Physics - Sound Wave Question with Solution | TestHub

In this figure${\mathrm{S}}_1$and${\mathrm{S}}_2$are sound sources.



${\mathrm{S}}_1{\mathrm{S}}_2=4\mathrm{\lambda }$

$\therefore \Delta x={\mathrm{S}}_2\mathrm{P}-{\mathrm{S}}_1\mathrm{P}=4\lambda \mathrm{s}\mathrm{i}\mathrm{n}\theta$

For minima$\Delta x=(2n+1)\frac{\lambda }{2}$

$\therefore 4\lambda \mathrm{s}\mathrm{i}\mathrm{n}\theta =(2n+1)\frac{\lambda }{2}$

$\Rightarrow \mathrm{s}\mathrm{i}\mathrm{n}\theta =\frac{(2n+1)}{8}$

$n=0;$$\mathrm{s}\mathrm{i}\mathrm{n}\theta =\frac{1}{8}\Rightarrow \theta ={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}\left(\frac{1}{8}\right)$

$n=1;\mathrm{s}\mathrm{i}\mathrm{n}\theta =\frac{3}{8}\Rightarrow \theta ={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}\left(\frac{3}{8}\right)$

$n=2;\mathrm{s}\mathrm{i}\mathrm{n}\theta =\frac{5}{8}\Rightarrow \theta ={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}\left(\frac{5}{8}\right)$

$n=3;\mathrm{s}\mathrm{i}\mathrm{n}\theta =\frac{7}{8}\Rightarrow \theta ={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}\left(\frac{7}{8}\right)$

For$n=4;\mathrm{s}\mathrm{i}\mathrm{n}\theta >1$it is impossible

In the quarter circle,$4$minima are heard, in the entire circle total number of minima will be$16$.