The graph between wave number `(vecv)` and angular frequency (`omega`) is

Options

A.
B.
C.
D.

Explanation

To solve the problem of finding the graph between wave number (ν) and angular frequency (ω), we can follow these steps:

### Step 1: Understand the relationship between wave number, angular frequency, and speed of light
The speed of light (C) is related to the angular frequency (ω) and the wavelength (λ) by the equation:
\[ C = \omega \cdot \lambda \]

### Step 2: Relate wavelength to wave number
The wave number (ν) is defined as the reciprocal of the wavelength:
\[ \nu = \frac{1}{\lambda} \]
Thus, we can express the wavelength in terms of wave number:
\[ \lambda = \frac{1}{\nu} \]

### Step 3: Substitute the expression for wavelength into the speed of light equation
Substituting λ in the speed of light equation gives:
\[ C = \omega \cdot \frac{1}{\nu} \]
Rearranging this equation leads to:
\[ \omega = C \cdot \nu \]

### Step 4: Identify the relationship between ω and ν
From the equation \( \omega = C \cdot \nu \), we see that angular frequency (ω) is directly proportional to wave number (ν). This indicates a linear relationship.

### Step 5: Determine the graph
In a graph where the x-axis represents wave number (ν) and the y-axis represents angular frequency (ω), the equation \( \omega = C \cdot \nu \) suggests that the graph will be a straight line passing through the origin. The slope of this line will be equal to the speed of light (C).

### Conclusion
The graph between wave number (ν) and angular frequency (ω) is a straight line with a slope equal to the speed of light (C).

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