Physics › 🌊 Waves & Sound

Sound & Acoustics

Every voice, drumbeat, and clap of thunder is just air molecules jostling their neighbors in a chain reaction of push and pull.

High school
💡
The big idea: Sound is a mechanical wave — a traveling pattern of squeezed and stretched air (or water, or steel) that carries energy without carrying the air itself anywhere. Frequency decides the pitch you hear and amplitude decides the loudness, while the medium the wave travels through decides how fast it gets to your ear. Once you can picture the compressions and rarefactions rippling outward, echoes, resonance, and the limits of human hearing all become simple consequences of one wave.
🎯 By the end, you'll be able to
  • Explain how sound travels as a longitudinal wave of compressions and rarefactions through a medium.
  • Distinguish pitch (frequency) from loudness (amplitude) and connect each to what the ear actually perceives.
  • Use v = fλ and simple travel-time reasoning to calculate wavelength, distance, or time delay for a sound wave, including echoes.
  • Describe resonance and explain why some objects ring loudly when driven at their own natural frequency.
📎 You should already know
  • Introduction to Waves (wavelength, frequency, amplitude, period)
  • Rearranging and solving simple algebraic formulas
  • Units and unit conversion (meters, seconds, Hz)

The Wave You Can't See

Clap your hands right now. What just happened, physically? Your palms slammed together and shoved the air molecules between them outward. Those molecules crashed into their neighbors, which crashed into theirs, and so on — a ripple of "bunched-up" air raced outward in every direction until it jiggled the eardrums in your head. That jiggle is all a sound wave is: energy passed from molecule to molecule, with no single molecule traveling far at all.

Because sound needs molecules to shove, it needs a medium — air, water, wood, steel, anything with particles close enough to bump into each other. That's why there's no sound in the vacuum of space, no matter what the movies show.

🔑 Sound Is a Longitudinal Wave

In a longitudinal wave, the medium moves back and forth along the same line the wave travels, creating alternating regions of compression (molecules squeezed close) and rarefaction (molecules spread apart). Two properties of that wave map directly onto what you hear:

  • Pitch ↔ frequency — more compressions per second sounds higher.
  • Loudness ↔ amplitude — bigger compressions (more energy) sound louder.

A healthy young human ear typically picks up frequencies from about 20 Hz (a deep rumble) to 20,000 Hz (a shrill, almost painful hiss) — that range is called the audible range, and it shrinks a bit with age.

\[ v = f\lambda \]
The universal wave equation: speed equals frequency times wavelength. It works for sound exactly like it works for any other wave.
\[ v_{air} \approx 331 + 0.6\,T \]
Speed of sound in dry air, in m/s, where T is the temperature in degrees Celsius. Warmer air molecules move faster and pass the wave along more quickly — that's why sound travels at about 343 m/s at a comfortable 20°C, but noticeably slower on a freezing day.
🎮 Interactive: Sound Waves in Motion LIVE
Drag the frequency and amplitude sliders and watch the compressions and rarefactions change — notice how frequency squeezes the ripples closer together while amplitude makes them bigger, not faster.
📝 Worked example: A tuning fork used to tune a guitar's A string vibrates at 440 Hz. If the speed of sound in the room is 343 m/s, what is the wavelength of the sound wave it produces?
  1. Start with v = fλ and rearrange to solve for wavelength: λ = v / f.
  2. Plug in the numbers: λ = 343 m/s ÷ 440 Hz.
  3. λ = 0.7795 m, which rounds to about 0.78 m — a little under 80 cm.
✓ λ ≈ 0.78 m (about 78 cm)

Echoes and Resonance: Sound Meeting Itself

An echo is just a reflection: sound bounces off a hard, distant surface and comes back to your ear a little later. Because you now know the speed of sound, a stopwatch and a cliff face are all you need to measure distance — which is exactly how early scientists first pinned down how fast sound actually travels.

Resonance is a different but related idea: every object has a natural frequency it "likes" to vibrate at, set by its size, shape, and stiffness. Drive it with a periodic push at exactly that frequency — a singer's sustained note driving a wine glass, a child's swing pushed in rhythm with its own back-and-forth, an engine part vibrating at a troublesome RPM — and the vibrations build up on each other, growing far larger than a single gentle push should allow. That's why the right note (not just a loud one) is what can crack a wine glass: it's frequency-matching, not raw volume, that makes resonance work.

📝 Worked example: You stand facing a cliff and shout. The echo comes back exactly 1.00 second later. If the speed of sound is 343 m/s, how far away is the cliff?
  1. The 1.00 s covers the sound's full round trip: out to the cliff AND back to you.
  2. Total distance traveled = speed × time = 343 m/s × 1.00 s = 343 m.
  3. That 343 m is there-and-back, so the one-way distance to the cliff is 343 m ÷ 2 = 171.5 m.
✓ The cliff is about 171.5 m away.
⚠️ Common Mixups
  • Pitch ≠ loudness. A whisper and a shout can be the exact same pitch (frequency) while differing hugely in loudness (amplitude) — they're independent dials.
  • No medium, no sound. Sound cannot travel through a vacuum — space really is silent, whatever the sci-fi soundtrack says.
  • Decibels aren't a simple ruler. The decibel scale for loudness is logarithmic, so a jump of +10 dB means roughly ten times more sound energy, not just "a bit louder."
  • Resonance needs the right frequency, not just volume. Driving an object with sound (or any periodic push) doesn't cause resonance unless the driving frequency matches its natural frequency.

Check your understanding

1. What kind of wave is sound as it travels through air?
Sound consists of compressions and rarefactions where air molecules move back and forth along the same direction the wave travels — the defining feature of a longitudinal wave.
2. A sound wave has a frequency of 500 Hz and travels at 340 m/s in air. What is its wavelength?
Using λ = v / f: λ = 340 m/s ÷ 500 Hz = 0.68 m.
3. A guitarist wants to make a string sound higher-pitched without changing how loud it is. What should change?
Pitch is determined by frequency, not amplitude. Raising the vibration frequency (e.g., by tightening the string or pressing a shorter length) raises the pitch while loudness (amplitude) can stay the same.
4. Sound generally travels faster through steel than through air. Why?
Speed of sound depends on how quickly a medium's particles can pass a vibration to their neighbors. Steel's stiff, tightly bonded structure transmits that push-pull much faster than the more loosely spaced, easily compressed molecules in air.
✅ Key takeaways
  • Sound is a longitudinal mechanical wave: molecules compress and spread out along the direction of travel, and it needs a medium — no sound in a vacuum.
  • Pitch is what your ear hears from frequency; loudness is what it hears from amplitude — they're independent properties.
  • Wave speed, frequency, and wavelength are linked by v = fλ, and the speed of sound in air rises with temperature (≈343 m/s at 20°C).
  • Echoes are reflected sound you can time to measure distance, while resonance happens when a periodic push matches an object's own natural frequency, building up large vibrations.