{"id":796,"date":"2026-08-12T11:20:30","date_gmt":"2026-08-12T11:20:30","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=796"},"modified":"2026-08-24T13:03:42","modified_gmt":"2026-08-24T13:03:42","slug":"speed-of-sound","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/speed-of-sound\/","title":{"rendered":"The Speed of Sound (and What Changes It)"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nThe speed of sound is the rate at which a pressure disturbance travels through a material, equal to about 343 m\/s in dry air at 20 \u00b0C. In a gas it is fixed by the temperature and by the gas itself, following v = sqrt(\u03b3RT\/M). Air pressure on its own does not change it.\n<\/p><\/div>\n\n<p>Count the seconds between a lightning flash and the thunder. Three seconds means the strike was roughly a kilometre away \u2014 a trick that works only because sound ambles along slowly enough to time with a wristwatch, while the light arrives essentially instantly.<\/p>\n\n<p>But that amble is not a fixed number. A trumpet plays sharp on a hot afternoon, an airliner cruising at 11 km hits Mach 1 far slower than it would at sea level, and a diver hears an outboard motor long before anyone at the surface does. Same physics \u2014 three different speeds.<\/p>\n\n<h2>What Is the Speed of Sound?<\/h2>\n\n<p>The speed of sound is how fast a pressure wave travels through a material: about 343 m\/s in air at 20 \u00b0C, roughly 1,480 m\/s in fresh water, and around 5,000 m\/s along a steel rail.<\/p>\n\n<p>Here is the thing most people picture wrongly. Sound is not a packet of air flying from the speaker to your ear. Each molecule shuffles back and forth by a fraction of a millimetre and shoves its neighbour, which shoves <em>its<\/em> neighbour \u2014 and the <strong>pattern<\/strong> of squeeze and stretch races away while the air itself stays put.<\/p>\n\n<p>Because that shuffling happens along the same line the wave travels, sound is a <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/transverse-vs-longitudinal-waves\/\">longitudinal wave<\/a> rather than the up-and-down ripple most diagrams of &#8220;a wave&#8221; show.<\/p>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/speed-of-sound-longitudinal-wave-compressions-rarefactions-travelling.webp\" width=\"1440\" height=\"640\" alt=\"Diagram of a longitudinal sound wave showing compressions and rarefactions travelling to the right at the speed of sound, with one wavelength marked\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:720px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">Sound moves as compressions and rarefactions. The air stays put; the pattern travels.<\/p>\n\n<p>So what sets the pace? Two properties fight it out in every material:<\/p>\n\n<ul>\n<li><strong>Stiffness<\/strong> \u2014 how hard the material pushes back when you squeeze it. Stiffer means each molecule passes the shove on sooner, so sound goes <em>faster<\/em>.<\/li>\n<li><strong>Inertia (density)<\/strong> \u2014 how heavy the molecules are. Heavier means they are more sluggish to accelerate, so sound goes <em>slower<\/em>.<\/li>\n<\/ul>\n\n<p>Every speed-of-sound formula you will ever meet is that same tug-of-war: the square root of stiffness divided by density.<\/p>\n\n<h2>The Speed of Sound Formula<\/h2>\n\n<p>For an ideal gas, the speed of sound is the square root of the adiabatic index times the gas constant times the absolute temperature, divided by the molar mass.<\/p>\n\n<div class=\"pf-formula\">v = sqrt(\u03b3RT \/ M)<\/div>\n\n<p>Every symbol, with its SI unit:<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Symbol<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Quantity<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">SI unit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Value for dry air<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>v<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Speed of sound<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">m\/s<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">the answer<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>\u03b3<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Adiabatic index (ratio of specific heats, c<sub>p<\/sub>\/c<sub>v<\/sub>)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">dimensionless<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">1.40<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>R<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Molar gas constant<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">J\/(mol\u00b7K)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">8.314<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>T<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Absolute temperature<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">K (kelvin, never \u00b0C)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">293.15 K at 20 \u00b0C<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>M<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Molar mass of the gas<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">kg\/mol<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">0.0290<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Note what is <em>missing<\/em> from that formula: pressure. Nowhere in <em>v<\/em> = sqrt(\u03b3RT\/M) does the air pressure appear \u2014 a point we will come back to, because it trips up almost everybody. The value of <em>R<\/em> used here is the standard <a href=\"https:\/\/physics.nist.gov\/cuu\/Constants\/index.html\" target=\"_blank\" rel=\"noopener\">molar gas constant published by NIST<\/a>, the same constant that drives the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/ideal-gas-law\/\">ideal gas law<\/a>.<\/p>\n\n<p>For everyday work in air, there is a shortcut worth memorising:<\/p>\n\n<div class=\"pf-formula\">v = 331.3 + 0.606 \u00d7 T  (T in \u00b0C, v in m\/s)<\/div>\n\n<p>It sits within about 1 m\/s of the exact formula between -20 \u00b0C and +40 \u00b0C, which is far tighter than most measurements you will ever make.<\/p>\n\n<p>And if you already know a sound&#8217;s frequency and wavelength, you do not need temperature at all \u2014 the same speed drops out of <em>v<\/em> = <em>f<\/em>\u03bb, the universal wave relationship. Our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/wave-speed\">Wave Speed Calculator<\/a> handles that rearrangement in either direction, and the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/frequency-formula\/\">frequency formula<\/a> covers where <em>f<\/em> comes from in the first place.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Speed of Sound Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/speed-of-sound.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>How Temperature Changes the Speed of Sound<\/h2>\n\n<p>Warming the air speeds sound up by roughly 0.6 m\/s for every degree Celsius \u2014 so sound travels about 24 m\/s faster on a 40 \u00b0C day than on a freezing one.<\/p>\n\n<p>Why? Temperature <em>is<\/em> molecular motion. Warm the gas and its molecules are already flying about faster, so each one reaches its neighbour sooner and passes the shove along more quickly.<\/p>\n\n<p>The dependence is on the <strong>square root of absolute temperature<\/strong>, not on temperature itself. Double the kelvin temperature and the speed rises by a factor of only sqrt(2), about 1.41.<\/p>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/speed-of-sound-dry-air-rising-306-metres.webp\" width=\"1440\" height=\"846\" alt=\"Graph showing the speed of sound in dry air rising from 306 metres per second at minus 40 degrees Celsius to 355 metres per second at plus 40 degrees Celsius\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:720px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;\">Speed of sound in dry air across everyday temperatures. Over this narrow range the square-root curve looks almost perfectly straight.<\/p>\n\n<h3>The Kelvin trap<\/h3>\n\n<p>This is the single most common way students lose marks on this topic. The <em>T<\/em> in <em>v<\/em> = sqrt(\u03b3RT\/M) is <strong>absolute temperature in kelvin<\/strong> \u2014 add 273.15 to your Celsius value before it goes anywhere near the formula.<\/p>\n\n<p>Drop 20 straight in instead of 293.15 and you will get about 90 m\/s. In practice, a good sanity check is that any answer for air near room temperature should land close to 340 m\/s. If it does not, check your kelvins first.<\/p>\n\n<h2>The Speed of Sound in Different Materials<\/h2>\n\n<p>Sound travels fastest in stiff solids, slower in liquids and slowest in gases \u2014 roughly 15 times faster in steel than in air.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Medium<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Speed (m\/s)<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Conditions<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Why it lands there<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Carbon dioxide<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">259<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">0 \u00b0C<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Heavy molecules (44 g\/mol) and a low \u03b3<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Air (dry)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">331<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">0 \u00b0C<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">The textbook reference value<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Air (dry)<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>343<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>20 \u00b0C<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Room temperature \u2014 the number to remember<\/strong><\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Helium<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">1,007<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">20 \u00b0C<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Very light molecules (4 g\/mol) accelerate easily<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Fresh water<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">1,482<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">20 \u00b0C<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Far stiffer than air, only ~800\u00d7 denser<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Seawater<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">~1,520<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">20 \u00b0C, 35 g\/kg salinity<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Salt raises stiffness more than density<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Aluminium (thin rod)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">~5,000<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Room temperature<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Stiff and unusually light for a metal<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Steel (thin rod)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">~5,050<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Room temperature, varies with alloy<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Huge stiffness beats its high density<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Steel (bulk)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">~5,960<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Room temperature<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Bulk waves are stiffer still than rod waves<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Outside gases the formula changes shape, but never its logic. In a liquid the speed is sqrt(K\/\u03c1), where <em>K<\/em> is the bulk modulus; along a thin solid rod it is sqrt(E\/\u03c1), with <em>E<\/em> the Young&#8217;s modulus.<\/p>\n\n<p>Stiffness over density, every time. Water is about 800 times denser than air, which alone would make sound <em>slower<\/em> \u2014 but water is roughly 15,000 times harder to compress, and stiffness wins decisively. For a wider comparison that brings light and vibrating strings into the picture, see our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/wave-speed-different-media\/\">wave speed in different media<\/a>.<\/p>\n\n<h2>Do Pressure and Humidity Change the Speed of Sound?<\/h2>\n\n<p>Air pressure alone does <strong>not<\/strong> change the speed of sound, but humidity does \u2014 by a few tenths of a percent.<\/p>\n\n<h3>Why pressure cancels out<\/h3>\n\n<p>Squeeze air into half the volume at the same temperature and you double its pressure \u2014 but you also double its density. Stiffness and inertia rise together, in lockstep, and the ratio that sets the speed does not budge.<\/p>\n\n<p>That is why pressure never appears in <em>v<\/em> = sqrt(\u03b3RT\/M). For an ideal gas the two effects cancel exactly.<\/p>\n\n<h3>So why is sound slower high up?<\/h3>\n\n<p>Because it is <em>cold<\/em> up there, not because the air is thin. At the top of the troposphere, around 11 km, the standard atmosphere sits at about -56.5 \u00b0C, and the speed of sound falls to roughly 295 m\/s.<\/p>\n\n<p>An airliner therefore reaches Mach 1 at a much lower true airspeed at cruise than it would at sea level. NASA&#8217;s own <a href=\"https:\/\/www1.grc.nasa.gov\/beginners-guide-to-aeronautics\/speed-of-sound-interactive\/\" target=\"_blank\" rel=\"noopener\">guide to the speed of sound<\/a> makes the same point for aircraft design: track the temperature, not the pressure.<\/p>\n\n<h3>The humidity nudge<\/h3>\n\n<p>Water vapour is lighter than the nitrogen and oxygen it displaces \u2014 18 g\/mol against about 29. Humid air is therefore slightly <em>less<\/em> dense than dry air at the same pressure, so sound moves marginally faster through it.<\/p>\n\n<p>The effect is real but small: going from bone-dry to fully saturated at 20 \u00b0C lifts the speed by roughly 1.3 m\/s, about 0.4%. Enough to matter for precision acoustics; not enough to change your thunder count.<\/p>\n\n<h2>Real-World Examples of the Speed of Sound<\/h2>\n\n<h3>Counting thunder<\/h3>\n\n<p>Light covers a kilometre in about three-millionths of a second; sound needs almost three full seconds. Count the gap and divide by three for the distance in kilometres \u2014 or by five for miles.<\/p>\n\n<h3>Sonar and echo sounding<\/h3>\n\n<p>Ships map the seabed by timing a pulse&#8217;s round trip, using roughly 1,500 m\/s for seawater. Halve the total time, because the sound has gone down <em>and<\/em> back.<\/p>\n\n<h3>Mach numbers and sonic booms<\/h3>\n\n<p>Mach number is simply an object&#8217;s speed divided by the local speed of sound. Because the divisor shrinks in cold air, the same aircraft at the same true airspeed sits at a higher Mach number when it climbs.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/FA-18_going_transonic.jpeg\"\n\n       alt=\"Jet aircraft near the speed of sound with a visible vapour cone\"\n\n       loading=\"lazy\"\n\n       style=\"width:100%;height:auto;border-radius:4px;\" width=\"1476\" height=\"1075\">\n\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">A vapour cone forms as an aircraft approaches the speed of sound. The cloud is condensation in the low-pressure region, not the sound barrier itself.<\/figcaption>\n\n<\/figure>\n\n<h3>Instruments that drift sharp<\/h3>\n\n<p>A flute or trumpet sets its pitch by resonating a column of air, and that resonance depends on the speed of sound inside the tube. As the instrument warms, the speed rises and the pitch creeps upwards \u2014 which is exactly why orchestras retune after warming up.<\/p>\n\n<h3>Medical ultrasound<\/h3>\n\n<p>Scanners convert echo times into depth by assuming sound moves at about 1,540 m\/s through soft tissue. Get that assumed speed wrong and every measurement on the image shifts with it.<\/p>\n\n<h2>Common Misconceptions About the Speed of Sound<\/h2>\n\n<h3>&#8220;Sound travels faster in denser materials&#8221;<\/h3>\n\n<p>Density on its own <em>slows<\/em> sound down \u2014 look at where \u03c1 sits in sqrt(K\/\u03c1). Steel beats air because its stiffness is millions of times greater, easily outrunning its higher density. Among gases, where stiffness is similar, the heavier gas really is the slower one: carbon dioxide trails air, helium leaves it standing.<\/p>\n\n<h3>&#8220;Sound is slower at altitude because the air is thin&#8221;<\/h3>\n\n<p>Thin air is not the reason \u2014 cold air is. Pressure and density fall together and cancel; the temperature drop is what pulls the speed down from 340 m\/s to about 295 m\/s at cruise altitude.<\/p>\n\n<h3>&#8220;Helium makes your voice higher by speeding up your vocal cords&#8221;<\/h3>\n\n<p>Your vocal folds vibrate at very nearly their normal rate, so the pitch you are producing barely changes. What shifts is the <strong>resonance<\/strong> of your vocal tract: sound moves about 2.9 times faster in helium, so the frequencies your throat amplifies jump upwards and the timbre turns squeaky.<\/p>\n\n<h3>&#8220;A sonic boom happens once, at the moment the barrier is broken&#8221;<\/h3>\n\n<p>The boom is not a one-off event. A supersonic aircraft drags a cone of shock waves behind it continuously, and anyone the cone sweeps over hears a boom \u2014 so the noise arrives at different places at different times for as long as the aircraft stays supersonic.<\/p>\n\n<h2>How the Speed of Sound Relates to Mach Number, Wavelength and the Doppler Effect<\/h2>\n\n<p>The speed of sound is the reference speed sitting inside several other acoustics formulas, which is why getting it right matters well beyond this one number.<\/p>\n\n<ul>\n<li><strong>Mach number:<\/strong> the ratio of an object&#8217;s speed to the local speed of sound. Mach 1 is not a fixed velocity \u2014 it depends entirely on the air temperature.<\/li>\n<li><strong>Wavelength:<\/strong> \u03bb = <em>v<\/em>\/<em>f<\/em>. Because <em>v<\/em> shifts with temperature, a 440 Hz note has a measurably different wavelength on a cold morning than on a hot afternoon.<\/li>\n<li><strong>The <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/doppler-effect\/\">Doppler effect<\/a>:<\/strong> every version of the Doppler formula contains <em>v<\/em>, so an error in the speed of sound propagates straight into your predicted frequency shift.<\/li>\n<\/ul>\n\n<p>One contrast is worth holding onto. Sound needs a medium and creeps along at a few hundred metres per second, while <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/modern-physics\/speed-of-light\/\">light<\/a> needs none and travels at 299,792,458 m\/s \u2014 nearly 900,000 times faster. In a vacuum, the speed of sound is not slow. It simply does not exist.<\/p>\n\n<h2>Worked Problems<\/h2>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">Find the speed of sound in air at 25 \u00b0C using the linear approximation.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Use the everyday shortcut, v = 331.3 + 0.606 \u00d7 T, with T in \u00b0C.<\/p>\n<p>Step 2: Substitute T = 25 \u00b0C, giving v = 331.3 + 0.606 \u00d7 25.<\/p>\n<p>Step 3: 0.606 \u00d7 25 = 15.15, so v = 331.3 + 15.15 = 346.45 m\/s.<\/p>\n<p><strong>Answer: v = 346.5 m\/s (4 s.f.)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">You see a lightning flash and hear thunder 6.0 s later. The air is at 20 \u00b0C. How far away was the strike?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: The light arrives effectively instantly, so the 6.0 s is the sound&#8217;s travel time. Use d = v \u00d7 t.<\/p>\n<p>Step 2: At 20 \u00b0C, v = 343 m\/s, so d = 343 m\/s \u00d7 6.0 s.<\/p>\n<p>Step 3: d = 2058 m.<\/p>\n<p><strong>Answer: d = 2.1 km (2 s.f.)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">Use v = sqrt(\u03b3RT\/M) to find the speed of sound in dry air at 30 \u00b0C. Take \u03b3 = 1.40, R = 8.314 J\/(mol\u00b7K), M = 0.0290 kg\/mol.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Convert to absolute temperature: T = 30 + 273.15 = 303.15 K.<\/p>\n<p>Step 2: Numerator: \u03b3RT = 1.40 \u00d7 8.314 J\/(mol\u00b7K) \u00d7 303.15 K = 3528.5 J\/mol.<\/p>\n<p>Step 3: Divide by molar mass: 3528.5 J\/mol \u00f7 0.0290 kg\/mol = 121,674 m<sup>2<\/sup>\/s<sup>2<\/sup>.<\/p>\n<p>Step 4: Take the square root: v = sqrt(121,674) = 348.8 m\/s.<\/p>\n<p><strong>Answer: v = 349 m\/s (3 s.f.) \u2014 within 0.7 m\/s of the shortcut formula&#8217;s 349.5 m\/s<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">What is the wavelength of concert A (440 Hz) in air at 20 \u00b0C?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Use the wave relationship v = f\u03bb, rearranged to \u03bb = v\/f.<\/p>\n<p>Step 2: At 20 \u00b0C, v = 343 m\/s, so \u03bb = 343 m\/s \u00f7 440 Hz.<\/p>\n<p>Step 3: \u03bb = 0.7795 m.<\/p>\n<p><strong>Answer: \u03bb = 0.780 m (3 s.f.)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">Find the speed of sound in helium at 20 \u00b0C, taking \u03b3 = 1.67 and M = 0.00400 kg\/mol. How does it compare with air?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: T = 20 + 273.15 = 293.15 K.<\/p>\n<p>Step 2: \u03b3RT = 1.67 \u00d7 8.314 J\/(mol\u00b7K) \u00d7 293.15 K = 4070.2 J\/mol.<\/p>\n<p>Step 3: Divide by M: 4070.2 \u00f7 0.00400 = 1,017,551 m<sup>2<\/sup>\/s<sup>2<\/sup>; v = sqrt(1,017,551) = 1008.7 m\/s.<\/p>\n<p>Step 4: Compare with air: 1008.7 \u00f7 343 = 2.94.<\/p>\n<p><strong>Answer: v = 1009 m\/s, about 2.9 times the speed in air \u2014 the molar mass is roughly 7 times smaller<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">An airliner cruises at 250 m\/s at 11 km, where the standard atmosphere temperature is -56.5 \u00b0C. What is its Mach number? Take \u03b3 = 1.40, M = 0.0290 kg\/mol.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: T = -56.5 + 273.15 = 216.65 K.<\/p>\n<p>Step 2: \u03b3RT = 1.40 \u00d7 8.314 \u00d7 216.65 = 2521.7 J\/mol; divide by M: 2521.7 \u00f7 0.0290 = 86,956 m<sup>2<\/sup>\/s<sup>2<\/sup>.<\/p>\n<p>Step 3: Local speed of sound: v = sqrt(86,956) = 294.9 m\/s.<\/p>\n<p>Step 4: Mach number = aircraft speed \u00f7 local speed of sound = 250 \u00f7 294.9.<\/p>\n<p><strong>Answer: Mach 0.848 \u2014 the same 250 m\/s would be only Mach 0.73 at 20 \u00b0C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">Sound travels along a steel rail with Young&#039;s modulus E = 200 GPa and density \u03c1 = 7850 kg\/m^3. Find its speed, then find how much sooner a sound reaches you through 1.0 km of rail than through the air at 20 \u00b0C.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: For a thin solid rod, v = sqrt(E\/\u03c1).<\/p>\n<p>Step 2: v = sqrt(200 \u00d7 10<sup>9<\/sup> Pa \u00f7 7850 kg\/m<sup>3<\/sup>) = sqrt(2.548 \u00d7 10<sup>7<\/sup> m<sup>2<\/sup>\/s<sup>2<\/sup>) = 5048 m\/s.<\/p>\n<p>Step 3: Time through the rail: t = 1000 m \u00f7 5048 m\/s = 0.198 s.<\/p>\n<p>Step 4: Time through the air: t = 1000 m \u00f7 343 m\/s = 2.915 s.<\/p>\n<p>Step 5: Difference = 2.915 &#8211; 0.198 = 2.717 s.<\/p>\n<p><strong>Answer: v = 5050 m\/s in the rail; the sound arrives about 2.7 s earlier through the steel<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is the speed of sound in m\/s, km\/h and mph?<\/summary><div class=\"pf-faq-item-answer\">\nThe speed of sound in dry air at 20 \u00b0C is 343 m\/s, which is 1,235 km\/h or 767 mph. At 0 \u00b0C it drops to 331 m\/s (1,192 km\/h, 741 mph). Any quoted figure is meaningless without a stated temperature and medium, because both change the answer significantly.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does temperature change the speed of sound?<\/summary><div class=\"pf-faq-item-answer\">\nYes \u2014 temperature is the dominant factor in air. The speed rises with the square root of absolute temperature, working out at roughly 0.6 m\/s per degree Celsius near room temperature. Sound travels about 24 m\/s faster on a 40 \u00b0C day than at freezing point.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is sound faster in water or in air?<\/summary><div class=\"pf-faq-item-answer\">\nSound is far faster in water: about 1,482 m\/s in fresh water at 20 \u00b0C, compared with 343 m\/s in air. Water is roughly 800 times denser, which alone would slow sound down, but it is also around 15,000 times harder to compress. Stiffness wins.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does air pressure affect the speed of sound?<\/summary><div class=\"pf-faq-item-answer\">\nNo \u2014 not on its own. Raising the pressure of a gas at fixed temperature raises its density by the same proportion, so the two effects cancel exactly and the speed is unchanged. Sound is slower at high altitude because the air there is cold, not because it is thin.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why does helium make your voice sound higher?<\/summary><div class=\"pf-faq-item-answer\">\nSound travels about 2.9 times faster in helium than in air, because helium molecules are far lighter. Your vocal folds keep vibrating at almost their usual rate, but the resonant frequencies of your vocal tract shift sharply upwards, changing the timbre. The pitch you produce barely moves.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is Mach 1?<\/summary><div class=\"pf-faq-item-answer\">\nMach 1 is any speed equal to the local speed of sound, so it is not a fixed velocity. At sea level on a standard day it is about 340 m\/s; at 11 km, where the air sits near -56.5 \u00b0C, it falls to roughly 295 m\/s. Mach number equals object speed divided by local sound speed.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the speed of sound in a vacuum?<\/summary><div class=\"pf-faq-item-answer\">\nThere is none. Sound is a pressure wave that needs particles to pass the disturbance along, so with no medium there is nothing to carry it. This is the fundamental difference from light, which travels through a vacuum at 299,792,458 m\/s.\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>The speed of sound is about 343 m\/s in dry air at 20 degrees Celsius. Temperature, the gas itself and humidity all shift it &#8211; but air pressure does not.<\/p>\n","protected":false},"author":1,"featured_media":798,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-796","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-waves"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/796","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=796"}],"version-history":[{"count":7,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/796\/revisions"}],"predecessor-version":[{"id":1454,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/796\/revisions\/1454"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/798"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}