Modulation Calculator

This modulation calculator helps find the amplitude modulation index using the amplitude of the modulation signal and the carrier signal. You can also calculate the frequency modulation index.

Modulation index0.440% modulation

Beat frequency4 Hzheard as 4 pulses a second — below about 20 Hz the ear follows the beating rather than hearing a separate tone

Beat period250 ms

Mean frequency442 Hzthe pitch actually perceived, with the beat as an amplitude wobble on top

Interval between them15.67 centsa semitone is 100 cents, and the ear can just detect about 5

Tuning usebeat to zerothe beat rate is the most sensitive tuning method there is: two tones a hundredth of a hertz apart still beat, once every 100 seconds

Alfvén velocity89.2062 km/sB ÷ √(µ₀ρ) — the speed of a wave travelling along a magnetic field line in a plasma, the magnetic analogue of a wave on a string

As a fraction of light0.0298%safely non-relativistic

At four times the density44.6031 km/shalf — it goes as the inverse square root of density, exactly like a wave on a heavier string

Sideband amplitude2half the modulating amplitude, in each of the two sidebands

Power in the sidebands7.41%even at 100% modulation only a third of the transmitted power carries information — which is why single-sideband exists

The formula

beat = |f₁ − f₂|; v_A = B ÷ √(µ₀ρ)

Beats are the most sensitive tuning tool there is

Two nearby frequencies produce an amplitude wobble at exactly their difference. The perceived pitch is their average; the beat is a slow swelling on top. Below about 20 Hz the ear follows the beating directly; above that it becomes a roughness and eventually a separate audible tone.

The sensitivity is remarkable. Two tones a hundredth of a hertz apart still beat — once every hundred seconds — so a musician can match pitches far more precisely by listening for beats than by comparing them directly. This is why piano tuners work by counting beats rather than by ear alone, and it is the basis of heterodyne measurement in electronics.

The Alfvén velocity is the same mathematics in a plasma: a magnetic field line behaves like a tensioned string, and disturbances run along it at B/√(µ₀ρ). It falls as the inverse square root of density exactly as a wave on a heavier string does, and it governs the propagation of solar and magnetospheric disturbances.

Amplitude modulation is worth one note: even at full 100% modulation, two thirds of the transmitted power sits in the carrier, which carries no information at all. That inefficiency is the entire reason single-sideband transmission was developed.