The hertz is the unit of frequency in the International System of Units (SI) and its symbol is Hz. It is defined as one event or cycle per second and represented as s⁻¹ in SI base units. One hertz equals one occurrence per second. We use this unit for periodic events. It is named after Heinrich Rudolf Hertz (1857–1894), who first demonstrated the existence of electromagnetic waves. We measure higher frequencies in kilohertz (kHz), megahertz (MHz), gigahertz (GHz), and terahertz (THz).
We commonly use hertz to describe periodic waveforms and musical tones, especially in radio and audio contexts. It also measures the clock speeds of computers and other electronics. Additionally, it is sometimes used to represent the energy of a photon through the Planck relation E=hν, where E is the photon’s energy, ν is its frequency, and h is the Planck constant.
Definition of Hertz (Hz)
The hertz, defined as one cycle per second, is the standard unit of frequency for periodic events. The International Committee for Weights and Measures established the definition of a second as the time it takes for 9,192,631,770 cycles of radiation to occur during the transition between the two hyperfine levels of the caesium-133 atom’s ground state. This indicates that the hyperfine splitting in the ground state of cesium-133 is exactly 9,192,631,770 hertz, denoted as νhfsCs =9,192,631,770 Hz. The hertz has a dimension of 1/time (T⁻¹), and in SI base units, it is expressed as the reciprocal of a second (1/s).
In English, “hertz” is also used in the plural form. As an SI unit, we can modify the hertz (Hz) with standard SI prefixes: kilohertz (kHz, 10³ Hz), megahertz (MHz, 10⁶ Hz), gigahertz (GHz, 10⁹ Hz), and terahertz (THz, 10¹² Hz). A frequency of one hertz means a periodic event happens once per second, while 100 Hz signifies that 100 events occur each second. This unit applies to any periodic event, such as a clock ticking at 1 Hz or a human heart beating at 1.2 Hz.
We typically express the occurrence rate for aperiodic or stochastic events in reciprocal seconds or inverse seconds (1/s or s⁻¹). In radioactivity, this rate is measured in becquerels (Bq). While frequency, angular velocity, angular frequency, and radioactivity all share the dimension T⁻¹, only frequency is measured in hertz. For example, a disc rotating at 60 revolutions per minute (rpm) has an angular velocity of 2π rad/s and a rotational frequency of 1 Hz. The relationship between a frequency f (in hertz) and an angular velocity ω (in radians per second) is ω=2πf and f=ω/2π
The hertz is named after Heinrich Hertz. As with all SI units named after people, the symbol starts with a capital letter (Hz), but when written in full, “hertz” is lowercase unless it begins a sentence or appears in a title.
The hertz is defined as one cycle per second. A cycle refers to a complete oscillation or vibration, which can be understood in the context of a wave: one complete wave consists of one crest and one trough. When a wave undergoes a complete cycle in one second, it has a frequency of 1 Hz.
Mathematically, frequency (f) is calculated as the number of cycles (N) divided by the time (T) in seconds:
For example, if a wave completes 50 cycles in 1 second, its frequency is 50 Hz. Similarly, if it completes 100 cycles in 2 seconds, the frequency is 50 Hz.
Applications of Hertz
The concept of frequency measured in hertz is used in various fields, from physics and engineering to music and medicine. Here are some of the most frequently used applications:
- Sound Waves:
- Sound is a type of mechanical wave that travels through mediums such as air, water, or solids. The pitch of a sound is determined by its frequency. Humans can generally hear frequencies ranging from approximately 20 Hz to 20,000 Hz (20 kHz). Low-frequency sounds are deep or bass sounds, while high-frequency sounds are sharp or treble sounds.
- Electromagnetic Waves:
- Electromagnetic waves, which include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, all have frequencies measured in hertz. Radio frequencies, for example, range from about 3 kHz to 300 GHz, and each range within this spectrum is used for different communication technologies such as AM/FM radio, television, mobile phones, and satellite communications.
- Electrical Engineering:
- In electrical engineering, the frequency of an alternating current (AC) is crucial. For example, in most countries, the standard frequency of electrical power is 50 Hz or 60 Hz. This means the current alternates 50 or 60 times per second, respectively. The frequency of AC affects the operation of electrical devices and is a key factor in the design of power systems.
- Digital Electronics:
- The clock speed of a computer processor, expressed in hertz, reflects the number of cycles it can perform per second. Modern processors often function at speeds measured in gigahertz (GHz), which means they can complete billions of cycles each second. This speed is a key factor in the computer’s overall performance and efficiency.
- Medical Imaging and Diagnostics:
- In medical diagnostics, ultrasound machines generate high-frequency sound waves, usually in the megahertz (MHz) range, to produce images of internal body structures. The frequency of these sound waves affects the resolution and depth of the images produced. Higher frequencies offer better image resolution but have limited penetration, making them ideal for imaging superficial structures. In contrast, lower frequencies are used for visualizing deeper structures.
- Astronomy:
- Astronomers use frequency to study various celestial phenomena. Radio telescopes are designed to capture radio waves emitted by stars, galaxies, and various other celestial bodies. By analyzing the frequency of these waves, scientists can infer important information about the object’s composition, motion, and distance.
Higher and Lower Frequencies
The frequency spectrum covers an extensive range, from extremely low frequencies (ELF) used in submarine communication to extremely high frequencies (EHF) used in advanced radar and communication systems. Here’s a brief overview:
| Frequency | Frequency Range | Applications |
| Extremely Low Frequencies (ELF) | 3 Hz to 30 Hz | Communication with submarines and in geophysics. |
| Very Low Frequencies (VLF) | 3 kHz to 30 kHz | Navigation and communication over long distances |
| Low Frequencies (LF) | 30 kHz to 300 kHz | AM radio and long-range communication |
| Medium Frequencies (MF) | 300 kHz to 3 MHz | AM radio and long-range communication |
| High Frequencies (HF) | 3 MHz to 30 MHz | shortwave radio, aviation, and maritime communication |
| Very High Frequencies (VHF) | 30 MHz to 300 MHz | FM radio, television broadcasting, and two-way communication |
| Ultra-High Frequencies (UHF) | 300 MHz to 3 GHz | Television broadcasting, mobile phones, and satellite communication |
| Super High Frequencies (SHF) | 3 GHz to 30 GHz | Radar, satellite communication, and microwave ovens |
| Extremely High Frequencies (EHF) | 30 GHz to 300 GHz | Advanced radar systems and high-frequency communication |
Practical Examples of Hertz
- Human Heartbeat:
- The human heartbeat is a rhythmic oscillation, and its frequency can be measured in hertz. For instance, a typical resting heart rate of 60 beats per minute translates to a frequency of 1 Hz (60 beats per minute / 60 seconds per minute = 1 beat per second).
- Musical Notes:
- In music, the pitch of a note corresponds to its frequency. The note A4, which is commonly used as a tuning reference, has a frequency of 440 Hz. This means that the sound wave vibrates 440 times per second.
- Household Electricity:
- In the United States, household electricity operates at 60 Hz. This means that the electrical current in a standard outlet oscillates 60 times per second. In contrast, many European countries use 50 Hz.
SI multiples of Hertz
| Submultiples | Multiples | ||||
|---|---|---|---|---|---|
| Value | SI symbol | Name | Value | SI symbol | Name |
| 10−1 Hz | dHz | decihertz | 101 Hz | daHz | decahertz |
| 10−2 Hz | cHz | centihertz | 102 Hz | hHz | hectohertz |
| 10−3 Hz | mHz | millihertz | 103 Hz | kHz | kilohertz |
| 10−6 Hz | μHz | microhertz | 106 Hz | MHz | megahertz |
| 10−9 Hz | nHz | nanohertz | 109 Hz | GHz | gigahertz |
| 10−12 Hz | pHz | picohertz | 1012 Hz | THz | terahertz |
| 10−15 Hz | fHz | femtohertz | 1015 Hz | PHz | petahertz |
| 10−18 Hz | aHz | attohertz | 1018 Hz | EHz | exahertz |
| 10−21 Hz | zHz | zeptohertz | 1021 Hz | ZHz | zettahertz |
| 10−24 Hz | yHz | yoctohertz | 1024 Hz | YHz | yottahertz |
| 10−27 Hz | rHz | rontohertz | 1027 Hz | RHz | ronnahertz |
| 10−30 Hz | qHz | quectohertz | 1030 Hz | QHz | quettahertz |
Conclusion
Hertz is a simple yet powerful concept that underlies many aspects of science, technology, and everyday life. As a unit of frequency, it allows us to measure and understand the oscillations and waves that govern various physical phenomena. Whether it’s the beat of your heart, the notes of a song, or the signals that power your devices, hertz is the universal language of cycles per second.