Two travelling waves produces a standing wave represented by equation.

      $\mathrm{y}=1.0 \mathrm{mm} \cos \left(1.57 {\mathrm{cm}}^{-1}\right) \mathrm{x} \sin \left(78.5 {\mathrm{s}}^{-1}\right)\mathrm{t}.$

The node closest to the origin in the region x > 0 will be at x is ……… cm.

Equation of standing wave is given by

        $\mathrm{y}=1.0 \cos (1.57) \mathrm{x} \sin (78.5) \mathrm{t}$

Comparing above equation with standard equation of wave given as

       $\begin{array}{l}\mathrm{y}=2\mathrm{A} \cos \mathrm{k} \mathrm{x} \sin \mathrm{\omega t}\\ \mathrm{k}=1.57, 2\mathrm{A}=1\Rightarrow \mathrm{A}=0.5\end{array}$

For node,

$$\begin{gathered} \cos \mathrm{kx}=0 \\ \Rightarrow \mathrm{kx}=\frac{\mathrm{\pi }}{2} \\ \Rightarrow \left(1.57\right)\mathrm{x}=\frac{\mathrm{\pi }}{2} \\ \Rightarrow \mathrm{x}=\frac{\mathrm{\pi }}{3.14}\mathrm{cm} \\ \Rightarrow \mathrm{x}=\frac{3.14}{3.14}\mathrm{cm} \\ \Rightarrow \mathrm{x}=1 \mathrm{cm} \end{gathered}$$