Sound laboratory
Hear sound and look inside it. Change one thing at a time and compare the result.
Here, plots are part of the experiments. The Physics button hides supplementary explanations, not the laboratory tools.
Theory
How to read sound
Frequency can move smoothly. The nearby name identifies the nearest piano note; it does not round the sound itself.
One semitone is 100 cents. Minus means below the nearest note; plus means above. The scale has 0 in the centre and −50 / +50 cents at the edges.
Green means within 5 cents of the nearest note, amber within 20 and red farther away. This is distance from 12-tone equal temperament, not a score for hearing or musical ability.
The wave’s vertical axis is relative signal displacement. An amplitude of 1 ranges from −1 to +1 relative units. These units are not hertz, decibels or measured air pressure.
Practice
What vibrates?
A source pushes the air next to it. Compression travels onward while the air particles move around their resting positions.
Run the experiment or move the slider step by step.
Why does this happen?
This is a schematic, one-dimensional longitudinal wave. Dots represent small volumes of air, not individual molecules; sizes and counts are not to scale. The sound is 220 Hz and the diagram runs 220 times slower. The dots move along the direction of travel instead of travelling with the wave.
Higher does not mean louder
Frequency counts vibrations per second. Amplitude describes how large the oscillation is.
Change frequency and amplitude separately. What changes when you listen?
A40 cents
Nearest note frequency: Hz
Why does this happen?
The graph always spans the same 10 milliseconds. More closely spaced oscillations mean a higher frequency. Amplitude changes the height of the wave without changing the number of oscillations. Perceived loudness also depends on frequency, timbre and the listener.
Two waves meet
At every instant we add the waves’ displacements. They sometimes reinforce one another and sometimes partly cancel.
Enable the third wave and build a different combined signal.
Nearest notes:
This nearest-note set does not form a standard triad.
Names refer to the nearest notes; the chosen frequencies are not snapped. ♯ / ♭ are two names for one pitch.
Why does this happen?
All curves share a 0–10 ms time scale and a zero phase origin. The vertical axis is relative displacement from −3 to +3 arbitrary units; each component has an amplitude of at most 1. Dashes identify components; the thick line is their sum. Intersections alone do not explain consonance.
Beats: almost the same pitch
Two nearby frequencies repeatedly reinforce and weaken each other. Closer frequencies produce slower beats.
Compare 440 and 442 Hz. Then try tuning the second sound.
A40 cents
A4+7.9 cents
Nearest note frequency: Hz
440 Hz + Hz · Beats per second:
Why does this happen?
With equal amplitudes, beat frequency is the difference between the two frequencies. The 440/442 Hz pair produces two amplitude maxima per second. The upper graph shows real fast oscillations over 10 ms; the lower graph shows the absolute amplitude envelope over 2 seconds. This is not a graph of perceived loudness.
Overtones change timbre
Add frequencies two, three or more times the fundamental. Changing their weights changes the waveform and the colour of the sound.
Add harmonics and compare the sound. Bars show how much of each harmonic is in the mixture.
A3
A3
A4
E5
A5
C♯6 / D♭6
E6
Why does this happen?
The first six harmonics are multiples of the fundamental. The first is the fundamental itself; the others are overtones. Every phase starts at zero. This spectrum is calculated from the chosen amplitudes: it is not a microphone recording or an input analyser. We are not imitating a real instrument.
One interval, two tunings
Pure tuning uses simple frequency ratios. Equal temperament divides the octave into 12 equal frequency ratios.
Choose an interval, then switch tunings and listen to the pair.
Frequency ratio: · 220 Hz + Hz
A30 cents
E4+2 cents
Nearest note frequency: Hz
Pure ratios Hz
12 equal semitones Hz
Pure relative to equal temperament cents relative to 12 equal semitones
Why does this happen?
This equal-temperament model uses 2^(n/12), where n is the number of semitones. For example, a pure fifth is 3/2 and an equal-tempered fifth is 2^(7/12): close, but different. The 2/1 octave matches in both tunings. This compares two models; neither is always the better tuning.
Games
Tune the sound
Make the beats as slow as possible. Aim for a steady sound.
Reference: 440 Hz. The second frequency is revealed after a successful check.
Tuned:
You can also follow the graph’s pulses. The count lasts only while this page is open.
Model: pure sine waves, all starting at zero phase. Relative amplitudes are shown before common output-level scaling; the attack and decay envelope is omitted. Amplitude is not perceived loudness.
Sources and model boundaries
Model: pure sine waves, all starting at zero phase. Relative amplitudes are shown before common output-level scaling; the attack and decay envelope is omitted. Amplitude is not perceived loudness.