The displacement of a string is given by 

$y(x,t)=0.06\sin \left(\frac{2\mathrm{\pi }x}{3}\right)\cos \left(120\mathrm{\pi }t\right)$ where x and y are in metre and t in second. The length of the string is 1.5 m and its mass is $3.0\times {10}^{-2}\mathrm{kg}.$

Given equation is $y(x,t)=0.06\sin \left(\frac{2\mathrm{\pi }x}{3}\right)\cos \left(120\mathrm{\pi }t\right)$

(i) Comparing with a standard equation of stationary wave

    $y (x , t) = a\sin \left(kx\right) \cos \left(\omega t\right)$

    Clearly, the given equation belongs to stationary wave.

     Hence, option (i) is not correct.

(ii) By comparing,

     $$\begin{gathered} \omega =120\mathrm{\pi } \\ \Rightarrow 2\mathrm{\pi }f =120\mathrm{\pi } \\ \Rightarrow f =60\mathrm{Hz} \end{gathered}$$

(iii)  $k=\frac{2\pi }{3}=\frac{2\pi }{\lambda }$

     $\Rightarrow \lambda = \mathrm{wavelength} = 3 \mathrm{m}$

     Frequency $= f =60 Hz$

    Speed $= v = f\lambda = (60 \mathrm{Hz}) (3 \mathrm{m}) = 180 \mathrm{m}/\mathrm{s}$

(iv) Since in stationary wave, all particles of the medium execute SHM with varying amplitude nodes.