The equation of a simple harmonic wave is given by $\mathrm{y}=5\sin \frac{\mathrm{\pi }}{2}(100\mathrm{t}-\mathrm{x})$ , where x and y are in metre and time is in second. The period of the wave in second will be

The given equation is $\mathrm{y}=5\sin \frac{\mathrm{\pi }}{2}(100\mathrm{t}-\mathrm{x})$

Comparing Eq. (i) with standard wave equation, given by $\mathrm{y}=\mathrm{Asin} (\mathrm{\omega t}-\mathrm{kx})$ ........(ii) We have  

$\mathrm{\omega }=\frac{100\mathrm{\pi }}{2}=50\mathrm{\pi }\Rightarrow \frac{2\mathrm{\pi }}{\mathrm{T}}=50\mathrm{\pi }\Rightarrow \mathrm{T}=\frac{2\mathrm{\pi }}{50\mathrm{\pi }}=0.04\mathrm{s}$