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Frequency is a fundamental concept in physics and engineering that measures the number of occurrences of a repeating event, such as a wave or a vibration, within a given period of time. In simpler terms, it represents how often a particular event or phenomenon happens. Understanding how to calculate frequency is crucial in various scientific and technological disciplines, as it allows us to analyze and manipulate waves, signals, and other cyclic phenomena. This guide will provide a comprehensive overview of the different methods and equations used to calculate frequency accurately, enabling individuals to confidently work with this fundamental measurement and enhance their understanding of the physical world.

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Frequency, or wave frequency, is a measurement of the total number of recorded oscillations over a specified period of time. Depending on the information available you may be able to calculate the frequency in one way or another. This article will cover some of the most common and useful ways to calculate wave frequency.

## Steps

### Calculate frequency based on wavelength

**Recipe.**When the wavelength and velocity of the oscillation are known in advance, the frequency can be calculated as follows:

**f = V / λ**

- In this formula,
*f*is the frequency,*V*is the wave velocity, and*λ*is the wavelength. - Example: A sound propagates through air with a wavelength of 322 nm, its speed is 320 m/s. What is the frequency of this sound wave?

**Convert wavelength to meters if necessary.**If the wavelength is given in nanometers, you need to convert this to the standard unit of meters by dividing that value by the number of nanometers in one meter.

- Note, when the value you are dealing with is very small or very large, you need to convert that value to standard scientific metric form. In this article, some values may not be recorded in standard form, but when you do an assignment or test or participate in scientific forums, you need to record the data in a standard form.
- Example: = 322 nm
- 322 nm x (1 m / 10^9 nm) = 3.22 x 10^-7 m = 0.000000322 m

**Divide the wave speed by the wavelength.**To calculate the frequency,

*f*, we take the propagation speed of the wave,

*V*, and divide it by the wavelength in meters,

*λ*.

- For example, f = V / λ = 320 / 0.000000322 = 993788819.88 = 9.94 x 10^8

**Record the answer.**After completing the previous step, you need to write down the calculated answer with the unit of frequency. The standard unit of frequency is Herzt,

*Hz*.

- Example: The frequency of this wave is 9.94 x 10^8 Hz.

### Calculate the frequency of electromagnetic waves in a vacuum

**Recipe.**The formula for calculating wave frequency in a vacuum is similar to the formula for calculating the frequency in a non-vacuum environment. However, in a vacuum, the wave speed is not affected by other factors, so the speed of electromagnetic waves in this case is equal to the mathematical constant of the speed of light. Therefore, the calculation formula is:

**f = C /**

- Where
*f*is the frequency,*C*is the speed of light, and*λ*is the wavelength. - For example, an electromagnetic wave has a wavelength of 573 nm when traveling in a vacuum. What is the frequency of this electromagnetic wave?

**Convert wavelengths to meters if necessary.**When the problem gives the wavelength in meters, we do not need to change. However, if the wavelength is given in another unit, such as a micrometer, you need to convert it to meters by dividing that value by the number of micrometers in a meter.

- Note that when the given values are very large or very small, we need to write those values in standard scientific notation. Here, values can be written in standard or non-standard form, but in assignments or tests as well as when participating in forums, you should write in standard scientific notation.
- Example: = 573 nm
- 573 nm x (1 m / 10^9 nm) = 5.73 x 10^-7 m = 0.000000573

**Divide the speed of light by the wavelength.**

^{[1] X Research Source}The speed of light is a constant, so in case the problem is given this value or not, we still use

*3.00 x 10^8 m/s*as the speed of light. Divide this value by the wavelength in meters.

- Example: f = C / = 3.00 x 10^8 / 5.73 x 10^-7 = 5.24 x 10^14

**Record the answer.**Calculating according to the steps above, we have the frequency value. When writing your answer, you need to include the units along with the value. The unit of frequency is Hertz,

*Hz*.

- Example: The frequency of the wave is 5.24 x 10^14 Hz.

### Calculate frequency based on time or period

**Recipe.**Frequency and time required to complete a wave oscillation are two quantities that are inversely proportional to each other. Therefore, the formula for calculating the frequency when the time to complete the oscillation is known is:

**f = 1 / T**

^{[2] X Research Source}

- Where
*f*is the frequency and*T*is the period time or amount of time required to complete one oscillation. - Example A: A wave completes an oscillation in 0.32 seconds. What is the frequency of this wave?
- Example B: In 0.57 seconds, a wave completes 15 oscillations. What is the frequency of the wave?

**Divide the number of oscillations by the total time.**Usually, the problem will state the time it takes to complete an oscillation, in this case we take the reciprocal of the period time (take

**1**divided by the period

**T**). If the period of time available is the period of multiple oscillations, you need to divide the number of oscillations by the total period of time it takes to complete all of them.

- Example A: f = 1 / T = 1 / 0.32 = 3.125
- Example B: f = 1 / T = 15 / 0.57 = 26.316

**Record the answer.**By doing the above calculation we will get the frequency of the wave. You need to include the frequency unit as Herzt,

*Hz*.

- Example A: The frequency of the wave is 3.125 Hz.
- Example B: The frequency of the wave is 26.316 Hz.

### Calculate frequency based on angular frequency

**Recipe.**Once the angular frequency of a wave is known, to calculate the standard frequency of that wave, we apply the formula:

**f = / (2π)**

^{[3] X Research source}

- where
*f*is the reference frequency and*ω*is the corner frequency. As with other problems,*π*is the constant pi. - For example, a wave moves in circular motion with an angular frequency of 7.16 radians per second. What is the frequency of the wave?

**Double the pi value.**To determine the denominator according to the above formula, we multiply the value of pi, or 3.14, by 2.

- Example: 2 * = 2 * 3.14 = 6.28

**Divide the angular frequency by the product of pi and 2.**Take the angular frequency of the wave, given in radians per second, and divide by 6.28, the value obtained by doubling the value of the constant pi.

- Example: f = / (2π) = 7.17 / (2 * 3.14) = 7.17 / 6.28 = 1.14

**Record the answer.**The final step when completing the calculation is to record the result obtained with the unit. The unit of frequency is Herzt,

*Hz*.

- Example: The frequency of the given wave is 1.14 Hz.

## Things you need

- Computer
- Pen
- Paper

wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 12 people, some of whom are anonymous, have edited and improved the article over time.

This article has been viewed 66,245 times.

Frequency, or wave frequency, is a measurement of the total number of recorded oscillations over a specified period of time. Depending on the information available you may be able to calculate the frequency in one way or another. This article will cover some of the most common and useful ways to calculate wave frequency.

In conclusion, calculating the frequency is a simple yet essential concept in various fields such as physics, engineering, and music. It helps in understanding the repetition rate of a wave, the occurrence of events, or the occurrence of data values in a dataset. By following the steps mentioned, one can determine the frequency accurately. It is important to keep in mind that frequency should not be confused with amplitude or wavelength, as they represent different aspects of a wave. With the understanding of frequency, one can delve into more complex concepts and applications that rely on this fundamental parameter.

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