Frequency Formula Basics: 2 Ways to Calculate Frequency

A blue and orange rendition of sound frequency waves — Frequency is inversely proportional to time period; as time period increases, frequency decreases. Elerium / Getty Images

Frequency is a fundamental concept when you're talking about waves, whether that means electromagnetic waves like radio waves and visible light, or mechanical vibrations like sound waves.

Knowing the frequency of a wave helps you gauge how often a repeating event occurs within a specific time frame. To determine frequency, you use what's called the frequency formula.

What Is the Frequency Formula?

Frequency, often denoted by the symbol f and measured in hertz (Hz), serves as a crucial metric for quantifying how frequently a repeating event occurs within a defined time interval. The core formula to calculate frequency is straightforward:

Frequency (f) = 1 / Time Period (T)

In mathematical terms, you can determine the frequency f by taking the reciprocal of the time period T. The unit of frequency is the hertz (Hz), named for Heinrich Hertz, a pioneer in the field of electromagnetism. One hertz signifies one wave cycle per second.

This inverse relationship between frequency and the time period (sometimes referred to as the wave period) implies that as the time period increases, the frequency decreases, and vice versa.

Here's another formula you can use to calculate frequency:

Frequency (f) = Wave Velocity (v) / Wavelength (λ)

Understanding these two frequency formulas will empower you to interpret the behavior of waves in diverse contexts.

Understanding Waves

To better understand the intricacies of frequency and how the frequency formula works, it's necessary to familiarize yourself with some essential terms and concepts related to waves.

Wave: A wave is a disturbance that travels through space, carrying energy. It transfers energy, rather than matter, from one point to another. Examples include sound waves, electromagnetic waves (such as light), and radio waves.
Wave cycle: One cycle of a wave refers to a complete waveform from a specific point in the wave to the same point in the next identical wave.
Wavelength: The distance between two consecutive points in a wave that are in phase (e.g., from one crest to the next crest or from one trough to the next trough) equals the wavelength (λ). People usually record wavelength in meters (m).
Wave velocity: Also known as wave speed, wave velocity (v) represents the rate at which a wave travels through a particular medium. People typically express this parameter in meters per second (m/s).
Time period: The time it takes for one complete wave cycle to occur is called the time period. It is measured in seconds (s).
Angular frequency: Denoted by the Greek letter omega (ω), angular frequency establishes a relationship between frequency and the time period of a wave.

The Importance of Frequency

Frequency has profound implications across many different scientific disciplines and practical applications, including:

Communication and telecommunications: Managing frequencies is fundamental to radio broadcasting, cellular networks and wireless communication. Systems allocate various frequency bands for specific communication purposes, ensuring signals don't interfere with each other.
Electromagnetic spectrum: This encompasses a wide range of frequencies, from extremely low frequencies (ELF) to extremely high frequencies (EHF). Visible light is also part of the electromagnetic spectrum, and the frequency determines the specific color of the light.
Energy and vibrations: Higher-frequency waves carry more energy per unit time than lower-frequency waves. This principle is crucial in engineering and construction, where understanding the frequency of mechanical vibrations helps to ensure the structural integrity of buildings.
Sound waves: With mechanical vibrations, frequency is the key to understanding pitch. A higher-frequency sound wave corresponds to a higher-pitched sound, while a lower-frequency sound wave results in a lower-pitched sound. Musicians use frequency to tune their instruments.

Practical Examples of the Frequency Formula

Here are two examples of how you might need to find frequency in real-world scenarios.

Example 1

A radio station broadcasts its signal with a frequency of 98.5 megahertz (MHz). Imagine you want to find the corresponding time period of one cycle of the radio wave.

To find the time period, you can use the frequency formula:

Frequency (f) = 1 / Time Period (T)

Rearranging the formula to solve for T, you get:

Time Period (T) = 1 / Frequency (f)

Plugging in the frequency of 98.5 MHz, you have:

Time Period (T) = 1 / 98.5 × 10⁶ Hz ≈ 10.15 nanoseconds (ns)

This calculation helps you determine that one cycle of the radio wave has a time period of approximately 10.15 nanoseconds.

Example 2

A guitar string vibrates with a frequency of 440 Hz when producing the note A4. Suppose you want to find the wavelength of this sound wave in air.

To find the wavelength, you can use the relationship between wave velocity, frequency and wavelength:

Wave Velocity (v) = Frequency (f) × Wavelength (λ)

Rearranging the formula to solve for λ, you get:

Wavelength (λ) = Wave Velocity (v) / Frequency (f)

The speed of sound in air is approximately 343 meters per second (m/s). Plugging in the frequency of 440 Hz, you have:

Wavelength (λ) = 343 m/s / 440 Hz ≈ 0.78 meters (m)

This calculation reveals the wavelength of the sound wave producing the note A4 is approximately 0.78 meters in air.

Different Frequency Ranges

Frequency can span a vast range of values. Here are some examples of different frequency bands and their applications:

Infrared (IR) waves: Remote controls, thermal imaging and spectroscopy use IR waves, which have frequencies slightly lower than those of visible light.
Microwaves: Microwave ovens, satellite communication, and radar systems utilize microwaves, which fall in the gigahertz (GHz) range.
Radio waves: Navigation systems, radio broadcasting, and wireless communication technologies like Wi-Fi and Bluetooth use radio waves, which have frequencies ranging from a few hertz to several gigahertz (GHz).
Ultraviolet (UV) waves: Sterilization and fluorescence use UV waves, which have frequencies higher than visible light and are known for their damaging effects on skin and DNA.
Visible light: Colors, from low to high frequency, include red, orange, yellow, green, blue, indigo, and violet. This spectrum of colors, each one corresponding to a specific frequency, makes up visible light. Understanding the frequency of light is fundamental to optics and photography.

This article was created in conjunction with AI technology, then was fact-checked and edited by a HowStuffWorks editor.