\(y=2 A \sin k x \cdot \cos \omega t\)

In a standing waves the function of amplitude \(\left(A_y\right)\) is given by \(A_y=2 A \sin k x\)

At mid-point of node and antinode \(x=\frac{\lambda}{8}\)

\(A_y=2 A \sin \frac{2 \pi}{\lambda} \times \frac{\lambda}{8}\left[k=\frac{2 \pi}{\lambda}\right]\)

\(\text { or } A_y=\frac{2 A}{\sqrt{2}}\)

\(\therefore A_y=\sqrt{2} A\)

Frequency is same at all points \(=\frac{\omega}{2 \pi}\)