Question

Two open pipes contain different gases. If they vibrate with fundamental frequencies, the ratio of velocities of sound in the gases is 2:1, then the
ratio of lengths of tube is

• A. 2:1
• B. 2:3
• C. 3:2
• D. 1:2

Answer 1

Answer: (A)

Given: $\frac{{\nu }_1}{{\nu }_2}=\frac{2}{1}$

Fundamental frequency in open, ${\nu }_o=\frac{\nu }{2L}$

So, ${\nu }_{o_1}=\frac{{\nu }_1}{2L_1}$

${\nu }_{o_2}=\frac{{\nu }_2}{2L_2}$

By problem:

${\nu }_{o_1}={\nu }_{o_2}$

$\frac{{\nu }_1}{2L_1}=\frac{{\nu }_2}{2L_2}$

$\frac{{\nu }_1}{{\nu }_2}=\frac{L_1}{L_2}$

$\frac{L_1}{L_2}=\frac{2}{1}(\because \frac{{\nu }_1}{{\nu }_2}=\frac{2}{1})$