Question

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. $\frac{\rho_{A}}{\rho_{A}}$
• D. $\frac{\left( \rho_{A} + \frac{1}{2}\rho_{0} \right)}{\left( \rho_{A} - \frac{1}{2}\rho_{0} \right)}$

Answer 1

Answer: (A)

$\frac{(\rho_{A} + \rho_{0})}{(\rho_{A} - \rho_{0})}$

Answer 2

Maximum pressure at closed end will be atmospheric pressure adding with acoustic wave pressure

So ${\rho A_{0}}_{\max}$ and ${\rho A_{0}}_{\min}$

Thus $\frac{\rho_{\max}}{\rho_{\min} = \frac{\rho_{A} + \rho_{0}}{\rho_{A} - \rho_{0}}}$