🎵 Music & Wave Physics

Sound Waves · Frequency · Harmonics · Music Theory · Synthesizer

〰️ Wave Visualizer

Frequency 4 Hz
Amplitude 60%

🔊 Play a Tone

Frequency 440 Hz (A4)
Waveform

📋 Wave Properties

speed = frequency × wavelength
v = f × λ
Frequency (f) — waves per second, measured in Hz. Determines pitch.
Amplitude (A) — height of wave from center. Determines loudness.
Wavelength (λ) — distance between peaks.
Period (T) — time for one full wave: T = 1/f
Speed of sound — ~343 m/s in air at 20°C

👂 Human Hearing

Range: 20 Hz – 20,000 Hz
Most sensitive: 1,000–4,000 Hz
Ultrasound: >20,000 Hz (bats, sonar)
Infrasound: <20 Hz (elephants, earthquakes)
The cochlea in your ear separates frequencies like a Fourier transform!

🔉 Decibels (dB)

0 dB — threshold of hearing
30 dB — whisper
60 dB — normal conversation
85 dB — hearing damage risk
120 dB — rock concert
140 dB — pain threshold
+6 dB ≈ double the amplitude
+10 dB ≈ perceived twice as loud

📊 Waveform Shapes

Different waveforms produce different timbres (tone quality). A synthesizer creates all of these electronically.

🎵 Waveform Guide

Sine — pure tone, single frequency. Smooth, mellow. Used in tuning forks, flutes.
Square — odd harmonics only. Hollow, buzzy. Found in old video game music, clarinets.
Sawtooth — all harmonics. Bright, buzzy. Violins, brass instruments, synthesizer leads.
Triangle — odd harmonics, weaker. Soft, nasal. Similar to sine but with slight edge.

🔬 Fourier's Insight

Any periodic waveform can be built from a sum of sine waves at different frequencies. This is the Fourier Series — the foundation of audio compression, MP3s, and signal processing.

f(t) = a₀ + Σ[aₙcos(nωt) + bₙsin(nωt)]

🎶 Harmonic Series Builder

Add harmonics (overtones) to a fundamental frequency. Each harmonic is a multiple of the fundamental.

Fundamental 3 Hz

📋 Harmonic Facts

The fundamental frequency (1st harmonic) determines the pitch.
The timbre (tone color) is determined by the mix of harmonics — why a piano and flute sound different at the same pitch.
Harmonic ratios create musical intervals:
2:1 = octave
3:2 = perfect fifth
4:3 = perfect fourth
5:4 = major third

🎸 Instruments & Harmonics

🎻 Violin/guitar — rich harmonics from string vibration modes
🎺 Trumpet — column of air vibrates in harmonics
🎹 Piano — struck string has inharmonic partials
🎤 Human voice — formants (resonances in throat/mouth) shape harmonics
Organ pipes are tuned to specific harmonics of their resonant cavity.

🎹 Interactive Piano — Play Notes

Click any key to hear that note. Each key's frequency is calculated from A4 = 440 Hz using equal temperament.

🎼 Note Frequencies

🎵 Musical Scales

Chromatic — all 12 notes per octave (equal semitones)
Major — C D E F G A B C (W W H W W W H)
Minor — A B C D E F G A (W H W W H W W)
Pentatonic — 5-note scale (common in folk/rock)
Blues — pentatonic + ♭5 "blue note"
W = whole step (2 semitones), H = half step (1 semitone)

📐 Equal Temperament

Each semitone = multiply by the 12th root of 2 (≈1.05946).

f(n) = 440 × 2^(n/12)
n = semitones from A4

A4 = 440 Hz, A5 = 880 Hz, A3 = 220 Hz. Each octave doubles the frequency.

Sound = pressure waves

Sound is a longitudinal wave — molecules in air compress and rarefy (spread out) as the wave passes. It needs a medium (air, water, solid) to travel. In the vacuum of space there is no sound.

Key terms
  • Frequency (Hz) — vibrations per second; determines pitch
  • Amplitude — wave height; determines loudness
  • Wavelength (λ) — distance between peaks
  • Timbre — tone quality; the harmonic mix of a sound
  • Resonance — when a frequency matches an object's natural vibration
  • Doppler Effect — frequency shift when source/observer move toward/away
  • Interference — two waves combining; constructive or destructive
Pythagoras and music

Pythagoras discovered (around 550 BC) that musical intervals that sound pleasing correspond to simple whole-number frequency ratios: octave = 2:1, fifth = 3:2, fourth = 4:3. This connects music to mathematics in a profound way.

🎯 Try this challenge

A musical note 'A' vibrates at 440 Hz. Each octave doubles the frequency. What frequency is A in the next octave up? What about two octaves up? How many times louder (in dB) does doubling the amplitude make a sound?

Continue Learning
Electromagnetic Spectrum