A wave is represented by the equation $\mathrm{y}=\mathrm{Asin}(10\mathrm{\pi x}+15\mathrm{\pi t}+\mathrm{\pi }/3)$ where x is in metre and t is in second. The expression represents

The equation of a plane wave moving in negative x-direction is given by
$$\begin{gathered} \mathrm{y}=\mathrm{Asin}\left[\frac{2\mathrm{\pi }}{\mathrm{\lambda }}(\mathrm{vt}+\mathrm{x})+\mathrm{\varphi }\right] \\ \mathrm{Comparing} \mathrm{the} \mathrm{given} \mathrm{equation} \mathrm{with} \mathrm{standard} \mathrm{equation}, \mathrm{we} \mathrm{have} \\ \frac{2\mathrm{\pi }}{\mathrm{\lambda }}=10\mathrm{\pi }\text{ and }\frac{2\mathrm{\pi }}{\mathrm{\lambda }}\mathrm{v}=15\mathrm{\pi } \\ \therefore \mathrm{\lambda }=\frac{2}{10}=0\cdot 2\mathrm{m} \\ \mathrm{and} \mathrm{V}=\frac{15\mathrm{\pi \lambda }}{2\mathrm{\pi }}=\frac{15\times 0\cdot 2}{2}=1\cdot 5\mathrm{m}/\mathrm{s} \\ \mathrm{Hence} \left(2\right) \mathrm{and} \left(3\right) \mathrm{are} \mathrm{correct}. \end{gathered}$$