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 wave 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)

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

The frequency of $2^{nd}$ overtone in an air column in a pipe closed at one end is given as, $\frac{5v}{4l}=f$

$⟹l=\frac{5v}{4f}=\frac{5\times 330}{4\times 440}=\frac{15}{16}m$

A pressure node is formed at the open end. Thus the value of pressure at the open end always has same value as the mean value $P_0$.