What is the phase difference between particle F and the origin?

The phase difference ($\Delta \phi$) between two points in a wave is a measure of how much one point is "ahead" or "behind" the other in its oscillation cycle. It is directly proportional to the distance between the points (path difference) and inversely proportional to the wavelength ($\lambda$).

The formula for the phase difference between two points separated by a distance $x$ is:

where:

• $\Delta \phi$ is the phase difference in radians.
• $x$ is the path difference (distance between the two points).
• $\lambda$ is the wavelength of the wave.

The question states that the particle F is at a distance $X$ from the origin (0). Therefore, the path difference $x$ in our formula is $X$.

Substituting $X$ for $x$ in the phase difference formula:

The calculated phase difference matches option A.

The final answer is $\text{A}$.