Illustrated Physics
physics, drawn
Concept

Timbre — where it appears

What distinguishes two sounds of the same pitch and loudness, carried by the relative strengths of their components and how those change with time. It is altered by distance as well as by the source, because absorption in air removes the high frequencies far faster than the low — 117 dB per kilometre at 8 kHz against 3.7 at 1.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Harmonics on a fixed string. Standing-wave patterns on a string clamped at both ends, at n = 1, 2, 3, 4. Only whole numbers of half-wavelengths fit, which is why the allowed frequencies are discrete.

Only some notes fit, and that is where discreteness comes from

A string clamped at both ends can vibrate at some frequencies and not others. A continuous object producing a whole-number list is the oldest quantisation in physics.

waves · Standing waves An f² law that is right in shape and out by 30× in size. Two absorption curves for air against frequency, both logarithmic, in decibels per kilometre. The lower one is the classical Stokes–Kirchhoff result computed from air's viscosity and thermal conductivity alone, and it goes as f^2.000 — exactly two, because the loss per cycle is fixed and the number of cycles per metre is proportional to the frequency. The upper one is the measured atmospheric absorption at 20 °C and 50 per cent humidity, which fits f^1.42 and is 30 times larger at 1 kHz and 211 times at 125 Hz. The excess is not a correction to viscosity: it is nitrogen and oxygen storing energy in vibration and giving it back late, at a rate the water vapour sets, and it is the mechanism that actually removes the treble from a distant sound.

The distance that takes the treble out

Spreading treats every frequency alike; absorption does not. The loss per cycle is roughly fixed and the number of cycles per metre goes as the frequency, so absorption climbs as f² and a sound gets duller with distance as well as quieter — which is the whole account of why a nearby thunderclap cracks and a distant one rumbles.

waves · Attenuation

Named alongside it

The objects these essays reach for when they reach for this one.

AbsorptionAttenuationBoundary conditionsDissipationHarmonic seriesIntensityNormal modesQuality factorQuantisationRelaxationSpectrumStanding wave

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