Question

Two waves of the same frequency and amplitude superpose to produce a resultant disturbance of the same amplitude. The phase difference between the waves is $\frac{x}{y}\pi$. Find $(x+y)$.

Answer 1

$A_1=A,A_2=A,A_R=A$
$A_R^2=A_1^2+A_2^2+2A_1{A}_2\cos \varphi$
$A^2=A^2+A^2+2A^2\cos \varphi$
$\cos \varphi =-\frac{1}{2}\Rightarrow \varphi ={120}^{\circ }=\frac{2\pi }{3}$
Comparing it with $\frac{x}{y}\pi$, we get
$(x+y)=5$
Final answer: $\left(5\right)$