{"id":801,"date":"2026-08-12T11:27:34","date_gmt":"2026-08-12T11:27:34","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=801"},"modified":"2026-08-24T13:03:42","modified_gmt":"2026-08-24T13:03:42","slug":"amplitude-physics","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/amplitude-physics\/","title":{"rendered":"What Is Amplitude in Physics?"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\n\nAmplitude is the maximum displacement of a particle from its rest (equilibrium) position as a wave or oscillation passes through it. Its symbol is A and its SI unit is the metre. Amplitude sets how much energy the wave carries \u2014 energy is proportional to amplitude squared \u2014 but it never changes the wave&#8217;s frequency, wavelength or speed.\n\n<\/p><\/div>\n\n<p>Turn the volume knob up and the song does not change key. The notes stay exactly where they were; they just hit you harder. What you have changed is amplitude \u2014 how far the speaker cone, and then the air, swings away from rest on every cycle.<\/p>\n\n<p>That one quantity decides whether an earthquake rattles a window or flattens a street, whether a radio signal is readable or lost in hiss, and whether a guitar string whispers or rings. Learn to read it off a graph and a surprising amount of wave physics stops being guesswork.<\/p>\n\n<h2>What Is Amplitude in Physics?<\/h2>\n\n<p>Amplitude is the maximum distance a point moves away from its rest position while oscillating, measured from the middle of the motion outwards. It is a magnitude, so it is always positive, and it is written as <strong>A<\/strong>.<\/p>\n\n<p>Picture a buoy bobbing on a swell. The water surface has a level it would settle at if the sea were flat \u2014 that is the rest position. Amplitude is how far above that level the buoy rises at the top of its climb.<\/p>\n\n<p>Because amplitude is a displacement, its SI unit is the <strong>metre (m)<\/strong>. In practice you will meet it in centimetres or millimetres for laboratory work, and in other units whenever something other than position is oscillating: pascals for the pressure swing of a sound wave, volts for an AC signal, amperes for an alternating current.<\/p>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/amplitude-physics-transverse-wave-measured-rest-position.webp\" width=\"1400\" height=\"846\" alt=\"Diagram of a transverse wave showing amplitude measured from the rest position to a crest, peak-to-peak displacement equal to twice the amplitude, and wavelength measured between successive crests\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:14px;font-style:italic;color:#1F2E47;margin-top:8px;\">Amplitude is the rest-to-crest distance. The full crest-to-trough span is peak-to-peak, which equals 2A.<\/p>\n\n<h3>Amplitude Is Measured From the Middle, Not End to End<\/h3>\n\n<p>Here is the single most common student slip: measuring from crest all the way down to trough and calling that the amplitude. That span is the <strong>peak-to-peak<\/strong> value, and it is twice too big.<\/p>\n\n<p>Halve it and you have the amplitude. Oscilloscopes and signal generators almost always quote peak-to-peak, so this conversion is one you will do constantly in a practical.<\/p>\n\n<h2>The Amplitude Formula and What Each Symbol Means<\/h2>\n\n<p>There is no standalone &#8220;amplitude equation&#8221; \u2014 amplitude is the constant <strong>A<\/strong> that sits in front of the sine in the displacement equation of any simple harmonic oscillation.<\/p>\n\n<div class=\"pf-formula\">y = A sin(\u03c9t + \u03c6)<\/div>\n\n<ul>\n<li><strong>y<\/strong> \u2014 displacement of the particle at time <em>t<\/em> \u2014 metre (m)<\/li>\n<li><strong>A<\/strong> \u2014 amplitude, the largest value <em>y<\/em> ever reaches \u2014 metre (m)<\/li>\n<li><strong>\u03c9<\/strong> \u2014 angular frequency, where \u03c9 = 2\u03c0f \u2014 radian per second (rad\/s)<\/li>\n<li><strong>t<\/strong> \u2014 time \u2014 second (s)<\/li>\n<li><strong>\u03c6<\/strong> \u2014 phase constant, which fixes where in the cycle the motion starts \u2014 radian (rad)<\/li>\n<\/ul>\n\n<p>Because sin never exceeds 1, <em>y<\/em> never exceeds <em>A<\/em>. That is the whole meaning of the symbol: A is the ceiling on the displacement.<\/p>\n\n<p>When you only have a graph or a trace to work from, use the peak and trough readings instead.<\/p>\n\n<div class=\"pf-formula\">A = (y_max &#8211; y_min) \/ 2<\/div>\n\n<p>Two further results follow straight from the displacement equation, and both are worth memorising because examiners lean on them heavily.<\/p>\n\n<div class=\"pf-formula\">v_max = A\u03c9   \u00b7   a_max = A\u03c9<sup>2<\/sup><\/div>\n\n<p>So a bigger amplitude means a faster maximum speed and a fiercer maximum acceleration \u2014 at exactly the same frequency. If you would rather feed in numbers than rearrange by hand, our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/simple-harmonic-motion\">Simple Harmonic Motion Calculator<\/a> takes an amplitude and a frequency and returns \u03c9, the period and both maxima with the working shown.<\/p>\n\n<p>Try it yourself below: drag the amplitude slider and watch two things at once \u2014 the total energy readout climbing steeply, and the period sitting completely still.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Simple Harmonic Motion Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:560px}@media(max-width:760px){.pf-sim-frame{height:840px}}<\/style><iframe src=\"\/labs\/simple-harmonic-motion.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>How Amplitude Carries a Wave&#8217;s Energy<\/h2>\n\n<p>Amplitude carries the energy, and it does so as a square: the energy of an oscillation is proportional to <strong>A<sup>2<\/sup><\/strong>, so doubling the amplitude multiplies the energy by four.<\/p>\n\n<p>The cleanest way to see this is a mass on a spring at the instant it reaches its furthest point. Everything is momentarily stationary, so all the energy is stored as <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/elastic-potential-energy\/\">elastic potential energy<\/a> in the spring.<\/p>\n\n<div class=\"pf-formula\">E = (1\/2)\u00b7k\u00b7A<sup>2<\/sup><\/div>\n\n<ul>\n<li><strong>E<\/strong> \u2014 total energy of the oscillation \u2014 joule (J)<\/li>\n<li><strong>k<\/strong> \u2014 spring constant \u2014 newton per metre (N\/m)<\/li>\n<li><strong>A<\/strong> \u2014 amplitude \u2014 metre (m)<\/li>\n<\/ul>\n\n<p>The same squaring shows up for travelling waves. At a fixed frequency, the intensity a wave delivers is proportional to the square of its amplitude \u2014 which is why NASA&#8217;s own primer describes <a href=\"https:\/\/science.nasa.gov\/learn\/basics-of-space-flight\/chapter6-2\/\" target=\"_blank\" rel=\"noopener\">amplitude as the strength or intensity of a wave<\/a>, the direct analogue of a sound&#8217;s loudness.<\/p>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/amplitude-physics-tripling-wave-multiplies-energy-nine.webp\" width=\"1400\" height=\"910\" alt=\"Diagram showing that tripling the amplitude of a wave multiplies its energy by nine, because energy is proportional to amplitude squared\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:700px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:14px;font-style:italic;color:#1F2E47;margin-top:8px;\">Because energy depends on A<sup>2<\/sup>, modest-looking amplitude increases cost a great deal of energy.<\/p>\n\n<p>This is why loudness is so expensive. To make a speaker sound twice as intense you must push four times the energy through it \u2014 and because our ears respond logarithmically, that only buys you about 6 dB on the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/decibel-formula\/\">decibel scale<\/a>.<\/p>\n\n<h2>Amplitude vs Wavelength, Frequency and Period<\/h2>\n\n<p>Amplitude measures how far the medium moves; wavelength, frequency and period measure how the wave repeats \u2014 and changing the amplitude leaves every one of the others untouched.<\/p>\n\n<p>It helps to think of the two directions on the graph. Amplitude is measured up the page. Wavelength is measured along it.<\/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;\">Quantity<\/th>\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;\">SI unit<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">What it measures<\/th>\n<th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Does changing amplitude alter it?<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Amplitude<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">A<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">metre (m)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Maximum displacement from rest<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">\u2014<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Wavelength<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">\u03bb<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">metre (m)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Distance between successive identical points<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>No<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Frequency<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">f<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">hertz (Hz)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Cycles passing a point each second<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>No<\/strong><\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Period<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">T<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">second (s)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Time for one complete cycle<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>No<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Wave speed<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">v<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">metre per second (m\/s)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">How fast the disturbance travels<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>No<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>That column of &#8220;No&#8221; is the point of the whole table. Amplitude lives on its own axis, independent of everything in the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/frequency-formula\/\">frequency and period relationship<\/a>.<\/p>\n\n<h2>How Do You Find Amplitude From a Graph?<\/h2>\n\n<p>To find amplitude from a graph, read off the highest and lowest values, subtract them, and halve the result. Three steps, no algebra.<\/p>\n\n<ol>\n<li>Find the rest position \u2014 the horizontal line the curve is symmetrical about, which is not always at zero.<\/li>\n<li>Read the peak value and the trough value, keeping the units the axis is labelled in.<\/li>\n<li>Apply A = (y<sub>max<\/sub> &#8211; y<sub>min<\/sub>) \/ 2, then convert to metres if the question wants SI units.<\/li>\n<\/ol>\n\n<p>Watch the axis. A trace showing 8.0 cm from crest to trough has an amplitude of 4.0 cm, which is 0.040 m \u2014 and dropping that factor of two is the mistake that costs the most marks in wave questions.<\/p>\n\n<h3>Peak, Peak-to-Peak and RMS<\/h3>\n\n<p>Electronics adds a third measure you will meet in AC work. The root-mean-square value is a kind of effective average, and for a pure sine wave it is fixed at A \/ sqrt(2), roughly 0.707A.<\/p>\n\n<p>So a mains supply quoted as 230 V RMS actually swings to a peak amplitude of about 325 V. All three numbers describe the same wave \u2014 they are just different ways of summarising its size.<\/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\/Tektronix_Oscilloscope_475A.jpg\"\n\n       alt=\"Oscilloscope trace of a sine wave showing the amplitude and peak-to-peak displacement\"\n\n       loading=\"lazy\"\n\n       style=\"width:100%;height:auto;border-radius:4px;\" width=\"1920\" height=\"1013\">\n\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">An oscilloscope shows peak-to-peak height directly; halve it to get the amplitude.<\/figcaption>\n\n<\/figure>\n\n<h2>Real-World Examples of Amplitude<\/h2>\n\n<p>Amplitude is not a textbook abstraction. It is the quantity engineers actually design around.<\/p>\n\n<p><strong>Sound and loudness.<\/strong> The amplitude of the pressure swing in the air is what your eardrum responds to. A whisper and a shout can share the same pitch and travel at the same 343 m\/s, yet differ by a factor of thousands in amplitude.<\/p>\n\n<p><strong>Earthquakes.<\/strong> Seismographs record ground-motion amplitude, and magnitude scales are built on its logarithm. Each whole step up the scale means roughly ten times the ground-motion amplitude and about 32 times the energy released \u2014 which is why a magnitude 7 is a different category of event from a magnitude 6, not merely a worse one.<\/p>\n\n<p><strong>Radio broadcasting.<\/strong> AM stands for amplitude modulation: the audio signal is encoded by varying the amplitude of a carrier wave while its frequency stays locked. FM does the opposite. That single design choice is why AM is more vulnerable to crackle \u2014 lightning and motors add amplitude noise.<\/p>\n\n<p><strong>Gravitational waves.<\/strong> These are the smallest amplitudes ever measured. A passing wave with strain around 10<sup>-21<\/sup> changes the length of LIGO&#8217;s 4 km arms by about 4 \u00d7 10<sup>-18<\/sup> m. Amplitude also identifies the source: a steadily spinning neutron star should emit <a href=\"https:\/\/www.ligo.caltech.edu\/page\/gw-sources\" target=\"_blank\" rel=\"noopener\">a continuous signal of constant frequency and amplitude<\/a>, unlike the rising chirp of a merger.<\/p>\n\n<p><strong>Musical instruments.<\/strong> Pluck a guitar string harder and you increase the amplitude of its vibration, not its frequency. The note is identical; only the volume changes \u2014 which is exactly why a guitarist can play the same chord loudly or softly.<\/p>\n\n<h2>4 Common Misconceptions About Amplitude<\/h2>\n\n<p>These four errors account for most of the marks lost on amplitude questions. Each one is worth ten seconds of checking.<\/p>\n\n<h3>Myth 1: Bigger amplitude means a higher pitch<\/h3>\n\n<p>It does not. Amplitude and frequency are independent quantities, so a louder note is not a higher note. For a mass on a spring the frequency is fixed by the spring constant and the mass, and no amount of extra amplitude will shift it.<\/p>\n\n<h3>Myth 2: Amplitude is the distance from crest to trough<\/h3>\n\n<p>That distance is peak-to-peak, and it equals 2A. Amplitude is measured from the rest position to one extreme only, so a wave with a 6 cm crest-to-trough span has an amplitude of 3 cm.<\/p>\n\n<h3>Myth 3: A bigger wave travels faster<\/h3>\n\n<p>For ordinary waves, speed is a property of the medium, not of the wave. Sound crosses a room at the same speed whether it is loud or quiet. Only at extreme amplitudes \u2014 a blast wave from an explosion \u2014 does the disturbance genuinely outrun the normal speed of sound.<\/p>\n\n<h3>Myth 4: Doubling the amplitude doubles the energy<\/h3>\n\n<p>It quadruples it. Energy depends on A<sup>2<\/sup>, so a factor of two in amplitude is a factor of four in energy. Perceived loudness rises by only about 6 dB, which is a further reminder that our ears and the physics are measuring different things.<\/p>\n\n<h2>How Amplitude Connects to SHM, Damping and Resonance<\/h2>\n\n<p>Amplitude is the one variable in <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/simple-harmonic-motion\/\">simple harmonic motion<\/a> you can set freely without disturbing anything else. Fix the mass and the spring, and the frequency is decided; the amplitude is still yours to choose.<\/p>\n\n<p>This independence has a name: isochronism. It is the reason pendulum clocks work at all, and why <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/pendulum-period-formula\/\">the period of a simple pendulum<\/a> depends on length and gravity but not on how far you pull it back.<\/p>\n\n<p>The small-angle caveat matters, though. At a swing of 20\u00b0 the true period is already about 0.8% longer than the simple formula predicts, and by 45\u00b0 the error has grown to nearly 4%.<\/p>\n\n<h3>Damping Eats Amplitude, Not Frequency<\/h3>\n\n<p>Real oscillators lose energy to friction and air resistance, so their amplitude decays \u2014 typically exponentially \u2014 while the frequency barely shifts. A struck tuning fork holds its note and simply fades.<\/p>\n\n<p>Because energy goes as A<sup>2<\/sup>, that fade is steeper than it looks. An amplitude that has fallen to half its starting value has already given up three quarters of its energy.<\/p>\n\n<h3>Resonance Is an Amplitude Phenomenon<\/h3>\n\n<p>Drive an oscillator at its natural frequency and the amplitude builds dramatically, because each push arrives in step with the motion. This is the mechanism behind a wine glass shattering to a sung note and behind the vibration limits engineers design bridges to avoid.<\/p>\n\n<p>Note what resonance actually does: it does not change the frequency you are driving at. It changes how large a response that frequency produces \u2014 and amplitude, in <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/transverse-vs-longitudinal-waves\/\">both transverse and longitudinal waves<\/a>, is the size of that response.<\/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\">An oscilloscope trace of a sound wave shows a total vertical swing of 8.0 cm from crest to trough. What is the amplitude in metres?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: The crest-to-trough span is the peak-to-peak value, so A = (y<sub>max<\/sub> &#8211; y<sub>min<\/sub>) \/ 2.<\/p>\n<p>Step 2: Substitute: A = 8.0 cm \/ 2 = 4.0 cm.<\/p>\n<p>Step 3: Convert to SI units: 4.0 cm = 4.0 \u00d7 10<sup>-2<\/sup> m = 0.040 m.<\/p>\n<p><strong>Answer: A = 0.040 m (2 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\">A particle oscillates according to y = 0.30 sin(50\u03c0t), with y in metres and t in seconds. State the amplitude, angular frequency, frequency and period.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Compare with the standard form y = A sin(\u03c9t), so A is the coefficient of the sine and \u03c9 is the coefficient of t.<\/p>\n<p>Step 2: Read them off: A = 0.30 m and \u03c9 = 50\u03c0 rad\/s = 157.08 rad\/s.<\/p>\n<p>Step 3: Convert: f = \u03c9 \/ 2\u03c0 = 50\u03c0 \/ 2\u03c0 = 25 Hz, and T = 1 \/ f = 1 \/ 25 = 0.040 s.<\/p>\n<p><strong>Answer: A = 0.30 m, \u03c9 = 157 rad\/s, f = 25 Hz, T = 0.040 s<\/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\">A mass on a spring has amplitude 0.15 m and frequency 2.0 Hz, and starts from the rest position moving upwards. Find its displacement at t = 0.10 s.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Starting at the rest position means \u03c6 = 0, so y = A sin(\u03c9t) with \u03c9 = 2\u03c0f.<\/p>\n<p>Step 2: \u03c9 = 2\u03c0 \u00d7 2.0 Hz = 12.566 rad\/s, so \u03c9t = 12.566 rad\/s \u00d7 0.10 s = 1.2566 rad.<\/p>\n<p>Step 3: y = 0.15 m \u00d7 sin(1.2566 rad) = 0.15 m \u00d7 0.9511 = 0.1427 m.<\/p>\n<p><strong>Answer: y = 0.14 m (2 s.f.)<\/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\">A spring of constant k = 40 N\/m oscillates with amplitude 0.12 m. Find the total energy. Then find the new total energy if the amplitude is doubled to 0.24 m.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: All the energy is elastic potential energy at maximum displacement, so E = (1\/2)\u00b7k\u00b7A<sup>2<\/sup>.<\/p>\n<p>Step 2: E = 0.5 \u00d7 40 N\/m \u00d7 (0.12 m)<sup>2<\/sup> = 0.5 \u00d7 40 \u00d7 0.0144 m<sup>2<\/sup> = 0.288 J.<\/p>\n<p>Step 3: With A = 0.24 m: E = 0.5 \u00d7 40 N\/m \u00d7 (0.24 m)<sup>2<\/sup> = 0.5 \u00d7 40 \u00d7 0.0576 m<sup>2<\/sup> = 1.152 J.<\/p>\n<p>Step 4: Check the ratio: 1.152 J \/ 0.288 J = 4.00, exactly as A<sup>2<\/sup> predicts for a doubling.<\/p>\n<p><strong>Answer: E = 0.288 J, rising to 1.15 J \u2014 four times larger<\/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\">A point on a vibrating machine part moves in SHM with amplitude 0.050 m at 3.0 Hz. Find its maximum speed and maximum acceleration.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Use v<sub>max<\/sub> = A\u03c9 and a<sub>max<\/sub> = A\u03c9<sup>2<\/sup>, with \u03c9 = 2\u03c0f.<\/p>\n<p>Step 2: \u03c9 = 2\u03c0 \u00d7 3.0 Hz = 18.850 rad\/s.<\/p>\n<p>Step 3: v<sub>max<\/sub> = 0.050 m \u00d7 18.850 rad\/s = 0.9425 m\/s.<\/p>\n<p>Step 4: a<sub>max<\/sub> = 0.050 m \u00d7 (18.850 rad\/s)<sup>2<\/sup> = 0.050 \u00d7 355.3 = 17.77 m\/s<sup>2<\/sup>.<\/p>\n<p><strong>Answer: v_max = 0.94 m\/s, a_max = 18 m\/s<sup>2<\/sup> (2 s.f.)<\/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\">The amplitude of a sound wave is increased by a factor of 3 at constant frequency. By how many decibels does the sound level rise?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: At a fixed frequency, intensity is proportional to amplitude squared, so tripling A multiplies the intensity by 3<sup>2<\/sup> = 9.<\/p>\n<p>Step 2: The change in sound level is \u0394L = 10 \u00b7 log10(I<sub>2<\/sub> \/ I<sub>1<\/sub>) = 10 \u00b7 log10(9).<\/p>\n<p>Step 3: log10(9) = 0.9542, so \u0394L = 10 \u00d7 0.9542 = 9.542 dB.<\/p>\n<p><strong>Answer: The level rises by about 9.5 dB<\/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\">A damped pendulum loses 10% of its amplitude on each complete swing. After 5 swings, what fraction of the original amplitude remains, and what fraction of the original energy?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Each swing multiplies the amplitude by 0.90, so after n swings A \/ A<sub>0<\/sub> = (0.90)<sup>n<\/sup>.<\/p>\n<p>Step 2: After 5 swings: A \/ A<sub>0<\/sub> = (0.90)<sup>5<\/sup> = 0.5905, which is 59.0% of the original amplitude.<\/p>\n<p>Step 3: Energy is proportional to A<sup>2<\/sup>, so E \/ E<sub>0<\/sub> = (0.5905)<sup>2<\/sup> = 0.3487.<\/p>\n<p>Step 4: Sanity check: the amplitude has roughly halved, and energy should therefore fall to roughly a quarter \u2014 0.35 is the right order.<\/p>\n<p><strong>Answer: About 59% of the amplitude remains, but only about 35% of the energy<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is the SI unit of amplitude?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe SI unit of amplitude is the metre (m), because amplitude is a displacement. You will also see it quoted in the unit of whatever quantity is oscillating: pascals for the pressure amplitude of a sound wave, volts for an AC voltage, amperes for an alternating current. The unit always matches the thing that is swinging.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does amplitude affect frequency?<\/summary><div class=\"pf-faq-item-answer\">\n\nNo \u2014 amplitude and frequency are completely independent. Changing how far an oscillator swings does not change how often it swings. A mass on a spring has its frequency fixed by the spring constant and the mass; a pendulum by its length and gravity. This is why turning up a speaker makes a note louder but never higher.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the difference between amplitude and wavelength?<\/summary><div class=\"pf-faq-item-answer\">\n\nAmplitude is the maximum displacement from the rest position, measured across the wave, while wavelength is the distance between two identical points on successive cycles, measured along the wave. Amplitude tells you how much energy the wave carries. Wavelength, combined with frequency, tells you how fast it travels. They are perpendicular measurements on the same graph.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is peak-to-peak amplitude?<\/summary><div class=\"pf-faq-item-answer\">\n\nPeak-to-peak amplitude is the full distance from the highest point of an oscillation to the lowest, which is exactly twice the amplitude. Oscilloscopes and signal generators normally quote peak-to-peak because it is the easiest span to read off a screen. To convert, simply halve it: A = (y_max &#8211; y_min) \/ 2.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does amplitude affect the speed of a wave?<\/summary><div class=\"pf-faq-item-answer\">\n\nNo \u2014 for ordinary waves the speed is set by the medium, not by the amplitude. A loud sound and a quiet sound both travel at about 343 m\/s in air at 20 \u00b0C. Only at extreme amplitudes, such as the blast wave from an explosion, does the disturbance travel faster than the normal speed of sound.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why does amplitude decrease with distance from the source?<\/summary><div class=\"pf-faq-item-answer\">\n\nAmplitude falls with distance because the wave&#8217;s energy spreads over an ever-larger area, and because the medium absorbs some of it. For a source radiating equally in all directions, intensity falls as 1 \/ r<sup>2<\/sup>, and since intensity is proportional to amplitude squared, amplitude falls as 1 \/ r. Damping in the medium removes further energy on top of that.\n\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>Amplitude is the maximum displacement of a particle from its rest position as a wave passes through it. This guide covers the formula, the SI unit, how to read amplitude off a graph, seven worked problems, and why doubling amplitude quadruples the energy.<\/p>\n","protected":false},"author":1,"featured_media":802,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-801","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\/801","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=801"}],"version-history":[{"count":7,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/801\/revisions"}],"predecessor-version":[{"id":1451,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/801\/revisions\/1451"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/802"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}