Two waves are simultaneously passing through a string and their equations are: y_1= A_1 sin k (x- vt ), y_2= A_2 sin k (x- vt +x_0). Given amplitudes…

Two waves are simultaneously passing through a string and their equations are : $\displaystyle y_1=\mathrm{A}_1 \sin \mathrm{k}(x-\mathrm{vt}), y_2=\mathrm{A}_2 \sin \mathrm{k}\left(x-\mathrm{vt}+x_0\right)$. Given amplitudes $\displaystyle \mathrm{A}_1=12 \mathrm{~mm}$ and $\displaystyle \mathrm{A}_2=5 \mathrm{~mm}$, $\displaystyle x_0=3.5 \mathrm{~cm}$ and wave number $\displaystyle \mathrm{k}=6.28 \mathrm{~cm}^{-1}$. The amplitude of resulting wave will be \_\_\_\_ mm.