1Which of these has the same dimensions as wave number?
Wave number and Rydberg constant both have the dimensions [L⁻¹].
Oscillations and wavesClass 11, Waves
Dimensional formula of Wave number
[L-1]
Waves per unit length, or 2π over the wavelength in the angular version. Both have one over length.
How to get the dimensional formula of wave number
- Start from the definition: wave number = 1 / wavelength.
- wavelength = length, so wavelength is [L] = [L].
- Put in the dimension of each part: 1 / [L].
- Add the powers of each base quantity: [L-1].
Quantities with the dimensions [L⁻¹]
Equal dimensions do not make them the same quantity. Compare wave number with the others in the full grid.
Three questions on wave number
2What is the SI unit of wave number?
The SI unit of wave number is the per metre (m⁻¹).
3Which one has different dimensions from the others?
Intensity of a wave is [M T⁻³]. The other three are all [L⁻¹].
An equation that uses wave number
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
y = A sin(ω t - k x)y[L]=A sin(omega t - k x)[L]Dimensionally consistentEvery term is [L]
y = displacementω = angular frequencyt = timex = displacement
Wave number: quick answers
What is the dimensional formula of wave number?
The dimensional formula of wave number is [L⁻¹]. It comes from wave number = 1 / wavelength.
What is the SI unit of wave number?
The SI unit of wave number is the per metre (m⁻¹).
Which quantities have the same dimensions as wave number?
Wave number shares [L⁻¹] with power of a lens, Rydberg constant. Equal dimensions do not make them the same quantity.