Question

A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude $P_A$ inside the tube. If the atmospheric pressure is $P_0$ then the ratio of maximum and minimum pressure at the closed end of the tube will be

• A. $\frac{P_A+P_0}{P_A-P_0}$
• B. $\frac{P_A+2P_0}{P_A-2P_0}$
• C. $\frac{P_A}{P_0}$
• D. ($\frac{P_A+\frac{1}{2}{P}_0}{P_A-\frac{1}{2}{P}_0}$)

Answer 1

The correct option is A

$\frac{P_A+P_0}{P_A-P_0}$

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

So $P_{max}$ = $P_A$ + $P_0$ and $P_{min}$ = $P_A$ - $P_0$

Thus $\frac{P_{max}}{P_{min}}$ = $\frac{P_A+P_0}{P_A-P_0}$