Explanation:
The given equation of \(SHM\) wave is
\(\begin{aligned}& y=0.03 \sin \pi(2 t-0.01 x) m \\& y=0.03 \sin (2 \pi t-0.01 \pi x) m\end{aligned}\)
Comparing it with general equation, we get
\(y=a \sin (\omega t-k x)\)
where, \(k=\dfrac{2 \pi}{\lambda} \Rightarrow \lambda=200 m\)
The phase difference between two particles is given by
\(\Delta \phi = kx = \frac{{2\pi }}{\lambda } \times x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
here, \(x = 25\;m\)
Substituting the values of \(x\) and \(\lambda\) in eq.(1), we get
\(\Delta \phi = \frac{{2\pi }}{{200}} \times 25 = \frac{\pi }{4}\,rad\)