Hertz
In 1887 Heinrich Hertz darkened a lecture room in Karlsruhe and watched a wire ring with a tiny gap. When the oscillator's spark crackled at the other end of the room, a spark of its own, a fraction of a millimetre long, jumped across the gap of the ring. This was the first time an electromagnetic wave was caught. Hertz himself saw the experiment as a test of Maxwell's theory and saw no practical use in it.
Some forty years later the unit of frequency was named after him. One hertz is one oscillation per second. The current in a socket makes 50 or 60 oscillations per second, the A string 440, and a Wi‑Fi signal about 2.4 billion.
| Notation | Hz |
| Definition | one oscillation per second · s⁻¹ · for periodic processes only |
| Reference values | Δν(¹³³Cs) — 9 192 631 770 Hz · at 1 Hz the angular frequency is 2π rad/s · 1 Hz — 60 rpm |
| Introduced | 1930, IEC · in the SI since 1960, replacing “cycles per second” |
| Standards | ISO 80000-3 · IEC 60050 · SI Brochure 9th ed. |
| Typical values | 50 Hz — mains · 440 Hz — the note A · 2.4 GHz — Wi‑Fi |
01 · Definition
How many times a second
Frequency f shows how many times a second a process repeats. A pendulum, a string, the current in a wire, a light wave — anything that returns to the same state at equal intervals. One such interval is called the period T. Frequency and period are reciprocal: with a period of 0.02 s the frequency is 50 Hz.
For a wave, frequency is linked to wavelength through the speed. Radio waves and light travel at speed c, so a 2.4 GHz wave is 12.5 cm long. Sound is slower, and the note A has a wavelength of about 78 cm.
How to find the rotation frequency without touching the disc
A disc with a white mark turns in the dark and is seen only during the flashes of the lamp on the right. If the flashes match the revolutions, the mark is in the same place every time and seems to stand still. If the flashes are a little slower, the mark creeps forward; if a little faster, backward. The slider sets the flash frequency. The third rotor turns at an unknown frequency: find it.
Move the slider slowly and watch the mark.
Engine speeds are usually written in rpm — revolutions per minute. To get hertz, divide rpm by 60. A fan at 1440 rpm makes 24 revolutions a second, a hard disk at 7200 rpm 120. An induction motor on 50 Hz mains turns a little slower than 3000 rpm, and with two pairs of poles about 1450.
Where the spark will jump in the ring
On the left, an induction coil drives Hertz's oscillator: two rods with balls and a spark gap between them. The length of the oscillator sets the wavelength, about twice as long as the oscillator itself. The blue line is the electric field along the room, and the brightness of the bands is its swing. On the right, a zinc sheet stands at the wall. It reflects the wave, and nodes appear in the room where there is no field. A wire ring on a stand is the receiver. The spark in its gap depends on two things: the field at that spot and whether the circumference of the ring matches the wavelength. The ring can be dragged across the scene. On the right is a magnifier on the ring gap and a spark counter.
The ring moves along the room. Watch where a spark lights up in its gap.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
A motor with one pair of poles on 50 Hz mains turns at almost 3000 rpm: 50 revolutions a second.
At 1 Hz the angular frequency is 2π rad/s, about 6.283. Mixing them up is an error of more than six times.
A 2.4 GHz Wi‑Fi wave is 12.5 cm long in vacuum, so router antennas are a few centimetres in size.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
The hertz equals the reciprocal second, but it is used only for periodic processes. For random nuclear decays the same reciprocal second is called the becquerel. Angular velocity is written in radians per second: 1 Hz corresponds to 2π rad/s. Mix these quantities up and the error is 6.28 times.
Since 1967 the second has been defined through a frequency: it is 9 192 631 770 periods of the radiation of the caesium-133 atom. The hertz and the second rest on one and the same number. Frequency is measured today more precisely than any other quantity, so many standards are reduced to counting it.
Catalogue of quantities
the whole index →The seven SI base units
A drop of acid changes the colour of the juice, salt colours the flame, water freezes at a tap. Below them are all Simetrium sheets, by discipline and alphabetically.
Open the index →