hertz

SI coherent derived unit with special name and symbol

Name

Symbol

Derived quantity

Expressed in terms of SI base units

hertz

frequency

s⁻¹

Definition

The hertz, symbol Hz, is the SI coherent derived unit of frequency.

One hertz is defined as one cycle per second.

The hertz is named after the German physicist Heinrich Hertz (1857 – 1894).

The fixed numerical value of the unperturbed ground state hyperfine transition frequency of the caesium 133 atom, Δν_Cs, is defined as 9 192 631 770 when expressed in the unit Hz.

$\Delta \nu _{Cs} \mspace{4mu} = \mspace{4mu} 9\ 192\ 631\ 770 \mspace{6mu} \text{Hz}$

Inverting this relation gives an exact expression for the hertz in terms of the SI defining constant Δν_Cs :

$1 \mspace{4mu} \text{Hz} \mspace{5mu} = \mspace{4mu} \dfrac{\Delta \nu _{Cs}}{9\ 192\ 631\ 770}$

The effect of this definition is that the hertz is equal to exactly ¹⁄_{9 192 631 770} of the frequency of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ¹³³Cs atom.

Periodicity

The unit hertz may be applied to any periodic event. For example, a clock might be said to tick at 1 Hz, or a human heart might be described as beating at 1.2 Hz.

However, the hertz should not be used for aperiodic or stochastic events. In general, the occurrence rate of such events should be expressed using the reciprocal second (¹⁄_s or s⁻¹), or in the specific case of radioactive decay, the becquerel should be used.

Whereas 1 Hz equals one cycle per second, 1 Bq is equal to one aperiodic radionuclide event per second.

Angular velocity

Even though angular velocity, angular frequency and the unit hertz all have the dimension ¹⁄_s, or s⁻¹, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as the radian per second.

Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2π rad/s or 1 Hz, where the former measures the angular velocity and the latter reflects the number of complete revolutions per second.

Vibration

Sound is a longitudinal wave which is an oscillation of pressure. Frequency of sound waves is perceived as pitch.

Each musical note corresponds to a particular frequency which can be measured in hertz. Human hearing falls in the range of 20 Hz to 20 000 Hz. Sounds with frequencies higher than human hearing are termed ultrasound. Sounds with frequencies below human hearing are termed infrasound.

Electromagnetic radiation

Electromagnetic radiation can be described by its frequency – the number of oscillations of the perpendicular electric and magnetic fields per second.

Radio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz).

Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz.

Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation.

Even higher frequencies exist, such as those of gamma rays, which can be measured in exahertz (EHz).

For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly referred to in terms of their wavelengths.

Signal processing

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal). The sampling frequency can be measured in samples per second, or hertz.

e.g. the sample rate of CD Audio is 44.1 kHz, and the audio stream of DVD Video is 48 kHz.

Computers

The central processing units (CPU) of computers are often labeled in terms of the frequency of their master clock signal, expressed in megahertz or gigahertz. This signal is a square wave, which is an electrical voltage that switches between low and high logic values at regular intervals.

For personal computers, CPU clock speeds have ranged from approximately 1 MHz in the late 1970s (Atari, Commodore, Apple computers) to up to 6 GHz in IBM POWER microprocessors.