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

\(\frac{d y}{d t}=A \omega \cos (\omega t-k x)\)

Take \(x=0\) and \(x=x_1\)

\(v_1=A \omega \cos (\omega t)\)

\(v_2=A \omega \cos (\omega t+k x)\)

\(\left|v_1\right|=\left|v_2\right|\)

\(|\cos (\omega t)|=|\cos (\omega t+k x)|\)

\(\therefore k x=\frac{\pi}{2}\)

or \(x=\frac{\lambda}{4}\)