# Wave Number --- How is it defined?

#### logearav

Joined Aug 19, 2011
243
Wavenumber is defined number of waves contained in unit distance. Mathematically wave number is 1/λ and also going by the formula
c = nλ,
1/λ is n/c. Going by this formula, n is frequency and c is speed of sound in vacuum that is 3X10^8 m.
Can we define wavenumber as number of waves produced in a distance of 3X10^8 metre?
In my exam, i had this question
Wave number is defined as number of waves
1)produced in one second
2)produced in a distance of 3*10^8 metre
3)produced in a distance of λ metre
4)produced in a distance of 1 metre.
I think both 2) and 4) are correct. Am i right?

#### mikeleeson

Joined Aug 22, 2012
26
Wavenumber is a measure of SPATIAL frequency: number of cycles in a given length. It is analogous to the common term 'frequency' which is a TEMPORAL frequency: number of cycles in a given time.
So the answer is given by your first sentence "..number of waves contained in unit distance".
In the SI system of units, the unit length is 1 metre - so answer 4 is correct.
Answer 1 gives you the temporal frequency in cycles per second [Hz].
Answer 2 gives you a number that is proportional to the wavenumber, but is wrong by a factor of 3x10E8 if you are using SI units.
Answer 3 gives you a value of 1; always.

I hope this is of some help.