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- Wavenumber To Wavelength Conversion Table
- Wavenumber To Wavelength Conversion Calculator
- Wavenumber To Wavelength Conversion Formula
By Lee Johnson
Most people are familiar with wavelengths, but a “wavenumber” is a little more puzzling. If you’re trying to make sense of this term and work out what to do with it, learning to convert the wavenumber to a wavelength helps you understand what a wavenumber is and extract some more usable information about the wave it describes. The conversion is simple as soon as you learn the definition of a wavenumber.
Note: In this converter conversion between wavelength and frequency are performed for electromagnetic waves only. Using the Frequency and Wavelength Converter Converter. This online unit converter allows quick and accurate conversion between many units of measure, from one system to another. This video introduces the physics concepts of Wavelength and Wavenumber as related to any form of traveling waves.
TL;DR (Too Long; Didn't Read)
Convert from wavenumber to wavelength by dividing 1 by the wavenumber. If the wavenumber is expressed in 1/m, you will get a result in m. If the wavenumber is expressed in 1/cm, you will get a result in cm. You can convert the result into the required unit in the usual way.
What Is a Wavenumber?
A wavenumber is the reciprocal of the wavelength of the wave. This tells you how many wavelengths fit into a unit of distance. It is analogous to frequency, which tells you how often a wave completes a cycle per unit of time (for a traveling wave, this is how many complete wavelengths pass a given point per second).
The standard scientific (SI) unit of distance is the meter (m), but in many cases wavelengths may be expressed in centimeters (cm) or other units. The wavelength is given the symbol λ, and the wavenumber is given the symbol k. It is defined by:
The wavenumber has units of 1/distance, or distance−1. For wavelengths expressed in meters, this is m−1, and if the wavelength is expressed in cm, the units of the wavenumber are cm−1.
Converting From Wavenumber to Wavelength
The definition of a wavenumber is quite simple, and it only depends on the wavelength. Converting from a wavenumber to a wavelength is a straightforward process. You can convert wavenumbers to wavelength using the formula:
So if you have a wavenumber (k), divide 1 by this number to get the wavelength. Using a wavenumber of 100 m−1 as an example, the wavelength is:
The wavelength of this is 1 cm. If this wavelength represents electromagnetic radiation, it would be a microwave, just beyond the infrared spectral region.
Getting the Right Units
Wavenumbers may be expressed in different units, notably cm−1. If you have a wavenumber in a different unit, you can convert it to a wavelength in the same way as in the previous section. The only difference is that the wavelength you’ll end up with will be in a different unit. If the wavenumber was expressed in cm−1, the resulting wavelength will be in cm. If the wavenumber was expressed in nm−1 (nanometers−1), then the wavelength will be in nm.
If you need your answer in a specific unit, convert your resulting wavelength into the required unit. In general, to change to a smaller unit of measurement, you multiply by the conversion factor (the number of smaller units per bigger unit). To change to a bigger unit of measurement, divide by the conversion factor.
For example, if you get a result in meters and you need it in nanometers, multiply the result in meters by 1,000,000,000 (or 109). To convert from nanometers to meters, you divide the result by 1,000,000,000. If you get a result in centimeters, but need it in meters, divide your result by 100. To convert from meters to centimeters, multiply your result by 100. You can use a conversion chart or an online converter to do this if you’re unsure.
- In some areas of physics (such as geophysics), you might encounter an “angular wavenumber.” This is very similar to wavenumber, except it’s multiplied by 2π, so it describes rotations or oscillations. The unit of an angular wavenumber is radians per meter. To convert an angular wavenumber to a wavelength, divide 2π by the angular wavenumber.
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By Lee Johnson
Waves can describe sound, light or even the wavefunction of particles, but every wave has a wavenumber. This describes how it varies through space, and this depends crucially on the wavelength of the wave or its speed and frequency. For physics or chemistry students, learning to calculate a wavenumber forms a vital part of mastering the subject. The good news is that there is a simple formula for the wavenumber, and you need only very basic information about the wave to calculate it.
TL;DR (Too Long; Didn't Read)
Use the equation:
ν= 1 / ?
= f / v
To calculate the spatial wavenumber (ν), noting that ? means wavelength, f means frequency and v means the speed of the wave.
Use the equation:
Wavenumber To Wavelength Conversion Table
k = 2π / ?
= 2π_f_ / v
To calculate angular wavenumber (k).
Wavenumber To Wavelength Conversion Calculator
What Is a Wavenumber?
Physicists and chemists use two different types of wavenumber – either the spatial wavenumber (often called spatial frequency) or the angular wavenumber (sometimes called the circular wavenumber). The spatial wavenumber tells you the number of wavelengths per unit distance, whereas the angular wavenumber tells you the number of radians (a measure of angle) per unit distance. Generally speaking, angular wavenumber is used in physics and geophysics, whereas spatial wavenumber is used in chemistry. Essentially, the equations are the same except the angular wavenumber uses 2π as the numerator, because this is the number of radians in a whole circle (equivalent to 360°).
Wavenumber To Wavelength Conversion Formula
Find the Information You Need About the Wave
Choose the Right Form of the Equation
Calculate the Wavenumber
Find the wavelength of the wave before calculating the angular or spatial wavenumber. Both quantities depend only on the wavelength, denoted by the symbol λ, and you can even read this directly from a visual representation of the wave as the distance between successive “peaks” or “troughs” of the wave.
If you don’t have the wavelength, you can use the relationship:
Where v stands for the speed of the wave and f stands for its frequency. This means you can calculate the wavenumber with a frequency and a speed, noting that for light waves, the speed is always v = c = 2.998 × 108 meters per second.
Use the following relationship to calculate the spatial wavenumber (represented here by ν, although other symbols are sometimes used):
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= f / v
Where the first definition simply represents the reciprocal of the wavelength, and the second expresses this as the frequency divided by the speed of the wave. Wavenumbers have units of length−1, e.g., for meters (m), this would be m−1. Gnuradio windows binary.
For the angular wavenumber (denoted by k), the formula is:
= 2π_f_ / v
Where again the first uses wavelength and the second translates this into a frequency and a speed.
Calculate the wavenumber using the appropriate equation. For a light wave with a wavelength of 700 nanometers or 700 × 10−9 m, representing red light, the calculation of angular wavenumber is:
= 2π / (700 × 10−9 m)
≅ 8.98 × 106 m−1
For a sound wave, with a frequency of 200 Hz and a speed of 343 meters per second (m s−1), the calculation of spatial wavenumber gives:
= 200 Hz / 343 m s−1