# Convert Frequency to Wavelength Worked Example Problem

## Frequency to Wavelength Spectroscopy Example Problem Wavelength is the distance between peaks or valleys of a wave, while frequency is a measure of how quickly waves repeat. Jorg Greuel / Getty Images

This example problem demonstrates how to find the wavelength of light from the frequency.

## Frequency vs Wavelength

The wavelength of light (or other waves) is the distance between subsequent crests, valleys, or other fixed points. The frequency is the number of waves that pass a given point in one second. Frequency and wavelength are related terms used to describe electromagnetic radiation or light. One simple equation is used to convert between them:

frequency x wavelength = speed of light

λ v = c, when λ is wavelength, v is frequency, and c is the speed of light

so

wavelength = speed of light / frequency

frequency = speed of light / wavelength

The higher the frequency, the shorter the wavelength. The usual unit for frequency is Hertz or Hz, which is 1 oscillation per second. Wavelength is reported in units of distance, which often ranges from nanometers to meters. Conversions between frequency and wavelength most often involve wavelength in meters because that's how most people remember the speed of light in a vacuum.

### Key Takeaways: Frequency to Wavelength Conversion

• Frequency is how many waves pass a defined point per second. Wavelength is the distance between successive peaks or valleys of a wave.
• Frequency multiplied by wavelength equals the speed of light. So, if you know either the frequency or the wavelength you can calculate the other value.

## Frequency To Wavelength Conversion Problem

The Aurora Borealis is a night display in the Northern latitudes caused by ionizing radiation interacting with the Earth's magnetic field and the upper atmosphere. The distinctive green color is caused by the interaction of the radiation with oxygen and has a frequency of 5.38 x 1014 Hz. What is the wavelength of this light?
Solution:
The speed of light, c, is equal to the product of the wavelength, &lamda;, and the frequency, ν.
Therefore
λ = c/ν
λ = 3 x 108 m/sec/(5.38 x 1014 Hz)
λ = 5.576 x 10-7 m
1 nm = 10-9 m
λ = 557.6 nm