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 $=\frac{3 V}{2 l_{1}}$
Second overtone of closed pipe $=\frac{5 V}{4 l_{2}}$
Since, ratio of frequency are same
$\frac{3 V}{2 l_{1}}=\frac{5 V}{4 l_{2}}$
$\Rightarrow \frac{l_{1}}{l_{2}}=\frac{4 \times 3}{2 \times 5}$
$=\frac{6}{5}$
Now, the ratio of fundamental frequencies:
$\frac{f_{1}}{f_{2}}=\frac{\frac{V}{2 l_{1}}}{\frac{V}{4 l_{2}}}$
$\Rightarrow \frac{2 l_{2}}{l_{1}}$
$=10: 6=5: 3$