Physics - Sound Wave Question with Solution | TestHub

The phase difference $\varphi$ is related to the path difference $\Delta x$ by the formula:

$\varphi =\frac{2\pi }{\lambda }\Delta x$

Substituting $\Delta x=\frac{\lambda }{4}$:

$\varphi =\frac{2\pi }{\lambda }\times \frac{\lambda }{4}=\frac{\pi }{2}$

The resultant amplitude $A_R$ of two interfering waves of amplitudes $A_1$ and $A_2$ is given by:

$A_R=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \varphi }$

Given $A_1=A_2=A$ and $\varphi =\frac{\pi }{2}$:

$A_R=\sqrt{A^2+A^2+2A^2\cos \left(\frac{\pi }{2}\right)}$

Since $\cos \left(\frac{\pi }{2}\right)=0$:

$A_R=\sqrt{2A^2}=\sqrt{2}A$

Answer: $\sqrt{2}A$