Question

$S_1,S_2$ are coherent sources (having initial phase difference zero) of sound located along $x-$axis separated by $4\lambda$ where $\lambda$ is the wavelength of sound emitted by them. The number of maxima located on the elliptical boundary, will be:

• A. $16$
• B. $12$
• C. $8$
• D. $4$

Answer 1

The correct option is A $16$

For maximum intensity,
the path difference $x=n\lambda$
Where $n$ is integer $i.e.,0,1,2,\mathrm{3......})$
From geometry:- $\begin{array}{c}\Delta xatc=0\\ \&\Delta xatA=4\lambda \end{array}\}\left(1\right)$

So at any general point between $A\&C$ (on the boundary of the ellipse) the value of $\Delta x$ will be between $0\text{and}4\lambda$
For maxima between $A\&C$ we will get the points
For $\begin{array}{c}\Delta x=\lambda \\ \Delta x=2\lambda \\ \Delta x=3\lambda \end{array}\}$
$\Rightarrow$ On one quadrant of the ellipse, there'll be four maxima.

So, total maxima on the boundary of the ellipse will be $=4\times 4=16$

Hence, $\left(A\right)$ is the correct answer.