Question

In an organ pipe (which may be closed or open) of 99 cm length, standing wave is set up whose equation is given by, longitudinal displacement(s) = 0.3 mm $cos\left[\left(\frac{2\pi }{0.8}\right)\right(z+0.01m\left)\right]cos400t$ where z is measured from the top of tube in metres and t is in seconds. Take end correction = 1 cm. Choose the correct statement(s).

• A. The upper end and lower end of tube are open and closed respectively
• B. The upper end and lower end of tube are closed and open respectively
• C. The air column is vibrating in third harmonic
• D. The air column is vibrating in second overtone

Answer 1

Answer: (A), (D)

The correct options are
A

The upper end and lower end of tube are open and closed respectively

D

The air column is vibrating in second overtone

At, z = –0.01m, x = max $\therefore$ upper end-open z = 0.99 m, x = min lower end-closed.

$\frac{2\pi }{0.8}=\frac{2\pi }{\lambda }=0.8m$

$l_{eff}=0.99+0.01=1m$

$\frac{l}{\lambda }=\frac{5}{4},l=5\left(\frac{\lambda }{4}\right)$ five half loops

$\Rightarrow$ second overtone.