Question

Two loudspeakers are emitting sound waves of wavelength $\lambda$ with an initial phase difference of $\frac{\pi }{2}$. At what minimum distance from O on line AB will one hear a maxima?

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

Answer 1

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

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