The equations of two waves are given by 
$\begin{array}{l}{y}_1=5 \sin 2\mathrm{\pi }(x-vt)cm\\ y_2=3 \sin 2\pi (x-vt+1.5)cm\end{array}$                                                     
These waves are simultaneously passing through a string. The amplitude of the resulting wave is 
 

Equations of the two waves are given as 

$\begin{array}{l}{y}_1=5\sin 2\pi (x-vt)cm\\ \therefore Amlitude,A_1=5cm\\ and{y}_2=3\sin 2\pi (x-vt+1.5)cm\\ \therefore A_2=3cm\\ Phasedifferencebetweenwaves{y}_{1}and{y}_{2}isgivenas\\ △\varphi =2\pi \left(1.5\right)=3\pi \\ A=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos (△\varphi )}\\ =\sqrt{A_1^2+A_2^2+2A_1{A}_2(-1)}[\therefore \cos 3\pi =\cos \pi =-1]\\ =\sqrt{{(A_1-A_2)}^2}\\ =A_1-A_2\\ =5-3=2cm\end{array}$