths given in i through iv. In solving this problem remember that the (Wavelength) X (Frequency) = (the Speed of the wave). The Frequency is given in waves per second. What does Wavelength and Frequency in part d have to do with playing the piano or other musical instruments? 3b &#8211; Suppose one has a wave that travels at a speed of 3 X 10^8 meters per second (the speed of light). Suppose we can produce waves with the following different Wavelengths: i- Wavelength of 10 centimeter (.1 meters) &#8211; microwave radiation ii- Wavelength of 10^(-5) meters &#8211; infrared radiation iii- Wavelength of 6 x 10^(-7) meters &#8211; green in the visible iv- Wavelength of 10^(-8) meters &#8211; ultraviolet radiation v- Wavelength of 10 ^(12) meters &#8211; gamma rays Calculate the Frequency for each of the Wavelengths given in i through v. In solving this problem remember that the (Wavelength) X (Frequency) = (the Speed of the wave). The Frequency is given in waves per second.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we can use the fundamental wave equation:Speed&nbsp;of&nbsp;the&nbsp;wave=Wavelength\u00d7Frequency\\text{Speed of the wave} = \\text{Wavelength} \\times \\text{Frequency}Speed&nbsp;of&nbsp;the&nbsp;wave=Wavelength\u00d7Frequency<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Speed of the wave<\/strong> is the speed at which the wave travels (in this case, the speed of light or the speed of sound),<\/li>\n\n\n\n<li><strong>Wavelength<\/strong> is the distance between successive wave peaks,<\/li>\n\n\n\n<li><strong>Frequency<\/strong> is how many waves pass a given point per second.<\/li>\n<\/ul>\n\n\n\n<p>We can rearrange the equation to find <strong>Frequency<\/strong>:Frequency=Speed&nbsp;of&nbsp;the&nbsp;waveWavelength\\text{Frequency} = \\frac{\\text{Speed of the wave}}{\\text{Wavelength}}Frequency=WavelengthSpeed&nbsp;of&nbsp;the&nbsp;wave\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3a. <strong>Speed of sound<\/strong> = 1125 feet per second<\/h3>\n\n\n\n<p><strong>Given Wavelengths:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>i. Wavelength of 1 foot<\/li>\n\n\n\n<li>ii. Wavelength of 10 feet<\/li>\n\n\n\n<li>iii. Wavelength of 0.1 foot<\/li>\n\n\n\n<li>iv. Wavelength of 4.25 feet<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s calculate the frequencies for each wavelength.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>For Wavelength of 1 foot:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Frequency=11251=1125&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{1125}{1} = 1125 \\text{ waves per second}Frequency=11125\u200b=1125&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 10 feet:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Frequency=112510=112.5&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{1125}{10} = 112.5 \\text{ waves per second}Frequency=101125\u200b=112.5&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 0.1 foot:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Frequency=11250.1=11250&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{1125}{0.1} = 11250 \\text{ waves per second}Frequency=0.11125\u200b=11250&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 4.25 feet:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Frequency=11254.25=264.7&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{1125}{4.25} = 264.7 \\text{ waves per second}Frequency=4.251125\u200b=264.7&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<p><strong>Relevance to playing musical instruments<\/strong>: In musical instruments, the <strong>wavelength<\/strong> of the sound waves determines the pitch we hear. A <strong>shorter wavelength<\/strong> (higher frequency) results in a higher pitch (e.g., a high note on a piano). Conversely, a <strong>longer wavelength<\/strong> (lower frequency) results in a lower pitch (e.g., a low note). So, understanding the relationship between <strong>wavelength<\/strong> and <strong>frequency<\/strong> is essential for tuning and playing instruments.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3b. <strong>Speed of light<\/strong> = 3 x 10^8 meters per second<\/h3>\n\n\n\n<p><strong>Given Wavelengths<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>i. Wavelength of 10 centimeters (0.1 meters) &#8211; microwave radiation<\/li>\n\n\n\n<li>ii. Wavelength of 10^(-5) meters &#8211; infrared radiation<\/li>\n\n\n\n<li>iii. Wavelength of 6 x 10^(-7) meters &#8211; green in the visible spectrum<\/li>\n\n\n\n<li>iv. Wavelength of 10^(-8) meters &#8211; ultraviolet radiation<\/li>\n\n\n\n<li>v. Wavelength of 10^12 meters &#8211; gamma rays<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s calculate the frequencies for each wavelength.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>For Wavelength of 0.1 meters (microwave radiation)<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>Frequency=3\u00d71080.1=3\u00d7109&nbsp;waves&nbsp;per&nbsp;second&nbsp;(3&nbsp;GHz)\\text{Frequency} = \\frac{3 \\times 10^8}{0.1} = 3 \\times 10^9 \\text{ waves per second (3 GHz)}Frequency=0.13\u00d7108\u200b=3\u00d7109&nbsp;waves&nbsp;per&nbsp;second&nbsp;(3&nbsp;GHz)<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 10^(-5) meters (infrared radiation)<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>Frequency=3\u00d710810\u22125=3\u00d71013&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{3 \\times 10^8}{10^{-5}} = 3 \\times 10^{13} \\text{ waves per second}Frequency=10\u221253\u00d7108\u200b=3\u00d71013&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 6 x 10^(-7) meters (green light in the visible spectrum)<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>Frequency=3\u00d71086\u00d710\u22127=5\u00d71014&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{3 \\times 10^8}{6 \\times 10^{-7}} = 5 \\times 10^{14} \\text{ waves per second}Frequency=6\u00d710\u221273\u00d7108\u200b=5\u00d71014&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 10^(-8) meters (ultraviolet radiation)<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>Frequency=3\u00d710810\u22128=3\u00d71016&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{3 \\times 10^8}{10^{-8}} = 3 \\times 10^{16} \\text{ waves per second}Frequency=10\u221283\u00d7108\u200b=3\u00d71016&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<ol start=\"5\" class=\"wp-block-list\">\n<li><strong>For Wavelength of 10^12 meters (gamma rays)<\/strong>:<\/li>\n<\/ol>\n\n\n\n<p>Frequency=3\u00d71081012=3\u00d710\u22124&nbsp;waves&nbsp;per&nbsp;second\\text{Frequency} = \\frac{3 \\times 10^8}{10^{12}} = 3 \\times 10^{-4} \\text{ waves per second}Frequency=10123\u00d7108\u200b=3\u00d710\u22124&nbsp;waves&nbsp;per&nbsp;second<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary of Results:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>i. Microwave radiation: <strong>3 x 10^9<\/strong> Hz<\/li>\n\n\n\n<li>ii. Infrared radiation: <strong>3 x 10^13<\/strong> Hz<\/li>\n\n\n\n<li>iii. Green light: <strong>5 x 10^14<\/strong> Hz<\/li>\n\n\n\n<li>iv. Ultraviolet radiation: <strong>3 x 10^16<\/strong> Hz<\/li>\n\n\n\n<li>v. Gamma rays: <strong>3 x 10^-4<\/strong> Hz<\/li>\n<\/ul>\n\n\n\n<p>These results show that waves with shorter wavelengths have higher frequencies. This principle also applies in the context of electromagnetic waves, where each region (radio waves, microwaves, infrared, visible, ultraviolet, and gamma rays) corresponds to specific wavelengths and frequencies.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-915.jpeg\" alt=\"\" class=\"wp-image-259137\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>.3a &#8211; Suppose one has a wave that travels at a speed of 1125 feet per second (about the speed of a sound wave). Suppose we can produce waves with the following different Wavelengths: i- Wavelength of 1 foot; ii- Wavelength of 10 feet, iii- Wavelength of 0.1 foot; iv- Wavelength of 4.25 feet. Calculate [&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-259134","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259134","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=259134"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/259134\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=259134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=259134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=259134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}