Question

An organ pipe of $3.9\pi m$ long, open at both ends is driven to third harmonic standing wave. If the amplitude of pressure oscillation is 1% of mean atmospheric pressure $[p_0={10}^{5}N/m^2]$. The maximum displacement of particle from means position will be
[Given velocity of sound = 200 m/s and density of air $=1.3kg/m^3$

• A. 2.5 cm
• B. 5 cm
• C. 1 cm
• D. 2 cm

Answer 1

The correct option is A 2.5 cm

Wavelength, $\lambda =\frac{2L}{n}=\frac{2\times 3.9\pi }{3}$ m

$⟹$ $k=\frac{2\pi }{\lambda }=\frac{2\pi \times 3}{2\times 3.9\pi }=\frac{1}{1.3}$

Also, $B=\rho v^2=1.3(200{)}^2$

Maximum displacement, $S=\frac{P}{Bk}$ where $P=0.01\times {10}^5$ $N/m^2$

$⟹$ $S=\frac{0.01\times {10}^5\times 1.3}{1.3\times (200{)}^2}=2.5\times {10}^{-2}$ m $=2.5$ cm