Wave number is

Options

A. `lamda `
B. `1/ lamda `
C. `(c )/(lamda)`
D. ` lamda xx v `

Answer

**Step-by-Step Solution:**

1. **Understanding Wave Number**:
The wave number is defined as the number of waves per unit distance. Specifically, it is the number of waves that fit into one centimeter of light.

2. **Mathematical Definition**:
The wave number (denoted as \( \tilde{\nu} \)) is mathematically expressed as the reciprocal of the wavelength (\( \lambda \)):
\[ \tilde{\nu} = \frac{1}{\lambda} \]
where \( \lambda \) is the wavelength of the light.

3. **Relationship with Frequency**:
The frequency (\( \nu \)) of a wave is related to its wavelength and the speed of light (\( c \)) by the equation:
\[ \nu = \frac{c}{\lambda} \]
Rearranging this gives us:
\[ \lambda = \frac{c}{\nu} \]

4. **Substituting into Wave Number**:
By substituting the expression for \( \lambda \) into the wave number formula, we get:
\[ \tilde{\nu} = \frac{1}{\lambda} = \frac{\nu}{c} \]
This shows that the wave number can also be expressed in terms of frequency and the speed of light.

5. **Conclusion**:
Therefore, the wave number is defined as the reciprocal of the wavelength and can also be expressed as the ratio of frequency to the speed of light.

**Final Answer**: The wave number is defined as \( \tilde{\nu} = \frac{1}{\lambda} \) and can also be expressed as \( \tilde{\nu} = \frac{\nu}{c} \).

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