# A Study of Wavelength, Energy, and Frequency With Their Formulas

From UV rays to radio waves, we are surrounded by waves and have developed various ways to measure, understand, and utilize them for our benefit. Wavelength is a very significant characteristic of a wave, and outlined in this article are the various wavelength equations.

Kundan Pandey

Last Updated: Feb 21, 2018

**Fast Fact:**

Every type of light has a different wavelength. UV rays and X-rays have shorter wavelengths, while radio waves move faster.

**Wavelength**is the distance between any two points which are at the same position on adjacent waves. For example, the distance between the highest points of two waves. The highest points on a wave are called crests and lowest are called toughs; crests are usually used for measuring wavelength, as they are easiest to measure.

**Wavelength Formula**

**λ = v / f**

λ = wavelength in m

ν = velocity of the wave in m/s

f = frequency of wave in Hz

As the speed of electromagnetic waves remains constant, v is often replaced by c, which is the speed of light in a vacuum and is around 3x10

^{8}m/s. Thus, the wavelength formula now becomes:

**λ = c / f**

All waves have different wavelengths, with radio waves having the longest wavelength (1m - 1km), and gamma the shortest (less than 0.01nm). The wavelength that is visible to us falls in the range of 380nm - 740nm.

**Frequency and Wavelength**

*nu*(although f is used here to avoid confusing it with v (velocity)) and is measured in Hertz (Hz). Formula for calculating frequency is:

**f = 1 / T**

T = time period

**Hz= v / λ**

or

**Hz= c / λ**

As you can see from the above equations, wavelength and frequency are inversely proportional. Hence, shorter the wavelength, higher will be the frequency of the wave and a longer wavelength will mean low frequency. For example, microwaves with wavelength in the range of 187 mm - 1 mm have frequency from 1 to 300x10

^{6}Hz; while x-rays whose wavelengths fall between 10nm to 0.01nm have frequency between 30x10

^{15}Hz and 100x10

^{18}Hz.

**Phase Velocity**

**v = fλ**

**Energy from Wavelength**

**E = hc / λ**

or

**E = hv / λ**

Here, h is the Planck's constant, with a value of approximately 6.63x10

^{-34}. Please note that v here is phase velocity and not frequency, though frequency can also be used to derive energy.

Electromagnetic waves are described using different characteristics, for example optical and infrared light are described by their wavelength, X-ray and gamma rays by their energy and radio waves by their frequency. As can be inferred from these equations, frequency, wavelength, and energy are mathematically inter-related, and the wavelength of a wave is inversely proportional to its frequency.