Question

An air column in a pipe, which is closed at one end, is in resonance with a vibrating tuning fork of frequency 264 Hz. If v = 330 m/s, the length of the column in cm is (are) :

• A. 31.25
• B. 62.5
• C. 93.75
• D. 125

Answer 1

Answer: (A), (C)

31.25
93.75

$v=f\lambda \Rightarrow \lambda =\frac{v}{f}=\frac{330}{264}=1.25m$

Fundamental mode $\frac{\lambda }{4}=L\Rightarrow L=\frac{1.25m}{4}=31.25cm$

First overtone $\frac{3\lambda }{4}=L\Rightarrow L=\frac{3\times 1.25m}{4}=93.75cm$

Second overtone $\frac{5\lambda }{4}=L\Rightarrow L=\frac{5\times 1.25m}{4}=156.25cm$

Hence A and C are correct options.