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)

Second overtone of open pipe $=\frac{3V}{2l_1}$
Second overtone of closed pipe $=\frac{5V}{4l_2}$
Since, ratio of frequency are same
$\frac{3V}{2l_1}=\frac{5V}{4l_2}$
$\Rightarrow \frac{l_1}{l_2}=\frac{4\times 3}{2\times 5}$
$=\frac{6}{5}$
Now, the ratio of fundamental frequencies:
$\frac{f_1}{f_2}=\frac{\frac{V}{2l_1}}{\frac{V}{4l_2}}$
$\Rightarrow \frac{2l_2}{l_1}$
$=10:6=5:3$