Two waves are simultaneously passing through a string and their equations are $y_1=A_1 \sin k(x-v t), y_2=A_2 \sin k\left(x-v t+x_0\right)$. Given amplitudes $A_1=12 m m$ and $A_2=5 m m$, $\mathrm{x}_0=3.5 \mathrm{~cm}$ and wave number $\mathrm{k}=6.28 \mathrm{~cm}^{-1}$. The amplitude of resulting wave will be $\_\_\_\_$ mm .