{"id":66959,"date":"2026-10-13T10:40:50","date_gmt":"2026-10-13T07:40:50","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66959"},"modified":"2026-10-13T10:40:50","modified_gmt":"2026-10-13T07:40:50","slug":"beat-frequency-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/beat-frequency-calculator\/","title":{"rendered":"Beat Frequency Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Find the Pulsing Rate of Two Nearby Tones<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66959\" data-favorite-title=\"Beat Frequency\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/beat-frequency-calculator\/\" data-favorite-excerpt=\"Enter the frequencies of two nearby tones in Hz, kHz, MHz or rpm to find the beat frequency, beat period, perceived pitch and interval in cents. Great for tuning instruments by ear.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-spectrum\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/physics\/beat-frequency-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66959\" data-post=\"66959\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">First frequency (f\u2081)<\/label><div class=\"term\">f\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"first_frequency_f\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 440\" min=\"0\" value=\"440\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"hz\" selected>Hz<\/option><option value=\"khz\">kHz<\/option><option value=\"mhz\">MHz<\/option><option value=\"rpm\">rpm<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-1\">Frequency of the first tone. 440 Hz is the standard concert pitch A\u2084.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Second frequency (f\u2082)<\/label><div class=\"term\">f\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"second_frequency_f\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 444\" min=\"0\" value=\"444\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"hz\" selected>Hz<\/option><option value=\"khz\">kHz<\/option><option value=\"mhz\">MHz<\/option><option value=\"rpm\">rpm<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Frequency of the second tone. When it is close to f\u2081 you hear a pulsing beat; when it is far away you hear two separate tones or roughness.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66959\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Beat Frequency Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Beat frequency (f_beat)<\/span><span class=\"result-term\">f_beat<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Beat period (T_beat) and details<\/span><span class=\"result-term\">T_beat<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66959\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Beat Frequency Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ f_{\\text{beat}} = |f_1 - f_2| \\,, \\qquad T_{\\text{beat}} = \\frac{1}{f_{\\text{beat}}} \\,, \\qquad f_{\\text{avg}} = \\frac{f_1 + f_2}{2} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(f_1\\) \u2014 frequency of the first tone (Hz)<\/li>\n<li>\\(f_2\\) \u2014 frequency of the second tone (Hz)<\/li>\n<li>\\(f_{\\text{beat}}\\) \u2014 beat frequency, the rate of the audible pulsing (Hz)<\/li>\n<li>\\(T_{\\text{beat}}\\) \u2014 beat period, the time between two successive loud maxima (s)<\/li>\n<li>\\(f_{\\text{avg}}\\) \u2014 average frequency, the pitch you actually perceive (Hz)<\/li>\n<\/ul>\n<p>When two tones of nearly equal frequency sound together, their waves alternately reinforce and cancel each other, so the loudness pulses at the difference frequency. The ear hears a single tone at \\(f_{\\text{avg}}\\) whose volume swells and fades \\(f_{\\text{beat}}\\) times per second.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Beat Frequency \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<p>{example}<\/p>\n<p><strong>Example:<\/strong> a violinist tunes the A string to a 440 Hz reference while the string currently vibrates at 444 Hz. Both frequencies are entered in Hz.<\/p>\n<p>\\[ f_{\\text{beat}} = |f_1 - f_2| = |440 - 444| = 4 \\text{ Hz} \\]<\/p>\n<p>\\[ T_{\\text{beat}} = \\frac{1}{f_{\\text{beat}}} = \\frac{1}{4} = 0.25 \\text{ s} \\,, \\qquad f_{\\text{avg}} = \\frac{440 + 444}{2} = 442 \\text{ Hz} \\]<\/p>\n<p><strong>Result:<\/strong> the beat frequency is 4 Hz (240 beats per minute), each beat lasting 0.25 s. The perceived pitch is 442 Hz, and the interval between the two tones is about 15.7 cents. Four clearly countable \"wah-wah\" pulses per second tell the player the string is still slightly sharp.<\/p>\n<p>{\/example}<\/p>\n\r\n<\/section>\n<h2>How to Use the Beat Frequency Calculator<\/h2>\n<ol>\n<li>Enter the <strong>First frequency (f\u2081)<\/strong> value, e.g. 440.<\/li>\n<li>Pick the matching unit (Hz, kHz, MHz or rpm) from the dropdown next to it.<\/li>\n<li>Enter the <strong>Second frequency (f\u2082)<\/strong> value with its unit.<\/li>\n<li>Read the results: the <strong>Beat frequency (f_beat)<\/strong> block shows the difference in Hz, kHz and beats per minute, while the <strong>Beat period (T_beat) and details<\/strong> block shows how long one beat lasts, the perceived pitch, the higher and lower tone, and the interval in cents.<\/li>\n<\/ol>\n<h2>What Are Beats and Why Do They Matter?<\/h2>\n<p>Beats are a classic example of wave interference. If two sound sources vibrate at slightly different frequencies, their pressure waves arrive at your ear with a phase difference that keeps drifting. Twice per beat cycle the waves are in phase and add up loudly; in between they are out of phase and partially cancel. The result is a single tone whose amplitude rises and falls rhythmically instead of two distinct pitches.<\/p>\n<p>This phenomenon has real practical value. Piano tuners, violinists and organ builders tune by listening to beats: play the reference and the instrument together, and adjust until the pulsing slows down and finally disappears at unison. Piano tuners intentionally leave slight offsets between strings, counting a slow beat (say 1\u20132 Hz) as the correct amount of \"life\" in a unison. In engineering, beat frequencies appear anywhere two periodic signals mix \u2014 detuned engines on a twin-engine aircraft, two motors running at nearly the same rpm, or electrical power grids with a slight frequency mismatch.<\/p>\n<p>Interpreting the result is mostly about speed. Below about 10\u201315 Hz the ear follows each pulse individually, which is the counting-friendly range used for tuning. As the beat frequency grows, the individual pulses blur into a rough, buzzy quality, and once the two tones lie far enough apart (roughly beyond a critical band, about 5% of the average frequency), you simply hear two separate notes. The calculator's output describes which of these regimes your inputs fall into.<\/p>\n<h2>Perceptual Ranges at a Glance<\/h2>\n<table>\n<thead>\n<tr>\n<th>Beat frequency<\/th>\n<th>What you hear<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0 Hz<\/td>\n<td>One steady tone \u2014 the frequencies are identical<\/td>\n<\/tr>\n<tr>\n<td>0\u20130.5 Hz<\/td>\n<td>Slow swelling and fading, longer than 2 s per cycle<\/td>\n<\/tr>\n<tr>\n<td>0.5\u201310 Hz<\/td>\n<td>Distinct, countable \"wah-wah\" pulsing (the tuning range)<\/td>\n<\/tr>\n<tr>\n<td>10\u201320 Hz<\/td>\n<td>Beats too fast to count; rough, buzzy tone quality<\/td>\n<\/tr>\n<tr>\n<td>20 Hz to ~5% of f_avg<\/td>\n<td>Roughness without distinct beats<\/td>\n<\/tr>\n<tr>\n<td>Above that<\/td>\n<td>Two separate pitches<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li>The formula assumes both tones have equal amplitude and are pure sine waves. With unequal amplitudes the loudness still pulses at \\(f_{\\text{beat}}\\), but the dips are shallower; with complex tones (real instruments), each harmonic pair produces its own beat.<\/li>\n<li>The tones must be close in frequency for true beats to occur. The calculator still reports the mathematical difference for any two inputs, and its description tells you when the difference is too large for audible beats.<\/li>\n<li>The beat frequency itself is not a pitch you hear \u2014 you hear one tone near \\(f_{\\text{avg}}\\) whose <em>loudness<\/em> changes \\(f_{\\text{beat}}\\) times per second.<\/li>\n<li>The listening thresholds (about 10\u201315 Hz for counting, roughly a 5% frequency gap for separation) are typical values; they vary between listeners and with sound level.<\/li>\n<li>The cent-based interval is only shown for tones inside the audible range (20 Hz \u2013 20 kHz).<\/li>\n<\/ul>\n<h2>Related Calculators<\/h2>\n<p>Beats are all about sound waves, so you may also find the <a href=\"https:\/\/wpcalc.com\/en\/physics\/speed-of-sound-in-air-calculator\/\">Speed of Sound in Air Calculator<\/a> and the <a href=\"https:\/\/wpcalc.com\/en\/physics\/sound-intensity-level-calculator\/\">Sound Intensity Level Calculator<\/a> useful for related acoustics problems. For another classic wave phenomenon, try the <a href=\"https:\/\/wpcalc.com\/en\/physics\/simple-pendulum-calculator\/\">Simple Pendulum Calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enter the frequencies of two nearby tones in Hz, kHz, MHz or rpm to find the beat frequency, beat period, perceived pitch and interval in cents. Great for tuning instruments by ear.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[62],"tags":[87],"class_list":["post-66959","post","type-post","status-publish","format-standard","hentry","category-physics","tag-waves-optics"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66959","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66959"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66959\/revisions"}],"predecessor-version":[{"id":66960,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66959\/revisions\/66960"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66959"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66959"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}