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<h1 class="content-title">
Mengenal Hukum Mersenne pada Senar dan Contoh di Kehidupan Sehari-hari | Fisika Kelas 8 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kresnoadi" class="">Kresnoadi</a> </p>
<p class="content-info"><span>July 26, 2019 • </span> <span>3 minutes read</span></p>
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<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Fisika_8_-_Hukum_Mersenne-01.png" alt="Hukum Mersenne" width="820" style="width: 820px;"></p>
<p style="text-align: justify;"><em>Artikel ini membahas tentang apa itu hukum mersenne dan hubungan frekuensi terhadap panjang jarak, luas penampang, massa jenis, dan gaya pada senar.</em></p>
<p style="text-align: center;">—</p>
<p><span id="more-7933"></span></p>
<p style="text-align: justify;">Siapa yang pernah main gitar? Coba <em>deh,</em> kamu liat <em>mamang-mamang</em> gitaris seperti Roma Irama atau Apoy Wali (sebentar, kenapa referensi saya ini ya?). Pokoknya, perhatiin saat mereka memetik gitar. Saat <em>menggenjreng</em> gitar di bagian belakang (dekat lubang), pasti bunyi yang keluar akan lebih nge-bass dibanding saat menggenjreng dekat dengan leher gitar.</p>
<p style="text-align: justify;">Bunyi yang timbul saat bagian ujung leher gitar digenjreng paling cuma “Cring! Cring! Cring!”</p>
<p style="text-align: justify;">Padahal, kita, kan menggunakan gitar yang sama. Tanpa diubah apapun. Tapi, kenapa <strong><a href="/ipa-kelas-8-jenis-jenis-bunyi-berdasarkan-frekuensinya" rel=" noopener">bunyi yang dihasilkan bisa berbeda ya?</a></strong></p>
<p style="text-align: justify;">Pertanyaan ini sudah dijawab oleh Marin Mersenne, ilmuwan Perancis, ratusan tahun yang lalu, saat ia membuat benda bernama Sonometer.</p>
<p style="text-align: justify;">Sonometer ini dibuat untuk mencari tahu hubungan antara frekuensi bunyi terhadap beberapa hal. Seperti jarak tumpuan senar, misalnya. Seperti yang di awal kita bahas. Ternyata, <strong>semakin panjang jarak senar, frekuensi yang dihasilkan akan semakin rendah.</strong></p>
<p style="text-align: justify;"><strong>Baca juga: <span style="color: #444444;"><a href="/bunyi" rel=" noopener" style="color: #444444;">Bagaimana Kita Bisa Mendengar Bunyi?</a></span></strong></p>
<p style="text-align: justify;">Selain panjang senar, Mersenne mendapatkan hubungan antara variabel lain. Seperti luas permukaan dan massa jenis.</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Fisika_8_-_Hukum_Mersenne_Artboard_4.png" alt="Hukum Mersenne" width="600" style="width: 600px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;">Ya, penemuan ini kemudian dirangkumnya ke dalam buku L’Harmonie Universelle pada tahun 1637. Akhirnya, dia pun mencetuskan <strong>H</strong><strong>ukum Mersenne</strong> yang telah disederhanakan menjadi seperti ini:</p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Fisika_8_-_Hukum_Mersenne-04.png" alt="Hukum Mersenne" width="600" style="width: 600px; display: block; margin: 0px auto;"></p>
<p style="text-align: justify;"><em>Eits</em>, tenang dulu. Jangan mikir yang aneh-aneh dulu. Meskipun keliatannya bikin mabok, tapi rumus itu gampang kok. Asal tahu konsepnya soal bagian mana yang berbanding terbalik dengan frekuensi, pasti ngeliat rumus itu gak serem lagi.</p>
<p style="text-align: justify;">Biar <em>nggak</em> lupa, mari kita ulang lagi.</p>
<p style="text-align: justify;">Bayangkan sebuah gitar. Ketika kamu <em>menggenjreng</em> di bagian depan (dekat leher gitar), pasti bunyinya nyaring. Itu artinya, semakin pendek jaraknya, frekuensinya semakin tinggi (berbanding terbalik). Begitu pula dengan massa jenis, dan luas permukaan senarnya.</p>
<p style="text-align: justify;">Yang dimaksud dengan luas permukaan senar di sini adalah bagian buletan yang sangat kecil dari senar itu yaa. Kalau di sedotan, luas permukaan adalah bagian luas dari “lingkaran” yang bolong itu. Kalau balik lagi ngebayangin senar, kamu pasti berpikir, ‘Itu mah kecil banget kak!’</p>
<p style="text-align: justify;"><em>Nah</em>, emang iya.</p>
<p style="text-align: justify;">Luas permukaan senar kecil, Tapi berpengaruh.</p>
<p style="text-align: justify;">Kalau kamu perhatiin, senar bagian atas gitar (yang tebal) bersuara nge-bass, sementara senar-senar bawah (yang tipis) dipakai gitaris untuk memetik melodi. Artinya, semakin tebal (luas permukaannya besar), maka frekuensinya rendah. Berbanding terbalik juga kan.</p>
<p style="text-align: justify;">Adapun variabel yang berbanding lurus terhadap frekuensi adalah gaya. Coba <em>deh</em>, kamu memetik gitar dengan lebih kencang, pasti suaranya lebih nyaring. Bandingkan dengan petikan yang lembut dan pelan, pasti bunyi yang keluar akan lebih syahdu (<em>halah syahdu</em>).</p>
<p style="text-align: justify;">Setelah paham konsepnya, kita coba yuk aplikasikan ke Hukum Mersenne tadi. Coba kerjain contoh simpel di bawah ini ya. Pikir dan <em>bayangin</em> dulu ya ke rumus tadi. Kalau perlu pakai coret-coretan <em>aja</em>. Baru <em>deh</em>,<em> kalo udah mentok,</em> bandingin sama penjelasannya (<em>tap </em>gambarnya).</p>
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<p style="text-align: justify;">Gimana? Sekarang sudah paham kan konsep Hukum Mersenne dan hubungan dari frekuensi bunyi terhadap berbagai variabelnya. Kalau kamu masih penasaran ingin menonton materi ini dalam bentuk video beranimasi, langsung aja tonton di <strong><a href="https://ruangguru.onelink.me/blPk/eaff0eb9" rel=" noopener">ruangbelajar!</a></strong></p>
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<nav class="footer-menu">
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</div>
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<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
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</a>
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<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
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</a>
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<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
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<picture>
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<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
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<picture>
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</a>
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</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>