Question

A tube of a certain diameter and of length 48cm is open at both ends. Its fundamental frequency of resonance is found to be $320Hz$. If velocity of sound in air is 320ms${}^{-1}$ the diameter of the tube is

• A. $1.33cm$
• B. $2.33cm$
• C. $3.33cm$
• D. $4.33cm$

Answer 1

The correct option is C $3.33cm$

$\lambda =\frac{v}{f}=\frac{320}{320}=1m$

As it is open at both ends correction at each end is $0.6r$.

$\therefore \frac{\lambda }{2}0.6r_{-}^{+}0.6r=l$

$50{}_{-}^{+}1.2r=48cm$

$1.2r=2cm$

$r=\frac{2}{1.2}=1.65$

$\therefore d=2r=3.33cm$