Question

When interference is produced by two progressive waves of equal frequencies, then the maximum intensity of the resulting sound are N times the intensity of each of the component waves. The value of N is

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

Answer: (C)

4

$y_1=A_0\sin \omega t$,

$y_2=A_0\sin \omega t+\varphi$,

also, $I\propto y^2={(y_1+y_2)}^2={\left(2A_0\sin \omega t+\varphi /2\cos \varphi /2\right)}^2=4{A_0}^2{\left(\sin \omega t+\varphi /2\right)}^2{\left(\cos \varphi /2\right)}^2$,