# Frequency Calculator

Created by Davide Borchia
Last updated: Jun 27, 2022
Table of contents:

Oscillating motions are ubiquitous in the physics world; from waves to quantum mechanics, from light to sound, our frequency calculator can help you find the solution to many simple problems involving waves.

We will start from the fundamentals. Here you will learn:

• What is a wave, and what is the frequency of a wave;
• How to calculate the frequency from the wavelength; and
• How to find the frequency of a wave from the period.

We will also give you some neat examples! Keep reading to learn the basics of periodic motion.

## What is a wave?

A wave is a periodic (usually) disturbance of a physical quantity that allows for the transfer of (and/or matter). Think of a simple pendulum, a sound, or a sine wave.

Waves come in many types and with many different characteristics, but in almost every case, we can define a set of fundamental quantities:

These quantities define the way the wave propagates in the medium and together can define many other less straightforward quantities, like:

• The wave velocity;
• The wavenumber;
• The reduced or angular wavelength.

Let's study the frequency of a wave with more attention.

## What is the frequency of a wave?

The frequency of a wave is a measure of the number of times the wave completes its periodic motion in a unit of time.

A completed "unit" of the periodic motion is called a cycle. Of course, we can define a cycle from any arbitrary point of the wave, but we usually take as reference the peak or valley of the wave.

Note that we specified unit of time: we can define other frequencies (angular frequency, spatial frequency, etc.); however, the temporal frequency is by far more common.

The measurement unit of the temporal frequency is the hertz, symbol $\text{Hz}$. The hertz is an SI derived unit since its definition relies on a base unit, the second. Remember the definition of frequency? In terms of units, it translates to:

$1\ \text{Hz} = \frac{1}{\text{s}}$

Which means that the value of one hertz equals to one oscillation per second.

## How to find the frequency of a wave

Here you will learn how to calculate the frequency of a wave.

Physicists associate frequency with many letters, usually choosing one according to the context or out of habit. The most common symbols are $f$ and $\nu$.

There are multiple equations for the frequency, depending on the known quantities. Here we will focus on how to calculate the frequency from the wavelength, and we will learn the formula for the frequency when you know the period of the wave.

#### Formula for the frequency from the wavelength

To calculate the frequency, if you know the wavelength $\lambda$, you need to use the velocity of the wave in the medium it is traveling in, $v$.

The equation for the frequency is:

$f = \frac{v}{\lambda}$

Where you can see the three quantities we already introduced. Try your hand at dimensional analysis!

#### Equation for the frequency if the period is known

You can use another way to calculate the frequency if you know the period of the oscillation. The period of a wave, $T$, is the time that separates two corresponding points in a periodic motion.

The relation between period and frequency is straightforward:

$f = \frac{1}{T}$

## How to use our frequency calculator

You can use our frequency calculator to find the frequency of a wave in the two ways we explained above.

If you know the wavelength, choose the velocity out of the presets, or erase the field and insert a custom value. Then, insert the wavelength (mind the measurement units): we will calculate the frequency and the period.

Let's say you are interested in the propagation of gravitational waves. These once elusive (but still hard to detect) events travel through the universe at the speed of light $c$ (it's the default value of our calculator). The wavelength of the first observed gravitational waves lies in the range of $100$ to $1000$ kilometers. Take the reference value of $\lambda=500\ \text{km}$, choose the correct measurement unit, and input that number:

\begin{align*} f& = \frac{c}{\lambda} =\frac{299,\!793\ \text{km}/\text{s}}{500\ \text{km}}\\ \\ &= 600\ \text{Hz} \end{align*}

If you know the period, you can insert it directly in our calculator, but remember to choose the proper speed to find the correct value of wavelength!

🔎 You can use our calculator in reverse to find the wavelength and period from the frequency!

Davide Borchia
Wave velocity of
light in vacuum
Wave velocity (v)
m/s
Wavelength (λ)
m
Period (T)
sec
Frequency (f)
Hz
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