Question

If 20 waves are present in 1 cm, what is the wavenumber of the wave?
A. 20 $m^{-1}$
B. 200 $m^{-1}$
C. 2000 $m^{-1}$
D. 10 $m^{-1}$

Answer 1

Wavenumber is a quantity defined as inverse of a wavelength. Wavelength is defined as the length between two successive crests (or troughs) of a wave. The quantities should be determined in terms of standard units.

Formula used:
The relation between the wavelength and the wave number for a certain wave is written as:
$\bar{\nu} = \dfrac{1}{\lambda}$

Complete step by step answer:
The wavelength for the given case; when 20 waves are present in 1cm, comes to be:
$\lambda = \dfrac{1}{20}$cm.
When we convert this to meters we get:
$\lambda = \dfrac{10^{-2}}{20}$m

The wavenumber comes out to be:
$\bar{\nu} = \dfrac{1}{\lambda} \dfrac{20}{10^{-2} m} = 2000 m^{-1}$.

Therefore the correct answer is option (C).

Additional information:
A wave is defined as a disturbance that propagates can carries energy or information from some source creating this wave to the required destination. A wave is basically characterized with the help of frequency, wavelength and amplitude. There can be two types of waves longitudinal or transverse. A longitudinal wave (like sound) requires a medium for propagation, while a transverse wave (like light) does not.
Frequency is the temporal rate of the given waves i.e., it is the number of wavelengths in unit time whereas wavenumber gives the spatial rate of the waves i.e., it is the number of waves in unit distance.

Note:
Another simple way of doing the same question is to consider another definition as wave number is also defined as the number of waves present in unit length or the complete cycles present in unit length. We are already given the wavenumber to be 20 waves per centimetre. On replacing centimetre with metre we get the required answer.