Question

A pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency 440Hz. The speed of the sound in air is 330m/s. Assume $P_0$ is maximum pressure amplitude then pick correct statements.

• A. length of pipe is $\frac{15}{16}m$
• B. length of pipe is $\frac{9}{16}m$
• C. pressure amplitude at mid point of pipe is $\frac{P_0}{\sqrt{2}}m$
• D. pressure amplitude at mid point of pipe is $P_0$

Answer 1

Answer: (A), (C)

The correct options are
A length of pipe is $\frac{15}{16}m$
C pressure amplitude at mid point of pipe is $\frac{P_0}{\sqrt{2}}m$

Second overtone frequency of pipe closed at one end=$\frac{5c}{4L}=440$

$⟹\frac{5\left(330\right)}{4L}=440$

$⟹L=\frac{15}{16}m$

For vibration in second overtone, $L=\frac{5\lambda }{4}$.

Phase of the wave at $L/2=\frac{2\pi }{\lambda }\times \frac{5\lambda }{8}=\frac{5\pi }{4}$.

Thus amplitude of the pressure at that point=$P_0\cos \frac{5\pi }{4}=\frac{P_0}{\sqrt{2}}$