§ Frequency · An instrument for curiosity

Frequency

Frequency means how many times something repeats each second. One repeat per second is one hertz (Hz).

One cycle compared with four cycles in one second1 Hz4 HzSame time window: one second

More repeats in the same time means higher frequency. A period is the time for one repeat. Waves also have amplitude, phase, and—when they travel—a wavelength.

Bands holding 220 Hz · selected

Audible sound · mechanical
About 20 Hz–20 kHz

Radio · electromagnetic
Below about 300 GHz; includes microwaves

Closest landmarks · selected

Voice fundamental150 Hz

Phone call audio1 kHz

Lowest piano A27.5 Hz

Whale call15 Hz

Bat call40 kHz

Each equal horizontal step multiplies frequency by ten; sound and electromagnetic waves share the frequency axisThermal peak temperature · kelvin, Celsius and Fahrenheit1-272 °C-458 °F10-263 °C-442 °F100-173 °C-280 °F1k727 °C1,340 °F10k9,727 °C17,540 °F100k1M10M100M1GBelow 1 K left of here10^-210^010^210^410^610^810^1010^1210^1410^1610^1810^2010^22Mechanical soundElectromagneticInfrasoundAudible soundUltrasoundRadioMicrowavesInfraredVisible lightUltravioletX-raysGamma raysContinues below 0.01 HzContinues above 10²² Hz

Move across the chart to read any frequency; the nearest landmark below is highlighted.

The temperature axis reads the other way round: it marks the blackbody whose thermal spectrum peaks at that frequency, by Wien’s displacement law. A thermal source emits a broad spectrum rather than one frequency, and the peak position depends on whether the spectrum is plotted per wavelength, as here, or per frequency.

This chart shows a selected range, not the limits of frequency. Slower and faster oscillations exist outside it. Sound and radio overlap in frequency but are different physical systems. Microwaves are part of radio. Category colors outside visible light are labels, not literal colors.

Frequency ledger
Frequency220 Hz
Period0.005 s
Wavelength1.559 m
Wave speed343 m/s
Octaves above 1 Hz7.781
BandAudible sound
Thermal peak temperature2.1e-9 K · -273 °C · -460 °F

Audible sound

Mechanical sound · Audible sound · About 20 Hz–20 kHz

A vibrating source makes pressure variations travel through air. Our ears turn a small range of these vibrations into sound.

Hearing limits vary with age, level, and the listener. Pitch is linked to frequency, while timbre depends on the mixture of harmonics. Doubling a musical frequency raises it by one octave.

Open this frequency in the Wave Lab

Work it out

Result
Frequency432 Hz
Period0.002 s
Wavelength0.794 m
Wave speed343 m/s
Octaves above 1 Hz8.755
BandAudible sound

Frequency, period, and wavelength are one number seen three ways. Period is 1 ÷ frequency; wavelength is speed ÷ frequency, so it changes with the medium while the source frequency does not.

Sound needs a material to travel through and moves at 343 m/s in air, roughly four times faster in water. Radio and light travel through a vacuum at 299,792,458 m/s.

Build this frequency in the Wave Lab

Reading the units

One hertz is one repeat per second. Every prefix after that multiplies by a thousand, so each new name adds three zeros.

UnitNameRepeats each secondIn wordsOn this chart
Hzhertz1oneA heartbeat, about 1 Hz
kHzkilohertz1,000a thousandPhone call audio, 1 kHz
MHzmegahertz1,000,000a millionFM radio, 100 MHz
GHzgigahertz1,000,000,000a billionWi-Fi and 5G, a few GHz
THzterahertz10¹²a trillionBody heat, 32 THz; visible light, 430–790 THz
PHzpetahertz10¹⁵a quadrillionUltraviolet, about 1 PHz
EHzexahertz10¹⁸a quintillionX-rays, tens of EHz

Each labelled step along the chart above multiplies frequency by one hundred; each faint line between them multiplies by ten.

How long is one repeat?

Period is one divided by frequency.

100 Hz → 1 ÷ 100 = 0.01 s, or 10 milliseconds.

1 kHz1 ms. 1 MHz1 µs. 1 GHz1 ns.

The pattern is worth remembering: kilo pairs with milli, mega with micro, giga with nano.

How long is the wave?

Wavelength is wave speed divided by frequency, so it depends on what the wave travels through.

Radio and light
metres ≈ 300 ÷ frequency in MHz. So 100 MHz is about 3 m, and 2,450 MHz is about 12 cm.

Sound in air
metres ≈ 343 ÷ frequency in Hz. So 100 Hz is about 3.4 m, and 440 Hz about 78 cm.

Higher frequency always means a shorter wave at a given speed.