a
The standard equation of a wave travelling along \(+ve \) \(x -direction\) is given by

\(y=A \sin (k x-\omega t)\)

where

\(A=\) Amplitude of the wave

\(k=\) angular wave number

\(\omega=\)angular frequency of the wave

Given: \(A=1 \mathrm{m}, \lambda=2 \pi \mathrm{m}, \quad v=\frac{1}{\pi} \mathrm{Hz}\)

As \(\quad k=\frac{2 \pi}{\lambda}=\frac{2 \pi}{2 \pi}=1\)

\(\omega=2 \pi v=2 \pi \times \frac{1}{\pi}=2\)

\(\therefore\) The equation of the given wave is

\(y=1 \sin (1 x-2 t)=\sin (x-2 t)\)