{"id":100107,"date":"2026-02-15T20:16:55","date_gmt":"2026-02-15T20:16:55","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100107"},"modified":"2026-07-12T07:47:02","modified_gmt":"2026-07-12T07:47:02","slug":"frequency-wavelength-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ms\/calculators\/frequency-wavelength-calculator\/","title":{"rendered":"Documented Phase-Speed Wavelength Calculator"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Phase-Speed Wavelength Calculator\",\"description\":\"Calculate wavelength,period,spatial wavenumber and angular frequency from frequency and a documented phase speed,or from the exact SI speed of light in vacuum.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/frequency-wavelength-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-12\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does the calculator determine wave speed from a material name?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Use a phase speed documented for the actual wave type,mode,direction,frequency and conditions. The calculator only applies lambda equals phase speed divided by frequency.\"}},{\"@type\":\"Question\",\"name\":\"Is the vacuum electromagnetic-wave speed exact?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Yes. In that mode the calculator uses the SI fixed value c equals299792458 metres per second for light in vacuum.\"}}]}<\/script>\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Documented phase-speed wavelength\",\"item\":\"https:\/\/vibromera.eu\/calculators\/frequency-wavelength-calculator\/\"}]}<\/script>\r\n<link rel=\"preconnect\" 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print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\r\n\r\n.vc-form-grid-wave{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:18px}.vc-hidden{display:none!important}.vc-result-note{margin:0;color:var(--vc-ink-secondary);font-size:13px}@media(max-width:600px){.vc-form-grid-wave{grid-template-columns:1fr}}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-wave\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">General periodic-wave relation<\/p><h1 class=\"vc-header-title\">Documented Phase-Speed Wavelength Calculator<\/h1><p class=\"vc-header-subtitle\">Calculate wavelength and related quantities from frequency and a documented phase velocity,or use the exact SI speed of light for an electromagnetic wave in vacuum.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">v<sub>p<\/sub>=f\u03bb<\/span><span class=\"vc-badge\">k=2\u03c0\/\u03bb<\/span><span class=\"vc-badge\">Reference arithmetic \u2014 no material-property lookup<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid-wave\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-basis\">Phase-speed basis<\/label><select class=\"vc-select\" id=\"vc-basis\"><option value=\"\">Select\u2026<\/option><option value=\"documented\">Documented phase speed<\/option><option value=\"vacuum\">Vacuum EM wave \u2014 exact c<\/option><\/select><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-freq\">Frequency f<\/label><input class=\"vc-input\" id=\"vc-freq\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 440\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-funit\">Frequency unit<\/label><select class=\"vc-select\" id=\"vc-funit\"><option value=\"\">Select\u2026<\/option><option value=\"Hz\">Hz<\/option><option value=\"kHz\">kHz<\/option><option value=\"MHz\">MHz<\/option><option value=\"GHz\">GHz<\/option><option value=\"THz\">THz<\/option><\/select><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-speed-wrap\"><label class=\"vc-label\" for=\"vc-speed\">Documented phase speed v<sub>p<\/sub><\/label><input class=\"vc-input\" id=\"vc-speed\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 343.2\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-sunit-wrap\"><label class=\"vc-label\" for=\"vc-sunit\">Phase-speed unit<\/label><select class=\"vc-select\" id=\"vc-sunit\"><option value=\"\">Select\u2026<\/option><option value=\"ms\">m\/s<\/option><option value=\"kms\">km\/s<\/option><\/select><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-wave-wrap\"><label class=\"vc-label\" for=\"vc-wave-type\">Wave type,mode,direction and conditions<\/label><input class=\"vc-input\" id=\"vc-wave-type\" type=\"text\" placeholder=\"e.g. longitudinal bulk wave,20 \u00b0C,stated alloy\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-source-wrap\"><label class=\"vc-label\" for=\"vc-source\">Phase-speed provenance<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"e.g. measured dispersion curve,report rev 2\"><\/div>\r\n<\/div><p id=\"vc-error\" role=\"alert\" style=\"margin:.75rem 0 0;color:#b42318\"><\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Model boundary:<\/strong> \u03bb=v<sub>p<\/sub>\/f uses the phase velocity for the same frequency,wave type,mode,direction and physical conditions. In dispersive media v<sub>p<\/sub> can vary with frequency and is not group velocity. The calculator does not infer elastic-wave speed from density or a material name and does not replace a dispersion\/material model.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Wave quantities<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\">\r\n<div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Wavelength \u03bb<\/div><div class=\"vc-rcard-value\" id=\"vc-r-scaled\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Wavelength in metres<\/div><div class=\"vc-rcard-value\" id=\"vc-r-lambda\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Period T<\/div><div class=\"vc-rcard-value\" id=\"vc-r-period\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Spatial angular wavenumber k<\/div><div class=\"vc-rcard-value\" id=\"vc-r-k\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Ordinary wavenumber 1\/\u03bb<\/div><div class=\"vc-rcard-value\" id=\"vc-r-nu\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Angular frequency \u03c9<\/div><div class=\"vc-rcard-value\" id=\"vc-r-omega\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Normalized frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-fhz\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Phase speed used<\/div><div class=\"vc-rcard-value\" id=\"vc-r-speed\">\u2014<\/div><\/div>\r\n<\/div><p class=\"vc-result-note\" id=\"vc-r-note\"><\/p><\/div><\/div>\r\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Formula,source and applicability<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Implemented relations<\/h3><div class=\"vc-formula-box\">v<sub>p<\/sub>=f\u03bb &nbsp;\u2192&nbsp; \u03bb=v<sub>p<\/sub>\/f<br>T=1\/f<br>k=2\u03c0\/\u03bb &nbsp;(rad\/m)<br>\u03bd&#771;=1\/\u03bb &nbsp;(cycles\/m)<br>\u03c9=2\u03c0f &nbsp;(rad\/s)<\/div><p>f is frequency in hertz,v<sub>p<\/sub> is phase speed in metres per second,\u03bb is wavelength in metres,T is period in seconds,k is spatial angular wavenumber,and \u03bd&#771; is ordinary spatial frequency. Dimensional check:(m\/s)\/(1\/s)=m.<\/p>\r\n<h3>Primary references<\/h3><p><a href=\"https:\/\/openstax.org\/books\/university-physics-volume-1\/pages\/16-key-equations\" target=\"_blank\" rel=\"noopener\">OpenStax University Physics,Volume1,Chapter16 key equations<\/a> gives v=\u03bb\/T=\u03bbf,k=2\u03c0\/\u03bb and v=\u03c9\/k. <a href=\"https:\/\/www.bipm.org\/documents\/20126\/41489670\/SI-App2-metre.pdf\/0e011055-9736-d293-5e56-b8b1b267fd68?download=true\" target=\"_blank\" rel=\"noopener\">BIPM SI Brochure,9th edition,Appendix2 v1.2 (19June2026)<\/a> states the fixed vacuum speed c=299792458m\/s.<\/p>\r\n<h3>Why there is no material drop-down<\/h3><p>A single label such as \u201csteel\u201d,\u201caluminium\u201d,\u201cconcrete\u201d,\u201cwater\u201d or \u201cair\u201d does not fully define phase speed. Elastic-wave speed depends on wave family and material properties; structural and guided waves may be dispersive. Fluid\/gas speeds depend on state and composition. Use project data for the relevant mode,direction,frequency and conditions. The vacuum mode is the only built-in speed because c is an exact SI defining constant.<\/p>\r\n<h3>No acceptance or detectability claim<\/h3><p>The result is general wave arithmetic,not an ISO calculation and not a defect-size,sensor-spacing or structural-mode criterion. Ultrasonic detectability and vibration sensor placement depend on the complete measurement and propagation problem,not wavelength alone.<\/p>\r\n<\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Reference wavelength arithmetic,not a material-property,dispersion,inspection or acceptance calculation. Scientific review:July2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var ids=['vc-r-scaled','vc-r-lambda','vc-r-period','vc-r-k','vc-r-nu','vc-r-omega','vc-r-fhz','vc-r-speed'];function num(raw){var s=String(raw).trim().replace(',','.');return \/^[+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s)?Number(s):NaN}function fmt(x){return Number(x.toPrecision(12)).toString()}function fmtSI(x){var a=Math.abs(x);if(a>=1e3)return fmt(x\/1e3)+' km';if(a>=1)return fmt(x)+' m';if(a>=1e-3)return fmt(x*1e3)+' mm';if(a>=1e-6)return fmt(x*1e6)+' \u00b5m';if(a>=1e-9)return fmt(x*1e9)+' nm';if(a>=1e-12)return fmt(x*1e12)+' pm';return fmt(x)+' m'}function clear(){ids.forEach(function(id){$(id).textContent='\u2014'});$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function range(x,lo,hi){return Number.isFinite(x)&&x>=lo&&x<=hi}function updateFields(){var d=$('vc-basis').value==='documented';['vc-speed-wrap','vc-sunit-wrap','vc-wave-wrap','vc-source-wrap'].forEach(function(id){$(id).classList.toggle('vc-hidden',!d)})}function setUrl(){var u=new URL(location),basis=$('vc-basis').value,map={basis:'vc-basis',f:'vc-freq',funit:'vc-funit',speed:'vc-speed',sunit:'vc-sunit',wave:'vc-wave-type',source:'vc-source'};Object.keys(map).forEach(function(key){var relevant=!['speed','sunit','wave','source'].includes(key)||basis==='documented',value=relevant?$(map[key]).value.trim():'';if(value)u.searchParams.set(key,value);else u.searchParams.delete(key)});history.replaceState(null,'',u.toString())}function fail(message){clear();$('vc-error').textContent=message}function calc(){updateFields();setUrl();var basis=$('vc-basis').value,fr=$('vc-freq').value.trim(),fu=$('vc-funit').value;if(!basis&&!fr&&!fu&&!$('vc-speed').value.trim()&&!$('vc-sunit').value&&!$('vc-wave-type').value.trim()&&!$('vc-source').value.trim()){clear();$('vc-error').textContent='';return}if(!basis||!fr||!fu){fail('Select the phase-speed basis and enter frequency with its unit.');return}var f0=num(fr),ff={Hz:1,kHz:1e3,MHz:1e6,GHz:1e9,THz:1e12}[fu],f=f0*ff;if(!range(f,1e-12,1e30)){fail('Normalized frequency must be from10\u207b\u00b9\u00b2 to10\u00b3\u2070Hz.');return}var v,basisText;if(basis==='vacuum'){v=299792458;basisText='vacuum electromagnetic wave;exact SI c'}else{var sr=$('vc-speed').value.trim(),su=$('vc-sunit').value,wave=$('vc-wave-type').value.trim(),source=$('vc-source').value.trim();if(!sr||!su||!wave||!source){fail('Enter documented phase speed with its unit,wave\/mode conditions and provenance.');return}var s0=num(sr),sf=su==='kms'?1000:1;v=s0*sf;if(!range(v,1e-12,1e15)){fail('Normalized phase speed must be from10\u207b\u00b9\u00b2 to10\u00b9\u2075m\/s.');return}basisText=wave+';provenance:'+source}var lambda=v\/f,T=1\/f,k=2*Math.PI\/lambda,nu=1\/lambda,omega=2*Math.PI*f;if(![lambda,T,k,nu,omega].every(function(x){return Number.isFinite(x)&&x>0})){fail('The calculated quantities exceed the finite numerical range.');return}$('vc-error').textContent='';$('vc-r-scaled').textContent=fmtSI(lambda);$('vc-r-lambda').textContent=fmt(lambda)+' m';$('vc-r-period').textContent=fmt(T)+' s';$('vc-r-k').textContent=fmt(k)+' rad\/m';$('vc-r-nu').textContent=fmt(nu)+' cycles\/m';$('vc-r-omega').textContent=fmt(omega)+' rad\/s';$('vc-r-fhz').textContent=fmt(f)+' Hz';$('vc-r-speed').textContent=fmt(v)+' m\/s';$('vc-r-note').textContent='Basis:'+basisText+'. 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