| Reference | Hertz (Hz) | Nanohertz (nHz) |
|---|---|---|
| European mains electricity | 50 Hz | 5 × 1010 nHz |
| Concert pitch A above middle C | 440 Hz | 4.4 × 1011 nHz |
| An FM radio station | 100000000 Hz | 1 × 1017 nHz |
| A Wi-Fi band | 2.4 × 109 Hz | 2.4 × 1018 nHz |
| A desktop processor clock | 3 × 109 Hz | 3 × 1018 nHz |
The hertz is the SI unit of frequency, equal to one cycle per second. Its symbol is Hz. It is a derived unit whose dimension is simply one divided by time, so a quantity in hertz counts how many times something repeats in a second.
It is named after Heinrich Hertz, who between 1886 and 1889 produced and detected radio waves in the laboratory and so confirmed Maxwell's prediction that light and electromagnetic waves are the same phenomenon. The unit was adopted internationally in 1960, replacing the older and more literal cycles per second, which is still occasionally seen on vintage equipment.
Sound occupies the low end of the scale. Human hearing runs from roughly 20 hertz to 20,000 hertz, though the upper limit falls with age and is usually well below 16,000 hertz by middle life. Musical pitch is frequency: the A above middle C is fixed at 440 hertz by convention, and each octave is a doubling, so the same note an octave higher is 880 hertz.
Mains electricity alternates at 50 hertz across most of the world and 60 hertz in North America and parts of Japan and South America. The split is historical rather than technical, dating from competing equipment standards in the late nineteenth century, and it is why appliances and clocks that depend on mains frequency cannot simply be moved between regions.
Screens and computing use it constantly. A display refreshing at 60 hertz redraws sixty times a second, and higher rates reduce visible motion blur. Processor clock speeds, once quoted in megahertz and now in gigahertz, count the same thing: how many times per second the internal clock ticks.
The unit also applies to anything periodic that is not a wave. Heart rate at 60 beats per minute is one hertz, a pendulum with a one-second period swings at one hertz, and the frequency of a rotating shaft in revolutions per second is expressed identically.
One hertz equals one cycle per second, 1000 millihertz, or one thousandth of a kilohertz.
The nanohertz is a unit of frequency equal to one billionth of a hertz. Its symbol is nHz. One nanohertz is one cycle per thousand million seconds, which is a little under thirty-two years, so a single oscillation at this frequency takes longer than most careers.
Almost nothing uses it, and then in 2023 it became one of the most discussed units in physics. Several pulsar timing array collaborations, working independently on four continents, reported evidence for a background of gravitational waves in the nanohertz band. The signal appears to come from pairs of supermassive black holes orbiting each other in the centres of merged galaxies across the whole history of the universe.
The measurement technique is remarkable. Millisecond pulsars are neutron stars that spin hundreds of times a second and emit a beam that sweeps past the Earth with extraordinary regularity, rivalling atomic clocks. A gravitational wave passing through the galaxy stretches and squeezes the space between the Earth and each pulsar, changing the arrival times of the pulses by a few hundred nanoseconds. By watching dozens of pulsars for two decades and looking for a specific pattern of correlation between them, astronomers detect waves whose wavelengths are measured in light years.
No instrument could work any other way at these frequencies. A detector must be comparable in size to the wavelength it seeks, and a nanohertz gravitational wave has a wavelength of tens of light years. The galaxy itself is the apparatus, and the pulsars are its markers.
The unit appears elsewhere only in the slowest of natural cycles. The precession of the Earth's axis takes about 26,000 years, roughly 1.2 nanohertz. Orbital variations in eccentricity, obliquity and precession that pace the ice ages, the Milankovitch cycles, run from about 0.5 nanohertz down to a tenth of that.
Below the nanohertz the concept of frequency becomes strained, because nothing has been observed long enough to see a full cycle, and the value is inferred from theory rather than counted.
One nanohertz equals 0.000000001 hertz, one cycle per thousand million seconds, or 0.001 microhertz.