Question

An air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency $440Hz$ The speed of sound waves in air is $330m/s$. End corrections may be neglected. Let $P_0$ denote the mean pressure at any point in the pipe, and $\Delta P_0$ the maximum amplitude of pressure variation. Then,

• A. length of the pipe is $\frac{15}{16}m$
• B. length of the pipe is $\frac{9}{16}m$
• C. the maximum pressure at the open end is $P_0$
• D. the minimum pressure at the open end is $P_0$

Answer 1

Answer: (A), (C), (D)

The correct options are
A length of the pipe is $\frac{15}{16}m$
C the maximum pressure at the open end is $P_0$
D the minimum pressure at the open end is $P_0$

For second overtone of a pipe closed at one end.
$f=\frac{5v}{4\ell }$
$\Rightarrow \ell =\frac{5v}{4f}=\frac{15}{16}m$
The open end is the position of a pressure node. So, there is no pressure variation at the open end.