Question

Among two interfering sources, let sound waves from source $S_1$, be ahead of the phase by ${90}^{\circ }$ relative to that of $S_2$. At an observation point $P$, if $P{S}_1-P{S}_2=1.5\lambda$, then the phase difference between the waves from $S_1$ and $S_2$ reaching $P$ is

• A. $3\pi$
• B. $\frac{5\pi }{2}$
• C. $\frac{7\pi }{2}$
• D. $4\pi$

Answer 1

The correct option is B $\frac{5\pi }{2}$

Initial phase difference,
$\Delta {\Phi }_1=\frac{\pi }{2}={90}^{\circ }.....\left(1\right)$
path difference, $\Delta x=P{S}_1-P{S}_2=1.5\lambda$


Thus the phase difference arised due to path difference is,
$\Delta {\Phi }_2=k\Delta x$
$\Delta {\Phi }_2=\frac{2\pi }{\pi }\times \Delta x$
Or, $\Delta {\Phi }_2=\frac{2\pi }{\lambda }\times 1.5\lambda =3\pi$
Now, the phase difference between the waves from $S_1$ and $S_2$ reaching $P$ is
$\Delta {\Phi }_{\text{net}}=\Delta {\Phi }_2-\Delta {\Phi }_1$
$\Rightarrow \Delta {\Phi }_{\text{net}}=3\pi -\frac{\pi }{2}$
Or, $\Delta {\Phi }_{\text{net}}=\frac{5\pi }{2}$