Q. A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude $\rho_{0}$ inside the tube. If the atmospheric pressure is $\rho_{A},$ then the ratio of maximum and minimum pressure at the closed end of the tube will be
A) $\frac{(\rho_{A} + \rho_{0})}{(\rho_{A} - \rho_{0})}$
B) $\frac{(\rho_{A} + 2\rho_{0})}{(\rho_{A} - 2\rho_{0})}$
C) $\frac{\rho_{A}}{\rho_{0}}$
D) $\frac{\left( \rho_{A} + \frac{1}{2}\rho_{0} \right)}{\left( \rho_{A} - \frac{1}{2}\rho_{0} \right)}$
Explanation
(a) Maximum pressure at closed end will be atmosphere pressure adding with acoustic wave pressure
So $\rho_{\max} = \rho_{A} + \rho_{0}$ and $\rho_{\min} = \rho_{A} - \rho_{0}$
Thus $\frac{\rho_{\max}}{\rho_{\min}} = \frac{\rho_{A} + \rho_{0}}{\rho_{A} - \rho_{0}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.