Question

Two sound sources of sound are placed along the diameter of a circle of radius $R(R>>4\lambda )$ How many minima will be heard as one moves along the perimeter of circle?

• A. $16$
• B. $12$
• C. $4$
• D. $8$

Answer 1

The correct option is A $16$

In this figure $S_1$ and $S_2$ are sound sources.
$S_1{S}_2=4\lambda$
$\therefore \Delta x=S_{2}P-S_{1}P=4\lambda sin\theta$
For minima $\Delta x=(2n+1)\frac{\lambda }{2}$
$\therefore 4\lambda sin\theta =(2n+1)\frac{\lambda }{2}$
$\Rightarrow sin\theta =\frac{2n+1}{8}$
$n=0;sin\theta =\frac{1}{8}\Rightarrow \theta =si{n}^{-1}\left(\frac{1}{8}\right)$
$n=t;sin\theta =\frac{3}{8}\Rightarrow \theta =si{n}^{-1}\left(\frac{3}{8}\right)$
$n=2;sin\theta =\frac{5}{8}\Rightarrow \theta =si{n}^{-1}\left(\frac{5}{8}\right)$
$n=3;sin\theta =\frac{7}{8}\Rightarrow \theta =si{n}^{-1}\left(\frac{7}{8}\right)$
For $n=4;sin\theta >1$ it is impossible
In quarter circle, 4 minima are heared, in entire circle total number of minima will be 16.