2 ways to calculate frequency

Frequency is a fundamental concept when talking about waves, whether electromagnetic waves such as radio waves and visible light, or mechanical vibrations such as sound waves.

Knowing the frequency of a wave allows you to estimate how often a repeating event occurs within a specific time frame. To determine the frequency, use what is 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 measure for quantifying how often a repeating event occurs within a given time interval. The core formula to calculate frequency is simple:

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 after Heinrich Hertz, a pioneer in the field of electromagnetism. One hertz means one wave cycle per second.

This inverse relationship between frequency and time period (also called 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:

Understanding these two frequency formulas will help you interpret the behavior of waves in different contexts.

Understanding waves

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

• golf: A wave is a disturbance that travels through space and carries 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 (for example from one crest to the next crest or from one trough to the next trough) is equal to the wavelength (λ). People usually record wavelength in meters (m).

• Wave speed: Wave speed (v), also known as wave speed, represents the speed at which a wave travels through a given medium. People usually 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 the frequency and time period of a wave.

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The importance of frequency

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

• Communications and telecommunications: Managing frequencies is fundamental to radio broadcasting, mobile networks and wireless communications. Systems allocate different frequency bands for specific communication purposes so that signals do not interfere with each other.

• Electromagnetic spectrum: This covers a wide frequency range, from extremely low frequencies (ELF) to extremely high frequencies (EHF). Visible light is also part of the electromagnetic spectrum and its frequency determines the specific color of the light.

• Energy and vibration: 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 ensure the structural integrity of buildings.

• Sound waves: In 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 at a frequency of 98.5 megahertz (MHz). Imagine that 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:

If you rearrange the formula for T, you get:

If you connect the 98.5 MHz frequency you will have:

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

Example 2

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

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

If you rearrange the formula to solve for λ, you get:

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

This calculation shows that the wavelength of the sound wave produced by the A4 note is approximately 0.78 meters in air.

Different frequency ranges

The frequency can span a wide 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 communications and radar systems use microwaves, which are in the gigahertz (GHz) range.

• Radio waves: Navigation systems, radio broadcasting, and wireless communications technologies such as Wi-Fi and Bluetooth use radio waves with frequencies ranging from a few hertz to a few gigahertz (GHz).

• Ultraviolet (UV) waves: Sterilization and fluorescence use UV waves, which have a higher frequency than visible light and are known for their damaging effects on the 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 corresponding to a specific frequency, constitutes visible light. Understanding the frequency of light is fundamental to optics and photography.

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

Original article: Basics of Frequency Formulas: 2 Ways to Calculate Frequency

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