Q. If $\lambda_{1},\lambda_{2},\lambda_{3}$ are the wavelengths of the waves giving resonance with the fundamental, first and second overtones respectively of a closed organ pipe, then the ratio of $\lambda_{1},\lambda_{2},\lambda_{3}$ is
A) 1:3:5
B) 1:2:3
C) 5:3:1
D) $1:\frac{1}{3}:\frac{1}{5}$
Explanation
(d) As is clear from figure
[image:15_image77.emf]
$l = \frac{\lambda_{1}}{4},\ \lambda_{2} = 4l$
$l = \frac{3\lambda_{2}}{4},\ \lambda_{2} = \frac{4l}{3}$
$l = \frac{5\lambda_{3}}{4},\ \lambda_{3} = \frac{4l}{5}$
$\therefore\ \ \ \ \lambda_{1}:\lambda_{2}:\lambda_{3} = 1:\frac{1}{3}:\frac{1}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.