Question

The second overtone of an open pipe A and a closed pipe B have the same frequencies at a given temperature. Both pipes contain air. The ratio of fundamental frequency of A to the fundamental frequency of B is :

• A. 3:5
• B. 5:3
• C. 5:6
• D. 6:5

Answer 1

Answer: (B)

5:3

Second overtone of open pipe is $\frac{3v}{2l_1}$

Second overtone of closed pipe is $\frac{5v}{4l_2}$

Since both are equal,

$\frac{3v}{2l_1}=\frac{5v}{4l_2}$

$\therefore \frac{l_1}{l_2}=\frac{6}{5}$

Ratio of fundamental frequencies are $\frac{f_1}{f_2}=\frac{\frac{v}{2l_1}}{\frac{v}{4l_2}}=2\times \frac{5}{6}=\frac{10}{6}=\frac{5}{3}$