An equation of a simple harmonic progressive wave is given by \(y=A \sin (100 \pi t-3 x)\). The distance between two particles having a phase difference of \(\left(\frac{\pi}{18}\right)\) in meter is

The correct option is (B).
Concept: The phase difference given \(\phi=\left(\frac{\pi}{3}\right)\), so we can obtain the distance between two particles by using the path difference:
\(\mathrm{k}\left(\mathrm{x}_2-\mathrm{x}_1\right)=\phi\)
Where, \(\mathrm{k}\) is the propagation constant.
The general equation of the wave is given by \(\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})\) on comparing with the given equation, \(\mathrm{k}=3\) and \(\omega=100 \pi\).
Therefore, the distance between two particles is given by,
\(\left(\mathrm{x}_2-\mathrm{x}_1\right)=\frac{\phi}{\mathrm{k}}=\frac{\pi}{9} \mathrm{~m}\)