b
Transverse wave equation 

\(y=a \sin (\omega t+k x)\)

Next crest appears at time interval of \(0.4 \mathrm{s}\)

So, the time period \(T=0.4\)

\(\therefore\) Angular Frequency \(\omega=\frac{2 \pi}{T}=\frac{2 \pi}{0.4}\)

\(\therefore\) Speed of the particle

\(\nu=\frac{d y}{d t}=a \omega \sin (\omega t+k x)\)

\(\nu_{\max }=a \omega\)

\(a=1 / 2 c m\)

\(=\frac{1}{2} \times \frac{2 \pi}{0.4}=\frac{2 \pi}{8} \times 10\)

\(=\frac{5 \pi}{2} \mathrm{cm} / \mathrm{s}\)