Q. Two speakers connected to the same source of fixed frequency are placed $2.0\ m$ apart in a box. A sensitive microphone placed at a distance of $4.0m\ $from their midpoint along the perpendicular bisector shows maximum response$.$ The box is slowly rotated until the speakers are in line with the microphone. The distance between the midpoint of the speakers and the microphone remains unchanged. Exactly five maximum responses are observed in the microphone in doing this. The wavelength of the sound wave is
A) $0.2\ m$
B) $0.4\ m$
C) $0.6\ m$
D) $0.8\ m$
Explanation
(b) Initially $S_{1}M = S_{2}M$
$\Rightarrow$ Path Difference $(\mathrm{\Delta}x) = S_{1}M - S_{2}M = 0$
[image:15_image47.png]
Finally when the box is rotated
Path Difference $= S_{1}M^{''''''''} - S_{2}M^{''''''''} \Rightarrow \mathrm{\Delta}x = 5 - 3 = 2m$
[image:15_image48.png]
For maxima
Path Difference = (Even multiple) $\frac{\lambda}{2} \Rightarrow \Delta x = (2n)\frac{\lambda}{2}$
For 5 maximum responses
$\Rightarrow 2 = 2(5)\frac{\lambda}{2}\ \left\{ \because\mathrm{\Delta}x = (2n)\frac{\lambda}{2} \right\} \Rightarrow \lambda = \frac{2}{5} = 0.4m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.