Question

Two loudspeakers are emitting sound waves of wavelength $\lambda$ with an initial phase difference of $\pi /2$ as shown in the given figure. At what minimum distance from O on line AB, will one hear a maxima?

• A. $25\lambda$
• B. $\frac{100\lambda }{\sqrt{15}}$
• C. $\frac{25\lambda }{3}$
• D. $50\lambda$

Answer 1

The correct option is C $\frac{25\lambda }{3}$

$\Delta \varphi =2n\pi$
$\Rightarrow \frac{\pi }{2}+\frac{2\pi }{\lambda dsin\theta }=2n\pi$
$\frac{2\pi }{\lambda dsin\theta }=(2n-\frac{1}{2}\pi )$
$sin\theta =(2n-\frac{1}{2}\frac{\lambda }{2d}=\frac{1}{2\times \lambda (2\times 3\lambda )}=\frac{1}{12}$
$\Rightarrow \frac{y}{\sqrt{100{\lambda }^2}}=\frac{1}{12}$
$144y^2=(100\lambda {)}^2$
$y\approx \frac{100\lambda }{12}=\frac{25\lambda }{3}$