The equations of two waves are given by :

$y_1=5\sin 2\pi \left(x-vt\right) \mathrm{cm}$

$y_2=3\sin 2\pi \left(x-vt+1.5\right) \mathrm{cm}$

These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Given equations can be written as,

$y_1=5\sin \left(2\pi x-2\pi vt\right) \mathrm{cm}$ and

$y_2=3\sin \left(2\pi x-2\pi vt+3\pi \right) \mathrm{cm}$

From the given equations we can conclude that the phase difference between the waves is $3\pi$ i.e. odd multiple of $\pi$. Therefore, destructive interference will happen.

$A=\left|A_1-A_2\right|=2 \mathrm{cm}$