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