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 $\Delta P_0$ be 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 $P_0$

The frequency of vibration of air column in second overtone:

$f=5.\frac{v}{4l}$

$\Rightarrow l=\frac{5v}{4f}=\frac{15}{16}m$

The open end is position of node of pressure. Hence, there is no pressure variation at open end. Hence, minimum and maximum pressure at open end will be $P_0$