Illustrated Physics
physics, drawn
Concept

Frequency modulation — where it appears

Carrying a signal by varying a tone's frequency rather than its strength. A steady wobble turns one spectral line into a central line with sidebands spaced by the wobble rate, and the heights of those lines are Bessel functions of the depth of the wobble divided by its rate.

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

One note becomes a comb. The spectrum of a steady tone heard through the turning horn, level with it, against frequency offset from the tone, for tones of 250 Hz (top), 1000 Hz and 4 kHz (bottom): the power in each line as a fraction of the whole, each row on its own baseline with the height of a row standing for all of the power, computed from the received sound over one turn. A pitch that swings periodically is not a shifted line but a comb of lines spaced by the rotation rate, 6.7 Hz, with powers Jₙ(β)², where β = 2πfr/c is 0.69, 2.75 and 11.0 for the three tones; the 1000 Hz comb matches the Bessel functions line for line. The comb is narrow for the low tone, which keeps 78% of its power in the central line, and broad for the high one, whose power is spread over about ±80 Hz — so the turning horn blurs the upper partials of an organ chord into a shimmer while its fundamentals stay nearly pure.

The loudspeaker that goes round

The swirling sound of a Hammond organ comes from a loudspeaker cabinet in which the speaker's horn turns, six or seven times a second, and the swirl is the Doppler effect — the horn's mouth swings towards and away from the listener at about six metres a second, and every note it plays rises and falls by a third of a semitone. But a pitch that rises and falls periodically is not a note being shifted: it is a note split into a comb of new frequencies, spaced by the rotation rate and spread in proportion to the note itself, so the turning horn leaves the bass nearly pure and blurs the treble into a shimmer. In a room each wall returns its own copy, swinging out of step with the others, and the copies beat against each other several times a turn.

waves · Doppler A better glass is harder to hit. The half-width of the resonance in cents, and its ring-up time, against Q at 600 Hz. One falls as the other rises, and their product is fixed. A glass of Q = 100 has a window of ±8.6 cents, inside what a steady voice can hold, and it gains only a hundredfold. A glass of Q = 1000 gains ten times as much, and asks for ±0.9 cents held for over a second. Where a voice's steadiness crosses the window is about the Q at which a voice stops being able to use a further increase, and that is near Q = 173.

The glass a voice can break

A singer can shatter a wine glass, and it is not done by loudness. A good glass answers a tone a thousand times more strongly than a steady push, and it charges for that three times over: the note must be within about a cent, it must be held for over a second, and the glass must be flawed enough to fail. A voice's vibrato turns out to matter far less than its aim.

waves · Resonance

Named alongside it

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

Bessel functionBessel functionsDoppler effectFractureImage sourceLeslie speakerQuality factorResonanceRetarded timeSidebandsVibrato

All concepts