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
$(a) \frac{(\rho_A + \rho_0)}{(\rho_A - \rho_0)} \quad (b) \frac{(\rho_A + 2 \rho_0)}{(\rho_A - 2 \rho_0)} (c) \frac{\rho_A}{\rho_A} \quad (d) \frac{\left(\rho_A + \frac{1}{2} \rho_0 \right)}{\left(\rho_A - \frac{1}{2} \rho_0 \right)}$
Text Solution
Verified by ExpertsA
Maximum pressure at closed end will be atmospheric pressure adding with acoustic wave pressure
So $\rho_{\max} = \rho_A + \rho_0$ and $\rho_{\min} = \rho_A - \rho_0$
Thus $\frac{\rho_{\max}}{\rho_{\min}} = \frac{\rho_A + \rho_0}{\rho_A - \rho_0}$
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