The particle displacement in a wave is given by

$y=0.2\times {10}^{–5}\cos (500t–0.025x)$

where the distances are measured in meters and time in seconds. Now

Following are equations of four waves :

(i) $y_1=a\sin \mathrm{\omega }\left(t-\frac{\mathit{x}}{\mathit{\nu }}\right)$ (ii) $y_2 =a\cos \mathrm{\omega }\left(t+\frac{\mathit{x}}{\mathit{\nu }}\right)$ (iii) $z_1 =a\sin \mathrm{\omega }\left(t-\frac{\mathit{x}}{\mathit{\nu }}\right)$ (iv) $z_2 =a\cos \mathrm{\omega }\left(t+\frac{\mathit{x}}{\mathit{\nu }}\right)$

Which of the following statements is/are correct?

The vibrations of a string of length $600 \mathrm{cm}$ fixed at both ends are represented by the equation

$y= 4 \sin \left(\mathrm{\pi } \frac{x}{15}\right) \cos (96 \mathrm{\pi }t)$

where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in seconds.